Abstract

We study a four-dimensional domain wall in twisted M-theory. The domain wall is engineered by intersecting D6 branes in the type IIA frame. We identify the classical algebra of operators on the domain wall in terms of a higher vertex operator algebra, which describes the holomorphic subsector of a 4d \mathcal{N}=1𝒩=1 supersymmetric field theory, and compute the associated mode algebra. We conjecture that the quantum deformation of the classical algebra is isomorphic to the bulk algebra of operators from which we establish twisted holography of the domain wall.

Highlights

  • Topological twists [1, 2] have been a standard tool to study a supersymmetric quantum field theory along with Ω−deformation [3, 4]

  • Different from the line and surface defects engineered by membranes, the domain wall-like defect is engineered by changing the G2-holonomy 7-manifold [37, 38]

  • Twisted supergravity [15] is defined as the supergravity in a background where the bosonic ghost Ψ of the local supersymmetry takes a nonzero value

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Summary

Introduction

Topological twists [1, 2] have been a standard tool to study a supersymmetric quantum field theory along with Ω−deformation [3, 4]. Different from the line and surface defects engineered by membranes, the domain wall-like defect is engineered by changing the G2-holonomy 7-manifold [37, 38] It passes tight constraints for the allowed BPS objects in twisted M-theory. The major difference between the higher VOA coming from the holomorphic twist and the familiar 2d VOA is that in the former case the descent operators play the key role to generate meromorphicity, which is the essential ingredient for the algebraic structure under the vertex operator algebra. Like the usual cohomological field theory, the set of Q-cohomology classes in the higher VOA includes a certain integrated version of the descent operators and in our case they are holomorphic descents of local Q-cohomology classes. We conjecture that the quantum deformation of our classical computation is isomorphic to the Koszul dual algebra of operators in the 5d Chern-Simons theory. We provide details of the key commutation relation computation in Appendix B

Twisted M-theory
Background
Compatibility of M2 and M5 branes in twisted M-theory
Higher vertex operator algebra
The boundary condition of the 5d gauge field
Physical observables on the domain wall
Algebra of operators on the domain wall
The large N limit
Conjecture
Conclusion and open questions
B Mode algebra computation
Full Text
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