S-duality for the Large N = 4 Superconformal Algebra
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In this paper, the authors prove some conjectures about vertex algebras which emerge in gauge theory constructions associated to the geometric Langlands program and present the conjectural kernel vertex algebra for the SU(2) duality transformation.Abstract:
We prove some conjectures about vertex algebras which emerge in gauge theory constructions associated to the geometric Langlands program. In particular, we present the conjectural kernel vertex algebra for the $$S T^2 S$$ duality transformation in SU(2) gauge theory. We find a surprising coincidence, which gives a powerful hint about the nature of the corresponding duality wall. Concretely, we determine the branching rules for the small $$N=4$$ superconformal algebra at central charge $$-9$$ as well as for the generic large $$N=4$$ superconformal algebra at central charge $$-6$$. Moreover we obtain the affine vertex superalgebra of $$\mathfrak {osp}(1|2)$$ and the $$N=1$$ superconformal algebra times a free fermion as quantum Hamiltonian reductions of the large $$N=4$$ superconformal algebras at $$c=-6$$.read more
Citations
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References
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Electric-Magnetic Duality And The Geometric Langlands Program
Anton Kapustin,Edward Witten +1 more
TL;DR: The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions as discussed by the authors.
Book
Generalized Vertex Algebras and Relative Vertex Operators
Chongying Dong,James Lepowsky +1 more
TL;DR: A Jacobi identity for relative untwisted vertex operators is given in this paper. But it is not a Jacobi for generalized vertex operator algebras and their modules.
Lectures on Electric-Magnetic Duality and the Geometric Langlands Program
TL;DR: In this paper, the authors provide an introduction to the recent work on the Montonen-Olive duality of N = 4 super-Yang-Mills theory and the Geometric Langlands Program.
Journal ArticleDOI
Infinite Chiral Symmetry in Four Dimensions
Christopher Beem,Christopher Beem,Madalena Lemos,Pedro Liendo,Pedro Liendo,Wolfger Peelaers,Leonardo Rastelli,Leonardo Rastelli,Balt C. van Rees,Balt C. van Rees +9 more
TL;DR: In this article, a new correspondence between four-dimensional conformal field theories with extended supersymmetry and two-dimensional chiral algebras was described, where the meromorphic correlators of the chiral algebra compute correlators in a protected sector of the fourdimensional theory.
Journal ArticleDOI
Infinite Chiral Symmetry in Four Dimensions
Christopher Beem,Christopher Beem,Madalena Lemos,Pedro Liendo,Pedro Liendo,Wolfger Peelaers,Leonardo Rastelli,Leonardo Rastelli,Balt C. van Rees,Balt C. van Rees +9 more
TL;DR: In this paper, a new correspondence between four-dimensional conformal field theories with extended supersymmetry and two-dimensional chiral algebras was described, where the meromorphic correlators of the chiral algebra compute correlators in a protected sector of the fourdimensional theory.