S-duality for the Large $N=4$ Superconformal Algebra
Publication Date
1-8-2020
Document Type
Article
Organizational Units
Mathematics
Keywords
Vertex algebras, Superconformal algebra, Duality, Gauge theory
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 ST2S" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">ST2SST2S 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" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">N=4N=4 superconformal algebra at central charge −9" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">−9−9 as well as for the generic large N=4" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">N=4N=4 superconformal algebra at central charge −6" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">−6−6. Moreover we obtain the affine vertex superalgebra of osp(1|2)" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">osp(1|2)osp(1|2) and the N=1" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">N=1N=1 superconformal algebra times a free fermion as quantum Hamiltonian reductions of the large N=4" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">N=4N=4 superconformal algebras at c=−6" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">c=−6c=−6.
Publication Statement
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Recommended Citation
Creutzig, Thomas, et al. “S-Duality for the Large N = 4 Superconformal Algebra.” Communications in Mathematical Physics, vol. 374, no. 3, 2020, pp. 1787–1808. doi: 10.1007/s00220-019-03673-4.