{"id":943,"date":"2021-09-26T10:57:58","date_gmt":"2021-09-26T01:57:58","guid":{"rendered":"https:\/\/hayashiyus.jp\/?p=943"},"modified":"2022-03-13T22:16:26","modified_gmt":"2022-03-13T13:16:26","slug":"new-post","status":"publish","type":"post","link":"https:\/\/hayashiyus.jp\/?p=943","title":{"rendered":"\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u3068AdS\/CFT\u5bfe\u5fdc"},"content":{"rendered":"\r\n

\u6a5f\u68b0\u5b66\u7fd2\u306e\u71b1\u529b\u5b66\u306f\uff0c\u91cf\u5b50\u91cd\u529b\u7406\u8ad6\u306e\u6b74\u53f2\u306b\u304a\u3051\u308b\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u71b1\u529b\u5b66\u3068\u540c\u3058\u3088\u3046\u306a\u6b74\u53f2\u7684\u4f4d\u7f6e\u306b\u3042\u308b\u306e\u304b\u3082\u3057\u308c\u306a\u3044\uff0e\u30d9\u30c3\u30b1\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30fb\u30db\u30fc\u30ad\u30f3\u30b0\u516c\u5f0f\u306e\u767a\u898b\u304c\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u71b1\u529b\u5b66\u3092\u751f\u307f\u51fa\u3057\uff0c\u30db\u30ed\u30b0\u30e9\u30d5\u30a3\u30fc\u539f\u7406\uff08\u5834\u306e\u91cf\u5b50\u8ad6\u3068\u91cd\u529b\u7406\u8ad6\u306e\u5bfe\u5fdc\uff09\u306e\u539f\u578b\u3068\u306a\u3063\u305f\u3088\u3046\u306b\uff0c\u6a5f\u68b0\u5b66\u7fd2\u306e\u65b0\u3057\u3044\u898b\u65b9\u304c\u751f\u307e\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\uff0e\u305f\u3060\u3057\uff0c\u91cf\u5b50\u91cd\u529b\u7406\u8ad6\u306e\u6b74\u53f2\u7684\u7d4c\u7def\u3068\u306f\u9006\u3055\u307e\u306b\uff0c\u6a5f\u68b0\u5b66\u7fd2\u306e\u5834\u5408\u306f\uff0c\u5148\u306b\u6a5f\u68b0\u5b66\u7fd2\u3068\u5834\u306e\u91cf\u5b50\u8ad6\u306e\u5bfe\u5fdc\u95a2\u4fc2\u304c\u307f\u3064\u304b\u308a\uff0c\u305d\u3053\u304b\u3089\u30db\u30ed\u30b0\u30e9\u30d5\u30a3\u30fc\u539f\u7406\u3092\u7d4c\u7531\u3057\u3066\u6a5f\u68b0\u5b66\u7fd2\u306e\u71b1\u529b\u5b66\u304c\u5c0e\u304b\u308c\u308b\u306e\u3067\u306f\u306a\u3044\u304b\uff0e\u305d\u3046\u601d\u308f\u305b\u308b\u7814\u7a76\u304c\u6700\u8fd1\u51fa\u3066\u304d\u3066\u3044\u308b1<\/a><\/sup>K. Hashimoto, S. Sugishita, A. Tanaka and A. Tomiya, “Deep learning and the \r\nAdS\/CFT correspondence”, Phys. Rev. D 98, 046019 (2018)<\/span>\uff0e<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n

\uff11. \u91cf\u5b50\u91cd\u529b\u7406\u8ad6\u306e\u6b74\u53f2<\/h4>\r\n\r\n\r\n
\r\n

\uff11\u2212\uff11. \u91cf\u5b50\u91cd\u529b\u7406\u8ad6\u306e\u6b74\u53f2<\/h4>\r\n


\r\n<\/p>\r\n

\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u71b1\u529b\u5b66\u306e\u767a\u898b\u304b\u3089\u30db\u30ed\u30b0\u30e9\u30d5\u30a3\u30fc\u539f\u7406\uff0c\"\mathrm{AdS_{d+2}} / \mathrm{CFT}_{d+1}\" \u5bfe\u5fdc\u307e\u3067\u306e\u6b74\u53f2\u7684\u7d4c\u7def\u3092\u6982\u8aac\uff0e<\/p>\r\n<\/div>\r\n

<\/p>\r\n

\r\n

\uff11\u2212\uff12. \u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u71b1\u529b\u5b66<\/h4>\r\n


\r\n<\/p>\r\n

Schwarzschild\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u306e\u8a08\u91cf\u306f<\/p>\r\n

(1) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle ds^{2} = -\left(1-\frac{r_{H}}{r}\right) d t^{2}+\frac{d r^{2}}{1-\frac{r_{\mathrm{H}}}{r}}+r^{2} d\Omega^{2}<\/p><\/p>\r\n

\u305f\u3060\u3057\uff0c\"r_{\mathrm{H}}=2M\"\uff0e\u307e\u305f\uff0c\u5730\u5e73\u7dda\u8fd1\u508d\u3067\u306f\u3053\u306e\u8a08\u91cf\u3092<\/p>\r\n

(2) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle ds^{2} = -\left(\frac{r-r_{\mathrm{H}}}{r_{\mathrm{H}}}\right) d t^{2} + \left(\frac{r_{\mathrm{H}}}{r - r_{\mathrm{H}}}\right) dr^{2} + r_{\mathrm{H}}^{2} d\Omega^{2}<\/p><\/p>\r\n

\u3068\u8fd1\u4f3c\u3067\u304d\u308b\uff0e\u534a\u5f84\u65b9\u5411\u306e\u5ea7\u6a19\u3092 \"\xi=2 \sqrt{r_{H}\left(r-r_{\mathrm{H}}\right)}\" \u3068\u7f6e\u304d\u76f4\u3057\uff0c\u6642\u9593\u3092\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u5316 \"t_{\mathrm{E}}=it\" \u3059\u308b\u3068\u3053\u306e\u8a08\u91cf\u306f<\/p>\r\n

(3) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle ds^{2} = \frac{\xi^{2}}{4 r_{\mathrm{H}}^{2}} dt^{2}_{\mathrm{E}} + d\xi^{2} + r_{\mathrm{H}}^{2} d\Omega^{2}<\/p><\/p>\r\n

\u3068\u306a\u308b\uff0e\u3053\u3053\u3067\u3053\u306e\u8a08\u91cf\u304c\u7279\u7570\u6027\u3092\u3082\u305f\u306a\u3044\u3068\u3044\u3046\u8981\u8acb\u3092\u8ab2\u3059\u3068 \"t_{\mathrm{E}}\" \u306f \"4 \pi r_{\mathrm{H}}\" \u306e\u5468\u671f\u3092\u3082\u3064\u3053\u3068\u304c\u5c0e\u304b\u308c\u308b\uff0e\u66f4\u306b\uff0c\u3053\u306e\u5468\u671f\u306f\u9006\u6e29\u5ea6\u306b\u6bd4\u4f8b\u3059\u308b\u305f\u3081\uff0c\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u306e\u6e29\u5ea6 \"T_{\mathrm{H}} = \frac{1}{8 \pi M}\" \u304c\u308f\u304b\u308b\uff0e\u3053\u3053\u304b\u3089\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u306e\u71b1\u529b\u5b66<\/p>\r\n

(4) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle T_{\mathrm{H}} dS = dM<\/p><\/p>\r\n

\u304c\u5c0e\u304b\u308c\u308b\uff0e\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u306e\u5730\u5e73\u7dda\u306e\u8868\u9762\u7a4d\u306f \"A_{\mathrm{H}} =4 \pi r_{\mathrm{H}}^{2}\" \u3068\u306a\u308b\u306e\u3067\uff0c\u6b21\u306eBekenstein-Hawking\uff08BH\uff09\u516c\u5f0f2<\/a><\/sup>J. D. Bekenstein, “Black holes and entropy”, Physical Review D. 7 (8): 2333\u20132346 (1973).<\/span>3<\/a><\/sup>S. W. Hawking, “Black hole explosions?”, Nature, 248, 30 (1974).<\/span>\u304c\u5c0e\u304b\u308c\u308b\uff0e<\/p>\r\n

(5) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle S_{\mathrm{BH}}(A) = 4 \pi M^{2} = \frac{A_{\mathrm{H}}}{4}<\/p><\/p>\r\n

\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u306e\u8868\u9762\u7a4d\u304c\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3068\u6bd4\u4f8b\u3059\u308b\u3053\u3068\u3092\u767a\u898b\uff0e<\/p>\r\n<\/div>\r\n

<\/p>\r\n

\r\n

\uff11\u2212\uff13. \u30db\u30ed\u30b0\u30e9\u30d5\u30a3\u30fc\u539f\u7406<\/h4>\r\n


\r\n<\/p>\r\n

\"d+2\" \u6b21\u5143\u306e\u91cd\u529b\u7406\u8ad6\u306f\uff0c\u91cd\u529b\u3092\u542b\u307e\u306a\u3044 \"d+1\" \u6b21\u5143\u306e\u91cf\u5b50\u7cfb\u3068\u7269\u7406\u7684\u306b\u7b49\u4fa1\u306b\u306a\u308b\u3068\u3044\u3046\u30db\u30ed\u30b0\u30e9\u30d5\u30a3\u30fc\u539f\u7406\u306e\u4eee\u8aac\u3092\uff0c\"d+2\" \u6b21\u5143\u306e\u30d0\u30eb\u30af\u6642\u7a7a\u4e0a\u306e\u91cd\u529b\u7406\u8ad6 \"\mathrm{AdS_{d+2}}\" \u3068\u305d\u306e\u5883\u754c\u4e0a\u306e\u5171\u5f62\u5834\u7406\u8ad6 \"\mathrm{CFT}_{d+1}\" \u306e\u5bfe\u5fdc\uff08\"\mathrm{AdS_{d+2}} / \mathrm{CFT}_{d+1}\" \u5bfe\u5fdc\uff09\u3068\u307f\u306a\u3057\u3066\u5177\u4f53\u7684\u306b\u8a08\u7b97\u3057\u3066\u3044\u304f\uff0e<\/p>\r\n

<\/p>

\"\"<\/center>

<\/p>\r\n

\"d+2\" \u6b21\u5143\u306e\u53cd\u30c9\u30b8\u30c3\u30bf\u30fc\u6642\u7a7a\u4e0a\u306eSchwarzschild\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u306e\u8a08\u91cf\u306f<\/p>\r\n

(6) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle ds^{2} = \frac{R^{2}}{z^2}\left( -f(z)dt^2 + \frac{dz^{2}}{f(z)} + \sum^{d}_{i=1}dx^{2}_{i} \right) \\<\/p><\/p>\r\n

\u3053\u306e\u8a08\u91cf\u3092Poincar\u00e9\u5ea7\u6a19\u3067\u66f8\u304d\u76f4\u3057\uff0c\u6642\u9593\u3092\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u5316 \"t_{\mathrm{E}}=it\" \u3059\u308b\u3068<\/p>\r\n

(7) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle ds^{2} = \frac{R^{2}}{z^2}\left( dt^2_{\mathrm{E}} + dz^{2} + \sum^{d}_{i=1}dx^{2}_{i} \right)<\/p><\/p>\r\n

\u3068\u306a\u308b\uff0e\u30d0\u30eb\u30af\u6642\u7a7a\u4e0a\u306e\u91cd\u529b\u7406\u8ad6\u306e\u5206\u914d\u95a2\u6570\u3068\u5883\u754c\u4e0a\u306e\u5171\u5f62\u5834\u7406\u8ad6\u306e\u5206\u914d\u95a2\u6570\u304c\u4e00\u81f4\u3059\u308b\u3053\u3068\u3092\u8981\u8acb\u3059\u308b \"\mathrm{AdS_{d+2}} / \mathrm{CFT}_{d+1}\" \u5bfe\u5fdc\u306e\u539f\u7406\uff0c\u30d0\u30eb\u30af\uff0f\u5883\u754c\u5bfe\u5fdc\u3092\u4f7f\u3063\u3066BH\u516c\u5f0f\u3092\u4e00\u822c\u5316\u3057\u305f\u516c\u5f0f\u3092\u5c0e\u304f\uff0e<\/p>\r\n

(8) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle Z_{\mathrm{gravity}} = Z_{\mathrm{CFT}} \\<\/p><\/p>\r\n

\u91cd\u529b\u7406\u8ad6\u3092\u53e4\u5178\u91cd\u529b\u3067\u8fd1\u4f3c\u3067\u304d\u308b\u5834\u5408\uff0c\u6b21\u304c\u6210\u308a\u7acb\u3064\uff0e<\/p>\r\n

(9) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle Z_{\mathrm{gravity}}\left(\phi_{i}\right) \simeq e^{- I_{\mathrm{gravity}}\left(\phi_{i}\right)}<\/p><\/p>\r\n

\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u5316\u3057\u305f\u6642\u7a7a\u4e0a\u3067\u306e\u4f5c\u7528 \"I_{\mathrm{gravity}}\" \u306f<\/p>\r\n

(10) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle I_{\mathrm{gravity}} = -\frac{1}{16 \pi} \int_{A} \sqrt{g}(R - 2 \Lambda) - \frac{1}{8 \pi} \int_{\partial A} \sqrt{h} K \\<\/p><\/p>\r\n

\u3068\u306a\u308b\u306e\u3067\uff0c\u6b21\u306eHubeny-Rangamani-Ryu-Takayanagi\uff08HRRT\uff09\u516c\u5f0f4<\/a><\/sup>S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from the anti\u2013de sitter space\/conformal field theory correspondence”, Physical review letters 96 (18), 181602 (2006).<\/span>5<\/a><\/sup>V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement
\r\nentropy proposal”, JHEP 07 062 (2007).<\/span>\u304c\u5c0e\u304b\u308c\u308b\uff0e<\/p>\r\n

(11) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle S_{\mathrm{HRRT}}(A) = -\left. \frac{\partial}{\partial n} \ln{Z_{\mathrm{gravity}}} \right|_{n=1} \\<\/p><\/p>\r\n

\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u30e1\u30f3\u30c8\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306b\u3088\u308bBH\u516c\u5f0f\u306e\u4e00\u822c\u5316\uff0e<\/p>\r\n<\/div>\r\n

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\uff12. \u6a5f\u68b0\u5b66\u7fd2\u306e\u71b1\u529b\u5b66\uff1f<\/h4>\r\n

\u6df1\u5c64\u5b66\u7fd2\u3092\u542b\u3080\u69d8\u3005\u306a\u6a5f\u68b0\u5b66\u7fd2\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\uff0c\u30de\u30eb\u30b3\u30d5\u78ba\u7387\u5834\u306e\u67a0\u7d44\u307f\uff1d\u5834\u306e\u91cf\u5b50\u8ad6\u306e\u67a0\u7d44\u307f\u3067\u8a18\u8ff0\u3067\u304d\u308b\u3053\u3068\u3092\u7d39\u4ecb\u3059\u308b\uff0e\u305d\u306e\u5f8c\uff0c\u6a5f\u68b0\u5b66\u7fd2\u306e\u30db\u30ed\u30b0\u30e9\u30d5\u30a3\u30fc\u539f\u7406\u3092\u4f7f\u3063\u3066\uff0c\u6a5f\u68b0\u5b66\u7fd2\u306e\u5834\u306e\u91cf\u5b50\u8ad6\u304b\u3089\u53e4\u5178\u7684\u306a\u6642\u7a7a\u3092\u5275\u767a\u3055\u305b\u308b\uff0e\u3053\u306e\u3068\u304d\u3042\u3089\u308f\u308c\u308b\u53e4\u5178\u6642\u7a7a\u306e\u71b1\u529b\u5b66\u304c\uff0c\u6a5f\u68b0\u5b66\u7fd2\u306e\u71b1\u529b\u5b66\u306b\u306a\u308b\uff0e<\/p>\r\n

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\uff12\u2212\uff11. \u6a5f\u68b0\u5b66\u7fd2\u306e\u5834\u306e\u91cf\u5b50\u8ad6<\/h4>\r\n


\r\n<\/p>\r\n

\u6700\u8fd1\uff0c\u5834\u306e\u91cf\u5b50\u8ad6\u3067\u8a18\u8ff0\u3055\u308c\u308b\u30c0\u30a4\u30ca\u30df\u30af\u30b9\u3092\u4f7f\u3063\u3066\u63a8\u8ad6\u3084\u5b66\u7fd2\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u3044\u3046\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u304d\u305f6<\/a><\/sup>D. Bachtis, G. Aarts and B. Lucini, “Quantum field-theoretic machine learning”, Phys. Rev. D 103, 074510 (2021).<\/span>\uff0e\u5177\u4f53\u7684\u306b\u306f\uff0c\"\phi^{4}\"-\u30b9\u30ab\u30e9\u30fc\u5834\u306e\u7406\u8ad6\u304c Hammersley-Clifford \u5b9a\u7406\u3092\u6e80\u305f\u3059\u3053\u3068\u304c\u308f\u304b\u308b\u306e\u3067\uff0c\u6df1\u5c64\u5b66\u7fd2\u3092\u542b\u3080\u69d8\u3005\u306a\u6a5f\u68b0\u5b66\u7fd2\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u30de\u30eb\u30b3\u30d5\u78ba\u7387\u5834\u306e\u67a0\u7d44\u307f\u306e\u4e2d\u3067\u518d\u69cb\u6210\u3067\u304d\u308b\uff0e<\/p>\r\n

\"\phi^{4}\"-\u30b9\u30ab\u30e9\u30fc\u5834\u306e\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3<\/p>\r\n

(12) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \mathcal{L}_{E}=\frac{\kappa}{2}(\nabla \phi)^{2}+\frac{\mu_{0}^{2}}{2} \phi^{2}+\frac{\lambda}{4} \phi^{4} \end{eqnarray*}\"<\/p><\/p>\r\n

\u683c\u5b50\u4e0a\u306e\u4f5c\u7528<\/p>\r\n

(13) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle I_{E}=-\kappa_{L} \sum_{\langle i j\rangle} \phi_{i} \phi_{j}+\frac{\left(\mu_{L}^{2}+4 \kappa_{L}\right)}{2} \sum_{i} \phi_{i}^{2}+\frac{\lambda_{L}}{4} \sum_{i} \phi_{i}^{4} \end{eqnarray*}\"<\/p><\/p>\r\n

\u975e\u7b49\u65b9\"\phi^{4}\"-\u30b9\u30ab\u30e9\u30fc\u5834\u306e\u4f5c\u7528<\/p>\r\n

<\/p>

\"\"<\/center>

<\/p>\r\n

(14) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle I(\phi ; \theta)=-\sum_{\langle i j\rangle} w_{i j} \phi_{i} \phi_{j}+\sum_{i} a_{i} \phi_{i}^{2}+\sum_{i} b_{i} \phi_{i}^{4} \end{eqnarray*}\"<\/p><\/p>\r\n

\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570<\/p>\r\n

(15) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \psi_{c} = \exp \left[-w_{i j} \phi_{i} \phi_{j}+\frac{1}{4}\left(a_{i} \phi_{i}^{2}+a_{j} \phi_{j}^{2}+b_{i} \phi_{i}^{4}+b_{j} \phi_{j}^{4}\right)\right] \end{eqnarray*}\"<\/p><\/p>\r\n

\"\phi^{4}\"-\u30b9\u30ab\u30e9\u30fc\u5834\u306e\u7406\u8ad6\u306f\u30de\u30eb\u30b3\u30d5\u6027\u3092\u6e80\u305f\u3059\uff0e<\/p>\r\n

(16) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle p(\phi ; \theta) = \frac{\exp \left[\sum_{c \in C} \ln \psi_{c}(\phi)\right]}{\int_{\boldsymbol{\phi}} \exp \left[\sum_{c \in C} \ln \psi_{c}(\boldsymbol{\phi})\right] d \boldsymbol{\phi}}=\frac{1}{Z} \prod_{c \in C} \psi_{c}(\phi) \end{eqnarray*}\"<\/p><\/p>\r\n

\u771f\u306e\u30e2\u30c7\u30eb \"q(\phi) = \frac{\exp [-\mathcal{A}]}{Z_{\mathcal{A}}}\" \u3068\u306eKL-\u30c0\u30a4\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9<\/p>\r\n

(17) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle D_{\mathrm{KL}}\left(p \| q\right) = \int_{-\infty}^{\infty} p(\boldsymbol{\phi} ; \theta) \ln \frac{p(\boldsymbol{\phi} ; \theta)}{q(\boldsymbol{\phi})} d \boldsymbol{\phi} \geq 0 \end{eqnarray*}\"<\/p><\/p>\r\n

\u5909\u5206\u30d9\u30a4\u30ba\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc \"\mathcal{F}\"<\/p>\r\n

(18) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle F_{\mathcal{A}} \leq\langle\mathcal{A} - I\rangle_{p(\phi ; \theta)}+F \equiv \mathcal{F} \end{eqnarray*}\"<\/p><\/p>\r\n

\u305f\u3060\u3057\uff0c\"F_{\mathcal{A}}=-\ln Z_{\mathcal{A}}\"\uff0c\"F=-\ln Z\"<\/p>\r\n<\/div>\r\n

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\uff12\u2212\uff12. \u6a5f\u68b0\u5b66\u7fd2\u306e\u71b1\u529b\u5b66<\/h4>\r\n


\r\n<\/p>\r\n

\u30d2\u30f3\u30c8\u30f3\u5834\u304c\u5171\u5f62\u4e0d\u5909\u6027\u3092\u3082\u3064\u5834\u5408\u306b\u3064\u3044\u3066\uff0c\u30d2\u30f3\u30c8\u30f3\u5834\u3092\u91cd\u529b\u7406\u8ad6\u3067\u8a18\u8ff0\u3055\u308c\u308b\u30d0\u30eb\u30af\u6642\u7a7a\u306e\u5883\u754c\u306b\u5bfe\u5fdc\u3059\u308b\u91cf\u5b50\u591a\u4f53\u7cfb\u3068\u307f\u306a\u3057\uff0c\u30d0\u30eb\u30af\uff0f\u5883\u754c\u5bfe\u5fdc \"Z_{\mathrm{gravity}} = Z_{\mathrm{CFT}}\" \u304b\u3089\u30d2\u30f3\u30c8\u30f3\u5834\u306e\u5206\u914d\u95a2\u6570 \"Z_{\mathrm{gravity}}\" \u3092\u8a08\u7b97\u3059\u308b\uff0e\u3053\u306e\u3068\u304d\u3042\u3089\u308f\u308c\u308b\u30d0\u30eb\u30af\u6642\u7a7a\u3092\u30d2\u30f3\u30c8\u30f3\u6642\u7a7a\u3068\u547c\u3076\uff0e<\/p>\r\n

\u30d2\u30f3\u30c8\u30f3\u6642\u7a7a\u4e0a\u306eSchwarzschild\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u306e\u8a08\u91cf<\/p>\r\n

(19) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle ds^{2} = \frac{R^{2}}{z^2}\left( -f(z)dt^2 + \frac{dz^{2}}{f(z)} + \sum^{d}_{i=1}dx^{2}_{i} \right) \\<\/p><\/p>\r\n

\uff11\u2212\uff13. \u306e\u624b\u9806\u306b\u5f93\u3063\u3066\u30d2\u30f3\u30c8\u30f3\u5834\u306e\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u30e1\u30f3\u30c8\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3092\u6b21\u306e\u3088\u3046\u306b\u5c0e\u51fa\u3059\u308b\uff0e<\/p>\r\n

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\"\"<\/center>

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(20) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle S_{\mathrm{H}}(A) = \frac{\operatorname{Area}(\gamma_{A})}{4} = \begin{cases} \frac{R^{d} L^{d-1}}{4} \int_{-\frac{l}{2}}^{\frac{l}{2}} d x \frac{\sqrt{1+\left(\frac{d z}{d x}\right)^{2}}}{z^{d}} & \text { $A_{\mathrm{S}}$: straight belt type } \\ \frac{R^{d} \cdot \operatorname{Vol}\left(\mathbf{S}^{d-1}\right)}{4} \cdot \int_{0}^{l} d r r^{d-1} \frac{\sqrt{1+\left(\frac{d z}{d r}\right)^{2}}}{z^{d}} & \text {$A_{\mathrm{D}}$: disk type } \end{cases}<\/p><\/p>\r\n

\u305f\u3060\u3057\uff0c\"\operatorname{Vol}\left(\mathbf{S}^{d-1}\right) = 2 \cdot \frac{\pi^{\frac{d}{2}}}{\Gamma\left(\frac{d}{2}\right)}\" \u306f\u5358\u4f4d \"d-1\" \u6b21\u5143\u7403\u306e\u4f53\u7a4d\uff0e<\/p>\r\n

<\/p>\r\n

\u76f8\u5bfe\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc<\/p>\r\n

(21) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle S\left(\rho_{1} \mid \rho_{0}\right) = \operatorname{Tr}\left[\rho_{1} \log \rho_{1}\right]-\operatorname{Tr}\left[\rho_{1} \log \rho_{0}\right] \geq 0<\/p><\/p>\r\n

\"\rho_{0}\" \u3092\u71b1\u5e73\u8861\u72b6\u614b\u306e\u30ab\u30ce\u30cb\u30ab\u30eb\u5206\u5e03\u306e\u5bc6\u5ea6\u884c\u5217<\/p>\r\n

(22) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \rho_{0} = \frac{e^{-H / T}}{\operatorname{Tr}\left[e^{-H / T}\right]}<\/p><\/p>\r\n

\u3068\u3057\uff0c\"\rho_{1}\" \u3092\u4e00\u822c\u306e\u975e\u5e73\u8861\u72b6\u614b\u306e\u5bc6\u5ea6\u884c\u5217\u3068\u3059\u308b\u3068<\/p>\r\n

(23) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle S\left(\rho_{1} \mid \rho_{0}\right) = \beta\left(F\left(\rho_{1}\right)-F\left(\rho_{0}\right)\right) \geq 0<\/p><\/p>\r\n

\u305f\u3060\u3057\uff0c\"F(\rho) = E(\rho)-T S(\rho)=\operatorname{Tr}[H \rho]+T \operatorname{Tr}[\rho \log \rho]\" \uff0e\u4eca\u5ea6\u306f\u5168\u7cfb\u304c\u57fa\u5e95\u72b6\u614b\u306b\u3042\u308b\u3068\u304d\u306e\u90e8\u5206\u7cfb\u306e\u5bc6\u5ea6\u884c\u5217 \"\rho_{\mathrm{A}} = e^{-H_{\mathrm{A}}}\" \u3068\u5168\u7cfb\u304c\u4efb\u610f\u306e\u52b1\u8d77\u72b6\u614b\u306b\u3042\u308b\u3068\u304d\u306e\u90e8\u5206\u7cfb\u306e\u5bc6\u5ea6\u884c\u5217 \"\rho_{\mathrm{A}}^{\prime}\" \u3092\u8003\u3048\u308b\u3068<\/p>\r\n

(24) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle S\left(\rho_{\mathrm{A}}^{\prime} \mid \rho_{\mathrm{A}}\right) = \Delta\left\langle H_{\mathrm{A}}\right\rangle - \Delta S_{\mathrm{A}} \geq 0<\/p><\/p>\r\n

\u305f\u3060\u3057\uff0c\"\Delta\left\langle H_{\mathrm{A}}\right\rangle = \operatorname{Tr}\left[H_{\mathrm{A}} \rho_{\mathrm{A}}^{\prime}\right] - \operatorname{Tr}\left[H_{\mathrm{A}} \rho_{\mathrm{A}}\right]\" \uff0e<\/p>\r\n

\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u30e1\u30f3\u30c8\u71b1\u529b\u5b66\uff08\u6a5f\u68b0\u5b66\u7fd2\u306e\u71b1\u529b\u5b66\uff09\u306e\u5c0e\u51fa\uff08\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u30e1\u30f3\u30c8\u71b1\u529b\u5b66\u7b2c\uff11\u6cd5\u5247\uff09<\/p>\r\n

(25) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \Delta S_{\mathrm{A}} = \Delta \left\langle H_{\mathrm{A}} \right\rangle \\<\/p><\/p>\r\n<\/div>\r\n

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Appendix.<\/h4>\r\n

\u3082\u3046\u4e00\u3064\u306e\u6a5f\u68b0\u5b66\u7fd2\u306e\u5834\u306e\u91cf\u5b50\u8ad6\uff0e<\/p>\r\n

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\r\n

\uff13\u2212\uff11. \u6df1\u5c64\u5b66\u7fd2\u306e\u5834\u306e\u91cf\u5b50\u8ad6<\/h4>\r\n


\r\n<\/p>\r\n

\u753b\u50cf\u3084\u6642\u7cfb\u5217\u306a\u3069\u306e\u9023\u7d9a\u7684\u306a\u5165\u529b\u4fe1\u53f7\u306f\uff0c\u4e0d\u898f\u5247\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3055\u308c\u3066\u3044\u305f\u308a\uff0c\u5024\u304c\u6b20\u640d\u3057\u3066\u3044\u305f\u308a\u3059\u308b\u305f\u3081\uff0c\u65e2\u5b58\u306e\u6df1\u5c64\u5b66\u7fd2\u30e2\u30c7\u30eb\u306e\u9069\u7528\u304c\u96e3\u3057\u3044\u5834\u5408\u304c\u3042\u308b\uff0e\u3053\u3046\u3057\u305f\u554f\u984c\u306b\u5bfe\u51e6\u3059\u308b\u305f\u3081\uff0c\u7279\u5fb4\u91cf\u3092\u30ac\u30a6\u30b9\u904e\u7a0b\uff08\"\mathcal{GP}\"\uff09\u3068\u3057\u3066\u8868\u73fe\u3057\uff0c\u96e2\u6563\u5316\u8aa4\u5dee\u3092\u78ba\u7387\u7684\u306b\u8a18\u8ff0\u3059\u308b\u300c\u78ba\u7387\u7684\u6570\u5024\u8a08\u7b97\u7573\u307f\u8fbc\u307f\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff08PNCNN\uff09\u300d\u304c\u63d0\u6848\u3055\u308c\u305f7<\/a><\/sup>M. Finzi, R. Bondesan and M. Welling, “Probabilistic Numeric Convolutional Neural Networks” (2020)<\/span>\uff0e\u3053\u306ePNCNN\u3092\u91cf\u5b50\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u306b\u62e1\u5f35\u3057\uff0c\u6df1\u5c64\u5b66\u7fd2\u304c\u5834\u306e\u91cf\u5b50\u8ad6\u306b\u306a\u308b\u4f8b8<\/a><\/sup>R. Bondesan and M. Welling, “The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning”, Proceedings of the 38th International Conference on Machine Learning, PMLR 139:1038-1048 (2021).<\/span>\u3092\u7d39\u4ecb\u3059\u308b\uff0e<\/p>\r\n

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\"\"<\/center>

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\u3053\u3053\u3067\u306f\u5165\u529b\u4fe1\u53f7\u3092 \"\mathcal{D}=\left\{\left(x_{i}, y_{i}\right)\right\}_{i=1}^{N}\" \u3068\u3057\uff0c\u5404\u4f4d\u7f6e \"x_{i} \in \mathcal{X}\" \u306b\u5bfe\u5fdc\u3059\u308b\u8f1d\u5ea6 \"y_{i}\" \u3092\u6301\u3064\u6709\u9650\u30b0\u30ea\u30c3\u30c9\u306e\u753b\u50cf\u306e\u3088\u3046\u306a\u30c7\u30fc\u30bf \"\mathcal{X}=\{1, \ldots, l\}^{\times d}\" \u3092\u60f3\u5b9a\u3059\u308b\uff0e\u3053\u306e\u96e2\u6563\u7684\u306a\u5165\u529b\u4fe1\u53f7\u3092\u9023\u7d9a\u7684\u306a\u4fe1\u53f7\u306e\u78ba\u7387\u5834 \"\varphi: \mathcal{X} \rightarrow \mathbb{R}\" \u3067\u88dc\u5b8c\u3057\uff0c\u305d\u308c\u305e\u308c\u306e\u753b\u50cf\u304c\u6301\u3064\u30e9\u30d9\u30eb\u3092\u4e88\u6e2c\u3059\u308b\u30bf\u30b9\u30af\u3092\u8003\u3048\u308b\uff0e\u307e\u305f\uff0c\u5165\u529b\u4fe1\u53f7\u306e\u5404\u4f4d\u7f6e\u306b\u5bfe\u5fdc\u3059\u308b\u4fe1\u53f7 \"\varphi_{x}\" \u3092\u96c6\u3081\u305f\u30d9\u30af\u30c8\u30eb\u3092 \"\boldsymbol{\varphi}\" \u3068\u3042\u3089\u308f\u3059\u3053\u3068\u306b\u3059\u308b\uff0e\u3053\u3053\u3067\u5165\u529b\u4fe1\u53f7\u3092\u30ac\u30a6\u30b9\u904e\u7a0b \"\boldsymbol{\varphi}^{(1)} \sim \mathcal{GP}\left(\mu^{\prime}, k^{\prime}\right)\" \u3067\u30a8\u30f3\u30b3\u30fc\u30c9\u3057\u305f\u3068\u304d\uff0c\u4e2d\u9593\u5c64\u306e\u4fe1\u53f7\u304c<\/p>\r\n

(26) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \boldsymbol{\varphi}^{(\ell+1)}=\sigma\left(\mathcal{B}^{(\ell)}\left(\mathcal{A}^{(\ell)} \boldsymbol{\varphi}^{(\ell)}\right)\right)<\/p><\/p>\r\n

\u3067\u4e0e\u3048\u3089\u308c\u308b\u78ba\u7387\u7684\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u3092\u8003\u3048\u308b\uff0e\u305f\u3060\u3057\uff0c\"\sigma\" \u306f\u4fe1\u53f7\u306e\u975e\u7dda\u5f62\u5909\u63db\uff0c\"\mathcal{B}\" \u306f\u4fe1\u53f7\u306b\u30d0\u30a4\u30a2\u30b9\u3092\u52a0\u3048\u308b\u64cd\u4f5c\uff0c\"\mathcal{A}\" \u306f\u4fe1\u53f7\u306e\u7dda\u5f62\u5909\u63db\u3092\u3042\u3089\u308f\u3057\u3066\u3044\u308b\uff0e\u307e\u305f\uff0c\u3053\u306e\u30e2\u30c7\u30eb\u3067\u306f\u6700\u7d42\u5c64\u306e\u624b\u524d\u3067\uff11\u5ea6\u3060\u3051\u30d7\u30fc\u30ea\u30f3\u30b0\u64cd\u4f5c \"\boldsymbol{\varphi}^{(L+1)}=\mathcal{P} \boldsymbol{\varphi}^{(L)}\"<\/p>\r\n

(27) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle (\mathcal{P} \boldsymbol{\varphi})_{a, x}= \begin{cases}\frac{1}{|\mathcal{X}|} \sum_{x \in \mathcal{X}} \varphi_{a, x} & \text { first element } \\ \varphi_{a, x} & \text { else }\end{cases}<\/p><\/p>\r\n

\u3092\u884c\u3046\uff08\u6dfb\u5b57\u306e \"a\" \u306f\u753b\u50cf\u306e\u30ab\u30e9\u30fc\u30c1\u30e3\u30f3\u30cd\u30eb\u3092\u3042\u3089\u308f\u3057\u3066\u3044\u308b\uff09\uff0e\u3053\u306e\u3068\u304d\u30d0\u30a4\u30a2\u30b9\u3068\u7dda\u5f62\u5909\u63db\u306e\u90e8\u5206\u3092 \"\mathcal{L}=\mathcal{B} \circ \mathcal{A}\" \u3068\u66f8\u304f\u3053\u3068\u306b\u3059\u308b\u3068\uff0c\u3053\u306e\u78ba\u7387\u7684\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\uff08PNCNN\uff09\u304c\u884c\u3046\u64cd\u4f5c\u3092\u307e\u3068\u3081\u3066<\/p>\r\n

(28) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \Phi=\mathcal{L}^{(L)} \circ \mathcal{P} \circ \sigma \circ \mathcal{L}^{(L-1)} \circ \cdots \sigma \circ \mathcal{L}^{(0)}<\/p><\/p>\r\n

\u3068\u3042\u3089\u308f\u3059\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u3053\u306e\u4e00\u9023\u306e\u30d7\u30ed\u30bb\u30b9\u3092\u91cf\u5b50\u5316\u3059\u308b\uff0e\u3064\u307e\u308a\uff0cPNCNN\u3092\u91cf\u5b50\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u306b\u62e1\u5f35\u3059\u308b\uff0e\u3053\u308c\u306f(5)\u5f0f\u3092\uff0c\u30e6\u30cb\u30bf\u30ea\u30fc\u6f14\u7b97\u5b50\u306e\u7a4d<\/p>\r\n

(29) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \widehat{U}_{\mathrm{NN}} = \widehat{U}_{\operatorname{lin}}\left(\boldsymbol{\xi}^{(L)}, S^{(L)}\right) \widehat{U}_{\mathcal{P}} \prod_{\ell=0}^{L-1} \widehat{U}_{\sigma} \widehat{U}_{\text {lin }}\left(\boldsymbol{\xi}^{(\ell)}, S^{(\ell)}\right)<\/p><\/p>\r\n

\u3067\u66f8\u304d\u76f4\u3059\u3053\u3068\u306b\u5bfe\u5fdc\u3059\u308b\uff0e\u3053\u306e\u3068\u304d\u3042\u3089\u308f\u308c\u308b\u91cf\u5b50\u5316\u3055\u308c\u305f\u4fe1\u53f7\u306e\u78ba\u7387\u5834\uff08\u91cf\u5b50\u5834\uff09\"\widehat{\boldsymbol{\varphi}}\" \u3092\u30d2\u30f3\u30c8\u30f3\u5834\u3068\u547c\u3076\uff0e(6)\u5f0f\u306e\u30e6\u30cb\u30bf\u30ea\u30fc\u6f14\u7b97\u5b50\u3067\u6642\u9593\u767a\u5c55\u3055\u305b\u3066\u671f\u5f85\u5024\u3092\u3068\u308c\u3070\uff0c\u753b\u50cf\u306e\u30e9\u30d9\u30eb \"c=1, \ldots, C\" \u306b\u5fdc\u3058\u305f\u51fa\u529b\u4fe1\u53f7\uff08\u4e88\u6e2c\u30e9\u30d9\u30eb\uff09\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e<\/p>\r\n

(30) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle l_{c} = \left\langle\zeta_{\mathcal{D}}\left|\widehat{U}_{\mathrm{NN}}^{\dagger} \widehat{\varphi}_{c} \widehat{U}_{\mathrm{NN}}\right| \zeta_{\mathcal{D}}\right\rangle<\/p><\/p>\r\n

\u307e\u305f\uff0c\u53e4\u5178\u7684\u306aPNCNN\u304c\u304d\u3061\u3093\u3068\u3053\u306e\u91cf\u5b50\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u306b\u542b\u307e\u308c\u3066\u3044\u308b\u3053\u3068\u3082\u78ba\u8a8d\u3067\u304d\u308b\uff0e<\/p>\r\n

(31) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \left|\left\langle\boldsymbol{\varphi}\left|\widehat{U}_{\mathrm{NN}}\right| \zeta_{\mathcal{D}}\right\rangle\right|^{2}=\left(\Phi \# \mathcal{G} \mathcal{P}\left(\mu^{\prime}, k^{\prime}\right)\right)(\boldsymbol{\varphi})<\/p><\/p>\r\n

\u30d2\u30f3\u30c8\u30f3\u5834\u306e\u751f\u6210\u6d88\u6ec5\u6f14\u7b97\u5b50\u306f\u4ee5\u4e0b\u3067\u4e0e\u3048\u3089\u308c\u308b\uff0e<\/p>\r\n

(32) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \widehat{\boldsymbol{b}}=\frac{1}{\sqrt{2}}(\widehat{\boldsymbol{\varphi}}+i \widehat{\boldsymbol{\pi}}), \ \ \widehat{\boldsymbol{b}}^{\dagger}=\frac{1}{\sqrt{2}}(\widehat{\boldsymbol{\varphi}}-i \widehat{\boldsymbol{\pi}}) \end{eqnarray*}\"<\/p><\/p>\r\n

\u57fa\u5e95\u72b6\u614b\u3068\u3057\u3066\u5e73\u5747\u304c \"0\"\u30fb\u5358\u4f4d\u5171\u5206\u6563\u306e\u30ac\u30a6\u30b9\u72b6\u614b \"|\Omega\rangle=|0, \mathbf{1}\rangle\" \u3092\u4eee\u5b9a\u3059\u308b\u3068 \"\widehat{\boldsymbol{b}}|\Omega\rangle=0\" \uff0c\u307e\u305f \"\left(\widehat{b}_{a_{1}, x_{1}}^{\dagger}\right)^{n_{i}} \cdots\left(\widehat{b}_{a_{m}, x_{m}}^{\dagger}\right)^{n_{m}} |\Omega\rangle\" \u3067\u30ab\u30e9\u30fc\u30c1\u30e3\u30f3\u30cd\u30eb \"a_{i}\"\u306e\u753b\u50cf\u306e\u4f4d\u7f6e \"x_{i}\" \u306b \"n_{i}\" \u500b\u306e\u30d2\u30f3\u30c8\u30f3\u7c92\u5b50\u3092\u751f\u6210\u3059\u308b\uff0e<\/p>\r\n

\u5168\u7cfb\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\uff0e<\/p>\r\n

(33) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \widehat{H}_{\mathrm{NN}} = i \left(\frac{d}{d t} \widehat{U}_{\mathrm{NN}}\right) \widehat{U}^{\dagger}_{\mathrm{NN}} \end{eqnarray*}\"<\/p><\/p>\r\n

\u5b9f\u306f\uff0c\uff12\u2212\uff11. \u306e\u5834\u306e\u91cf\u5b50\u8ad6\u3068\uff13\u2212\uff11. \u306e\u5834\u306e\u91cf\u5b50\u8ad6\u306f\u95a2\u4fc2\u304c\u3042\u308b\uff0e<\/p>\r\n<\/div>\r\n

<\/p>

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    \u6a5f\u68b0\u5b66\u7fd2\u306e\u71b1\u529b\u5b66\u306f\uff0c\u91cf\u5b50\u91cd\u529b\u7406\u8ad6\u306e\u6b74\u53f2\u306b\u304a\u3051\u308b\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u71b1\u529b\u5b66\u3068\u540c\u3058\u3088\u3046\u306a\u6b74\u53f2\u7684\u4f4d\u7f6e\u306b\u3042\u308b\u306e\u304b\u3082\u3057\u308c\u306a\u3044\uff0e\u30d9\u30c3\u30b1\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30fb\u30db\u30fc\u30ad\u30f3\u30b0\u516c\u5f0f\u306e\u767a\u898b\u304c\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u71b1\u529b\u5b66\u3092\u751f\u307f\u51fa\u3057\uff0c\u30db\u30ed\u30b0\u30e9\u30d5\u30a3\u30fc\u539f\u7406\uff08\u5834\u306e\u91cf\u5b50\u8ad6\u3068\u91cd\u529b […]<\/p>\n","protected":false},"author":135576855,"featured_media":963,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"{title}\n\n{excerpt}\n\n{url}","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"class_list":["post-943","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/hayashiyus.jp\/wp-content\/uploads\/2021\/09\/AdobeStock_300164798.jpeg?fit=6930%2C2950&ssl=1","jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/pcnxx5-fd","_links":{"self":[{"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/posts\/943","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/users\/135576855"}],"replies":[{"embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=943"}],"version-history":[{"count":100,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/posts\/943\/revisions"}],"predecessor-version":[{"id":2216,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/posts\/943\/revisions\/2216"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/media\/963"}],"wp:attachment":[{"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=943"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=943"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=943"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}