Abstract

In the presence of an Ω-deformation, local operators generate a chiral algebra in the topological-holomorphic twist of a four-dimensional mathcal{N} = 2 supersymmetric field theory. We show that for a unitary mathcal{N} = 2 superconformal field theory, the chiral algebra thus defined is isomorphic to the one introduced by Beem et al. Our definition of the chiral algebra covers nonconformal theories with insertions of suitable surface defects.

Highlights

  • It has been suggested by Kevin Costello that an Ωdeformation [8, 9] of Kapustin’s construction should give rise to a chiral algebra

  • In the presence of an Ω-deformation, local operators generate a chiral algebra in the topological-holomorphic twist of a four-dimensional N = 2 supersymmetric field theory

  • We show that for a unitary N = 2 superconformal field theory, the chiral algebra defined is isomorphic to the one introduced by Beem et al Our definition of the chiral algebra covers nonconformal theories with insertions of suitable surface defects

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Summary

Topological twists

A twist of a quantum field theory [5, 6] is an operation which changes the action of the rotation symmetry in such a way that its generator M is shifted to M ′, differing by a generator F of a global symmetry:. A twisted theory is equivalent to the original theory if the spacetime is flat — the twist merely relabels some symmetry generators and changes what we should call the energy-momentum tensor — but the difference becomes important otherwise. In the case of N = (2, 2) supersymmetric field theories, there are essentially two such topological twists. For theories with local N = (2, 2) superconformal symmetry, the full topological invariance, for an appropriate definition of the energy-momentum tensor, follows from the superconformal algebra. The two twists are exchanged under the involution (2.7): MA ↔ MB , QA ↔ QB , FV ↔ FA

Ω-deformations
Localization of Ω-deformed B-twisted gauge theories
Kapustin’s topological-holomorphic twist
Ω-deformed topological-holomorphic theories and chiral algebras
Vector multiplets and hypermultiplets
Adding surface defects
Nonconformal theories with surface defects
A Ω-deformations for vector and chiral multiplets
Full Text
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