Saved in:
Bibliographic Details
Main Authors: Bashmakov, Vladimir, Del Zotto, Michele, Hasan, Azeem
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2305.10422
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866909069109886976
author Bashmakov, Vladimir
Del Zotto, Michele
Hasan, Azeem
author_facet Bashmakov, Vladimir
Del Zotto, Michele
Hasan, Azeem
contents In this paper we study the geometric origin of non-invertible symmetries of 2d theories arising from the reduction of 6d $(2,0)$ theories on four-manifolds. This generalizes and extends our previous results in the context of class $\mathcal S$ theories to a wider realm of models. In particular, we find that relative 2d field theories, such as the chiral boson, have a higher dimensional origin in four-manifolds that are not null cobordant. Moreover, we see that for the 2d theories with a 6d origin, the non-invertible symmetries have a geometric origin as a sum over topologies from the perspective of the 7d symmetry TFT. In particular, we show that the Tambara-Yamagami non-invertible symmetries $TY(\mathbb Z_N)$ can be given a geometric origin of this kind. We focus on examples that do not depend on spin structures, but we analyse the simplest of such cases, finding an interesting parallel between the extra choices arising in that context and symmetry fractionalization in Maxwell theories.
format Preprint
id arxiv_https___arxiv_org_abs_2305_10422
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Four-manifolds and Symmetry Categories of 2d CFTs
Bashmakov, Vladimir
Del Zotto, Michele
Hasan, Azeem
High Energy Physics - Theory
In this paper we study the geometric origin of non-invertible symmetries of 2d theories arising from the reduction of 6d $(2,0)$ theories on four-manifolds. This generalizes and extends our previous results in the context of class $\mathcal S$ theories to a wider realm of models. In particular, we find that relative 2d field theories, such as the chiral boson, have a higher dimensional origin in four-manifolds that are not null cobordant. Moreover, we see that for the 2d theories with a 6d origin, the non-invertible symmetries have a geometric origin as a sum over topologies from the perspective of the 7d symmetry TFT. In particular, we show that the Tambara-Yamagami non-invertible symmetries $TY(\mathbb Z_N)$ can be given a geometric origin of this kind. We focus on examples that do not depend on spin structures, but we analyse the simplest of such cases, finding an interesting parallel between the extra choices arising in that context and symmetry fractionalization in Maxwell theories.
title Four-manifolds and Symmetry Categories of 2d CFTs
topic High Energy Physics - Theory
url https://arxiv.org/abs/2305.10422