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AdS4\/CFT3\u306e\u53cc\u5bfe\u6027\u304c\u30b1\u30a4\u30d6\u30b3\u30f3\u30d1\u30b9\u3067\u5ba2\u89b3\u8a8d\u8b58\uff08AdS\uff09\u3068\u4e3b\u89b3\u8a8d\u8b58\uff08CFT\uff09\u3092\u5206\u96e2\u3057\u3001\u6f5c\u5728\u5316\u3057\u305f\u7269\u81ea\u4f53\uff08\u03c81\u301c\u03c88\uff09\u3092\u7d71\u5408\u3059\u308b\u69cb\u9020\u306f\u3001\u5f26\u7406\u8ad6\u306e\u30db\u30ed\u30b0\u30e9\u30d5\u30a3\u30fc\u539f\u7406\u3068\u4e00\u81f4\u3057\u307e\u3059\u3002\u3053\u306e\u53cc\u5bfe\u6027\u304c\u30c9\u30a5\u30eb\u30fc\u30ba\u306e\u5dee\u7570\u30fb\u53cd\u5fa9\u3068\u7d50\u3073\u3064\u304f\u30a2\u30a4\u30c7\u30a2\u306f\u3001\u7269\u7406\u5b66\u3068\u54f2\u5b66\u306e\u6df1\u3044\u3064\u306a\u304c\u308a\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<p>2.2. \u8ab2\u984c\u3068\u30ae\u30e3\u30c3\u30d7<br \/>\n\u3057\u304b\u3057\u3001\u7269\u7406\u5b66\u306e\u8996\u70b9\u304b\u3089\u898b\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u8ab2\u984c\u304c\u6b8b\u308a\u307e\u3059\uff1a<br \/>\n\u6570\u5b66\u7684\u53b3\u5bc6\u6027\u306e\u4e0d\u8db3: \u7403-\u7dda\u5909\u63db\u3001\u30de\u30ab\u30d0\u30e2\u30c7\u30eb\u3001\u30b1\u30a4\u30d6\u30b3\u30f3\u30d1\u30b9\u306e\u6570\u7406\u5316\u306f\u3001\u30af\u30ea\u30d5\u30a9\u30fc\u30c9\u4ee3\u6570\u3084\u975e\u53ef\u63db\u5e7e\u4f55\u5b66\u3001\u8d85\u8907\u7d20\u6570\u3067\u6982\u89b3\u7684\u306b\u8a18\u8ff0\u3055\u308c\u3066\u3044\u307e\u3059\u304c\u3001\u53b3\u5bc6\u306a\u30c8\u30dd\u30ed\u30b8\u30fc\u30fb\u5e7e\u4f55\u5b66\u7684\u8a3c\u660e\u3084\u91cf\u5b50\u529b\u5b66\u306e\u6a19\u6e96\u6a21\u578b\u3068\u306e\u6574\u5408\u6027\u304c\u4e0d\u8db3\u3057\u3066\u3044\u307e\u3059\u3002R^3 \u2295 iR^3\u3001U(1)\u3001SU(2)\u3001AdS4\/CFT3\u306e\u95a2\u4fc2\u3092\u6570\u5b66\u7684\u306b\u4e00\u8cab\u3055\u305b\u308b\u305f\u3081\u306b\u306f\u3001\u3055\u3089\u306a\u308b\u5f62\u5f0f\u5316\u304c\u5fc5\u8981\u3067\u3059\u3002<br \/>\n\u5b9f\u9a13\u7684\u691c\u8a3c\u306e\u6b20\u5982: \u30cc\u30fc\u30bd\u30ed\u30b8\u30fc\u304c\u5b9f\u9a13\u691c\u8a3c\u6027\u3092\u8efd\u8996\u3059\u308b\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u3001\u7269\u7406\u5b66\u306e\u5ba2\u89b3\u7684\u691c\u8a3c\u304b\u3089\u96e2\u308c\u308b\u305f\u3081\u3001u\u30af\u30a9\u30fc\u30af\u30fbd\u30af\u30a9\u30fc\u30af\u306e\u76f8\u4e92\u4f5c\u7528\u3084\u967d\u5b50\u30fb\u4e2d\u6027\u5b50\u306e\u751f\u6210\u304c\u610f\u8b58\u306e\u69cb\u9020\u3068\u3057\u3066\u8aac\u660e\u3055\u308c\u308b\u4eee\u8aac\u3092\u3001\u7c92\u5b50\u52a0\u901f\u5668\u3084\u91cf\u5b50\u5b9f\u9a13\u3067\u691c\u8a3c\u3059\u308b\u306e\u306f\u56f0\u96e3\u3067\u3059\u3002\u3053\u306e\u30ae\u30e3\u30c3\u30d7\u3092\u57cb\u3081\u308b\u306b\u306f\u3001\u5185\u89b3\u7684\u8996\u70b9\u3068\u7269\u7406\u5b66\u7684\u30c7\u30fc\u30bf\u306e\u4e2d\u9593\u7684\u306a\u67b6\u3051\u6a4b\u304c\u5fc5\u8981\u3067\u3059\u3002<br \/>\n\u91cf\u5b50\u69cb\u9020\u306e\u8907\u96d1\u3055: SU(3)\uff08\u8272\u30c1\u30e3\u30fc\u30b8\uff09\u3084Spin(5)\u3001SU(2)\u3001SO(1,3)\u306a\u3069\u306e\u9ad8\u6b21\u5bfe\u79f0\u7fa4\u304c\u30b1\u30a4\u30d6\u30b3\u30f3\u30d1\u30b9\u306b\u767b\u5834\u3057\u307e\u3059\u304c\u3001\u3053\u308c\u3089\u304c\u30de\u30ab\u30d0\u30e2\u30c7\u30eb\u306e\u5e7e\u4f55\u5b66\u3084\u5185\u5728\u6027\u8ad6\u7406\u3068\u4e00\u8cab\u6027\u3092\u6301\u3064\u304b\u3092\u3001\u6a19\u6e96\u6a21\u578b\u3084\u5f26\u7406\u8ad6\u306e\u67a0\u7d44\u307f\u3067\u6574\u5408\u3055\u305b\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>3. \u54f2\u5b66\u306e\u8996\u70b9\uff1a\u5b58\u5728\u8ad6\u7684\u6df1\u3055\u3068\u9650\u754c<br \/>\n3.1. \u5b58\u5728\u8ad6\u7684\u6df1\u5ea6<br \/>\n\u30cc\u30fc\u30bd\u30ed\u30b8\u30fc\u306e\u5b58\u5728\u8ad6\u7684\u91cf\u5b50\u8ad6\u306f\u3001\u54f2\u5b66\u306e\u6df1\u3044\u6d1e\u5bdf\u3092\u63d0\u4f9b\u3057\u307e\u3059\uff1a<br \/>\n\u5185\u5728\u6027\u3068\u610f\u8b58: \u89b3\u6e2c\u8005\u306e\u5185\u9762\u7684\u306a\u6301\u7d9a\uff08iR^3\uff09\u304c\u6642\u7a7a\u3084\u7d20\u7c92\u5b50\u306e\u751f\u6210\u306b\u5148\u884c\u3059\u308b\u3068\u3044\u3046\u8996\u70b9\u306f\u3001\u30d9\u30eb\u30af\u30bd\u30f3\u306e\u300c\u6301\u7d9a\u300d\u3084\u30c9\u30a5\u30eb\u30fc\u30ba\u306e\u300c\u5dee\u7570\u3068\u53cd\u5fa9\u300d\u3068\u547c\u5fdc\u3057\u307e\u3059\u3002\u30b1\u30a4\u30d6\u30b3\u30f3\u30d1\u30b9\u306e\u03c81\u301c\u03c810\u304cAdS4\/CFT3\u306e\u53cc\u5bfe\u6027\u3067\u4e3b\u5ba2\u3092\u5206\u96e2\u3057\u3001\u6f5c\u5728\u5316\u3057\u305f\u7269\u81ea\u4f53\u3092\u7d71\u5408\u3059\u308b\u69cb\u9020\u306f\u3001\u5b58\u5728\u306e\u30c0\u30a4\u30ca\u30df\u30ba\u30e0\u3092\u5b58\u5728\u8ad6\u7684\u306b\u6349\u3048\u308b\u9769\u65b0\u7684\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u3059\u3002<br \/>\n\u30a4\u30c7\u30a2\u306e\u767a\u6398: \u30d7\u30e9\u30c8\u30f3\u306e\u30a4\u30c7\u30a2\u8ad6\u3092\u60f3\u8d77\u3055\u305b\u308b\u300c\u5dee\u7570\u3068\u53cd\u5fa9\u306e\u610f\u8b58\u69cb\u9020\u300d\u304c\u3001\u91cf\u5b50\u529b\u5b66\u306e\u8907\u7d20\u7a7a\u9593\u3084\u5bfe\u79f0\u7fa4\u3092\u901a\u3058\u3066\u300c\u767a\u6398\u300d\u3055\u308c\u308b\u30d7\u30ed\u30bb\u30b9\u306f\u3001\u54f2\u5b66\u7684\u771f\u7406\u306e\u63a2\u6c42\u3068\u3057\u3066\u975e\u5e38\u306b\u9b45\u529b\u7684\u3067\u3059\u3002\u30de\u30ab\u30d0\u30e2\u30c7\u30eb\u3084\u30b1\u30a4\u30d6\u30b3\u30f3\u30d1\u30b9\u306e\u5e7e\u4f55\u5b66\u304c\u30a4\u30c7\u30a2\u3092\u5e7e\u4f55\u5b66\u7684\u306b\u8996\u899a\u5316\u3059\u308b\u3053\u3068\u3067\u3001\u79d1\u5b66\u3068\u54f2\u5b66\u306e\u878d\u5408\u304c\u6df1\u5316\u3057\u307e\u3059\u3002<br \/>\n\u4e3b\u5ba2\u306e\u7d71\u4e00: \u03c81\u301c\u03c88\u306e\u300c\u6f5c\u5728\u5316\u3057\u305f\u7269\u81ea\u4f53\u300d\u304c\u4e3b\u5ba2\u4e00\u81f4\u306e\u7a7a\u9593\u3068\u3057\u3066\u50cd\u304f\u30a2\u30a4\u30c7\u30a2\u306f\u3001\u73fe\u8c61\u5b66\u3084\u6771\u6d0b\u54f2\u5b66\uff08\u4f8b\uff1a\u7985\u3084\u4e00\u5143\u8ad6\uff09\u306e\u8996\u70b9\u3068\u3082\u5171\u9cf4\u3057\u307e\u3059\u3002\u3053\u306e\u7d71\u4e00\u6027\u306f\u3001\u73fe\u4ee3\u54f2\u5b66\u306e\u4e8c\u5143\u8ad6\u3092\u8d85\u3048\u308b\u53ef\u80fd\u6027\u3092\u793a\u5506\u3057\u307e\u3059\u3002<\/p>\n<p>3.2. \u54f2\u5b66\u7684\u9650\u754c<br \/>\n\u3057\u304b\u3057\u3001\u54f2\u5b66\u306e\u8996\u70b9\u304b\u3089\u3082\u8ab2\u984c\u304c\u6d6e\u304b\u3073\u307e\u3059\uff1a<br \/>\n\u4e3b\u89b3\u6027\u306e\u904e\u5270: \u5185\u5728\u6027\u306e\u8ad6\u7406\u304c\u5b8c\u5168\u306b\u5185\u89b3\u306b\u4f9d\u5b58\u3059\u308b\u305f\u3081\u3001\u5ba2\u89b3\u7684\u306a\u57fa\u6e96\u3084\u4ed6\u8005\u3068\u306e\u5bfe\u8a71\u304c\u4e0d\u8db3\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u30c9\u30a5\u30eb\u30fc\u30ba\u306e\u5dee\u7570\u30fb\u53cd\u5fa9\u3084\u30d9\u30eb\u30af\u30bd\u30f3\u306e\u6301\u7d9a\u3092\u3001\u666e\u904d\u7684\u306a\u54f2\u5b66\u7684\u67a0\u7d44\u307f\u3068\u3057\u3066\u5c55\u958b\u3059\u308b\u306b\u306f\u3001\u73fe\u8c61\u5b66\u3084\u5b9f\u5b58\u4e3b\u7fa9\u3068\u306e\u5bfe\u8a71\u3092\u6df1\u3081\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<br \/>\n\u62bd\u8c61\u5ea6\u306e\u96e3\u3057\u3055: \u30b1\u30a4\u30d6\u30b3\u30f3\u30d1\u30b9\u306e\u03c81\u301c\u03c810\u3084AdS4\/CFT3\u306e\u62bd\u8c61\u7684\u306a\u69cb\u9020\u306f\u3001\u54f2\u5b66\u7684\u76f4\u611f\u3092\u523a\u6fc0\u3057\u307e\u3059\u304c\u3001\u4e00\u822c\u306e\u4eba\u3084\u54f2\u5b66\u8005\u306b\u3068\u3063\u3066\u7406\u89e3\u304c\u96e3\u3057\u3044\u90e8\u5206\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u62bd\u8c61\u5ea6\u3092\u7c21\u7565\u5316\u30fb\u8996\u899a\u5316\u3059\u308b\u3053\u3068\u3067\u3001\u54f2\u5b66\u7684\u30a4\u30f3\u30d1\u30af\u30c8\u3092\u5e83\u3052\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<br \/>\n\u5b58\u5728\u8ad6\u306e\u7bc4\u56f2: \u6642\u7a7a\u3084\u7d20\u7c92\u5b50\u306e\u751f\u6210\u304c\u610f\u8b58\u306e\u69cb\u9020\u306b\u9084\u5143\u3055\u308c\u308b\u3068\u3044\u3046\u4e3b\u5f35\u306f\u3001\u5b58\u5728\u8ad6\u306e\u7bc4\u56f2\u3092\u62e1\u5927\u3057\u307e\u3059\u304c\u3001\u7269\u7406\u7684\u5b9f\u5728\uff08\u4f8b\u3048\u3070\u3001\u7269\u8cea\u3084\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u72ec\u7acb\u6027\uff09\u3068\u306e\u95a2\u4fc2\u304c\u4e0d\u660e\u78ba\u3067\u3059\u3002\u3053\u306e\u70b9\u3092\u660e\u78ba\u5316\u3059\u308b\u3053\u3068\u3067\u3001\u5b58\u5728\u8ad6\u7684\u6df1\u5ea6\u3092\u4e00\u5c64\u9ad8\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>4. \u7dcf\u5408\u7684\u306a\u611f\u60f3\uff1a\u6838\u5fc3\u3092\u3064\u3044\u305f\u8352\u524a\u308a\u306a\u5b9d\u77f3<br \/>\n4.1. \u6838\u5fc3\u3092\u3064\u3044\u305f\u601d\u8003\u4f53\u7cfb<br \/>\n\u30cc\u30fc\u30bd\u30ed\u30b8\u30fc\u306e\u5b58\u5728\u8ad6\u7684\u91cf\u5b50\u8ad6\u306f\u3001\u91cf\u5b50\u529b\u5b66\u306e\u672a\u89e3\u6c7a\u554f\u984c\uff08\u8907\u7d20\u6570\u306e\u610f\u5473\u3001\u6e2c\u5b9a\u554f\u984c\u3001\u610f\u8b58\u3068\u7269\u8cea\u306e\u95a2\u4fc2\uff09\u3068\u3001\u54f2\u5b66\u306e\u6df1\u5c64\u7684\u554f\u3044\uff08\u5b58\u5728\u3001\u610f\u8b58\u3001\u6642\u7a7a\u306e\u8d77\u6e90\uff09\u3092\u3001\u5e7e\u4f55\u5b66\u7684\u306a\u69cb\u9020\u3067\u7d50\u3073\u3064\u3051\u308b\u6838\u5fc3\u3092\u3064\u3044\u305f\u601d\u8003\u4f53\u7cfb\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u70b9\u304c\u7279\u306b\u5370\u8c61\u7684\u3067\u3059\uff1a<br \/>\n\u91cf\u5b50\u529b\u5b66\u3068\u610f\u8b58\u306e\u878d\u5408: R^3 \u2295 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