S-duality for the Large N = 4 Superconformal Algebra
| Autor: | Davide Gaiotto, Thomas Creutzig, Andrew R. Linshaw |
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| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
Vertex (graph theory) Pure mathematics FOS: Physical sciences 01 natural sciences High Energy Physics::Theory Vertex operator algebra Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Quantum Algebra (math.QA) Gauge theory Representation Theory (math.RT) 0101 mathematics Mathematical Physics Mathematics 010102 general mathematics S-duality Statistical and Nonlinear Physics 16. Peace & justice Superalgebra Langlands program High Energy Physics - Theory (hep-th) 010307 mathematical physics Superconformal algebra Central charge Mathematics - Representation Theory |
| Zdroj: | Communications in Mathematical Physics. 374:1787-1808 |
| ISSN: | 1432-0916 0010-3616 |
| Popis: | 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 $c=-6$. Comment: Relationship between large and small N=4 superconformal VOAs is clarified |
| Databáze: | OpenAIRE |
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