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Modular invariance

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the torus partition function must be invariant under the modular group
143: 15: 216: 161:, modular invariance is an additional requirement for 236: 8: 50:. Unsourced material may be challenged and 243: 229: 146:. The name comes from the classical name 114:Learn how and when to remove this message 178:two-dimensional conformal field theory 7: 197: 195: 165:. This helps in getting rid of some 48:adding citations to reliable sources 215:. You can help Knowledge (XXG) by 14: 199: 20: 1: 134:is the invariance under the 288: 194: 272:Theoretical physics stubs 171:gravitational anomalies 150:of this group, as in 140:large diffeomorphisms 63:"Modular invariance" 44:improve this article 209:theoretical physics 207:This article about 138:such as SL(2,Z) of 128:theoretical physics 132:modular invariance 224: 223: 176:Equivalently, in 163:one-loop diagrams 124: 123: 116: 98: 279: 245: 238: 231: 203: 196: 167:global anomalies 119: 112: 108: 105: 99: 97: 56: 24: 16: 287: 286: 282: 281: 280: 278: 277: 276: 252: 251: 250: 249: 192: 190: 120: 109: 103: 100: 57: 55: 41: 25: 12: 11: 5: 285: 283: 275: 274: 269: 264: 254: 253: 248: 247: 240: 233: 225: 222: 221: 204: 189: 186: 122: 121: 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 284: 273: 270: 268: 265: 263: 262:String theory 260: 259: 257: 246: 241: 239: 234: 232: 227: 226: 220: 218: 214: 210: 205: 202: 198: 193: 187: 185: 183: 179: 174: 172: 168: 164: 160: 159:string theory 155: 153: 149: 148:modular group 145: 141: 137: 133: 129: 118: 115: 107: 104:December 2009 96: 93: 89: 86: 82: 79: 75: 72: 68: 65: –  64: 60: 59:Find sources: 53: 49: 45: 39: 38: 34: 29:This article 27: 23: 18: 17: 217:expanding it 206: 191: 175: 169:such as the 156: 152:modular form 131: 125: 110: 101: 91: 84: 77: 70: 58: 42:Please help 30: 256:Categories 188:References 74:newspapers 31:does not 267:Symmetry 154:theory. 182:SL(2,Z) 142:of the 88:scholar 52:removed 37:sources 90:  83:  76:  69:  61:  211:is a 144:torus 136:group 95:JSTOR 81:books 213:stub 67:news 35:any 33:cite 184:. 173:. 157:In 126:In 46:by 258:: 130:, 244:e 237:t 230:v 219:. 117:) 111:( 106:) 102:( 92:· 85:· 78:· 71:· 54:. 40:.

Index


cite
sources
improve this article
adding citations to reliable sources
removed
"Modular invariance"
news
newspapers
books
scholar
JSTOR
Learn how and when to remove this message
theoretical physics
group
large diffeomorphisms
torus
modular group
modular form
string theory
one-loop diagrams
global anomalies
gravitational anomalies
two-dimensional conformal field theory
SL(2,Z)
Stub icon
theoretical physics
stub
expanding it
v

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