Geometric Langlands From Six Dimensions
By E. Witten. 2009
169 citations recorded by the source corpus.
Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally understood as a consequence of the existence of a certain exotic supersymmetric conformal field theory in six dimensions. The same six-dimensional theory also gives a useful framework for understanding some recent mathematical results involving a counterpart of geometric Langlands duality for complex surfaces. (This article is based on a lecture at the Raoul Bott celebration, Montreal, June 2008.)
Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/40642066e01c6aa3113be24c70999c1ec49aabf1
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Citations in the corpus
- S-duality and 2d topological QFT (2009, background): “pondence is provided by the existence of the six-dimensional (2,0) superconformal field theory, whose compactification on a torus of modular parameter τ yields N = 4 SYM with holomorphic coupling τ(see [3] for a recent discussion). Gaiotto [1] has recently discovered a beautiful generalization of this”
- On the Defect Group of a 6D SCFT (2015, background): “The basis vectors Zv then have the interpretation as the partition function of a five-dimensional SU(N)/Zp gauge theory restricted to gauge bundles of StiefelWhitney class v [11].”
- Framed BPS states (2010, unknown): “Extra data must be specified which determine a projection of the vector space of partition functions to a one-dimensional subspace [49].”
- Local subsystems in gauge theory and gravity (2016, background): “Interestingly it has been conjectured in [58] that the slice of a spacetime outside a black hole horizon should have precisely this structure.”
- Reading between the lines of four-dimensional gauge theories (2013, background): “They are not standard consistent local quantum field theories by themselves, but can be viewed either as generalizations of local quantum field theories where the expectation values are elements of a vector space rather than well-defined numbers [33] (see also [38,39,40,41], and [42] and references ”
- Generalized global symmetries (2014, background): “18 We caution the reader that the term “conformal block” here is used in a somewhat nonstandard fashion, following the terminology introduced in [46] in analogy to conformal blocks in two-dimensional RCFTs, which have a specific relation to 3d TQFTs.”
- Fivebranes and Knots (2011, background): “The details, which are described in [84], will not be important in the present paper.”
- Anomaly polynomial of general 6D SCFTs (2014, background): “Also, the partition functions of N=(2, 0) theories are known to behave rather like conformal blocks of two-dimensional chiral CFTs [35–38], and it would be interesting to understand what happens in N=(1, 0) cases.”
- Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2 (2015, background): “complex structure of the torus, and the S duality group is interpreted as the mapping class group of the torus. The superconformal invariance of 6d theory play a crucial role in deriving 4d S duality [68]. Here we focus on the remaining ve cases, namely Z n with n= 3;4;6;8;12. Note that for n6= 3 we”
- Coupling a QFT to a TQFT and duality (2014, unknown): “For more details, see [5-10].”
- General Argyres-Douglas theory (2012, background): “For the partition [2, 1], we have p2 = 1, p3 = 1, and for the partition [1, 1, 1], the order of pole is p2 = 1, p3 = 2.”