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Quantum Gravity Partition Functions in Three Dimensions
Alexander Maloney, Edward Witten
We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be…
Conformal Field Theory In Four And Six Dimensions
Edward Witten
The goal of these notes is to give a brief explanation of how electric-magnetic duality in four dimensions is related to the existence of an unusual conformal field theory in six d…
Gauge Theory And Wild Ramification
Edward Witten
The gauge theory approach to the geometric Langlands program is extended to the case of wild ramification. The new ingredients that are required, relative to the tamely ramified ca…
Geometric Endoscopy and Mirror Symmetry
Edward Frenkel, Edward Witten
The geometric Langlands correspondence has been interpreted as the mirror symmetry of the Hitchin fibrations for two dual reductive groups. This mirror symmetry, in turn, reduces t…
Three-Dimensional Gravity Revisited
Edward Witten
We consider the problem of identifying the CFT's that may be dual to pure gravity in three dimensions with negative cosmological constant. The c-theorem indicates that three-dimens…