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arXiv · 2411.04849

5d-4d Correspondence in Twisted M-theory on a Conifold

Meer Ashwinkumar·Mir Faizal·Arshid Shabir·Douglas J. Smith·Yehao Zhou
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Abstract

We study twisted M-theory in a general conifold background, and describe it in terms of a 5d non-commutative Chern-Simons-matter theory, which is equivalent to 5d non-commutative Chern-Simons theory for a supergroup. In an equivalent description as twisted type IIA string theory, the matter degrees of freedom arise from topological strings stretched between stacks of D6-branes. In order to study 5d Chern-Simons-matter theories with a boundary, we first construct and investigate the properties of a 4d non-commutative gauged chiral WZW model. We prove the gauge invariant coupling of this 4d theory to the bulk 5d Chern-Simons theory defined on $\mathbb{R}_+ \times \mathbb{C}^2 $, and further generalize our results to the 5d Chern-Simons-matter theory. We also investigate the toroidal current algebra of the 4d chiral WZW model that arises from radial quantization along one of the complex planes. Finally, we show that a gauged non-commutative chiral 4d WZW model arises from the partition function for quantum 5d non-commutative Chern-Simons theory with boundaries in the BV-BFV formalism, and further generalize this 5d-4d correspondence to the 5d non-commutative Chern-Simons-matter theory for the case of adjoint matter.

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BibTeXRIS

Meer Ashwinkumar, Mir Faizal, Arshid Shabir, Douglas J. Smith, Yehao Zhou. 2025-01-22. 5d-4d Correspondence in Twisted M-theory on a Conifold. https://doi.org/10.1007/jhep05(2025)073

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