SL(2, ℤ) action on QFTs with ℤ2 symmetry and the Brown-Kervaire invariants

Lakshya Bhardwaj; Yasunori Lee; Yuji Tachikawa

doi:10.1007/JHEP11(2020)141

SL(2, ℤ) action on QFTs with ℤ₂ symmetry and the Brown-Kervaire invariants

Lakshya Bhardwaj, Yasunori Lee^*, Yuji Tachikawa

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider an analogue of Witten’s SL(2, ℤ) action on three-dimensional QFTs with U(1) symmetry for 2k-dimensional QFTs with ℤ₂ (k − 1)-form symmetry. We show that the SL(2, ℤ) action only closes up to a multiplication by an invertible topological phase whose partition function is the Brown-Kervaire invariant of the spacetime manifold. We interpret it as part of the SL(2, ℤ) anomaly of the bulk (2k + 1)-dimensional ℤ₂ gauge theory.

Original language	English
Article number	141
Journal	Journal of High Energy Physics
Volume	2020
Issue number	11
DOIs	https://doi.org/10.1007/JHEP11(2020)141
Publication status	Published - Nov 2020

Bibliographical note

Publisher Copyright:
© 2020, The Author(s).

Keywords

Duality in Gauge Field Theories
Topological Field Theories
Topological States of Matter

ASJC Scopus subject areas

Nuclear and High Energy Physics

Access to Document

10.1007/JHEP11(2020)141

Cite this

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KW - Duality in Gauge Field Theories

KW - Topological Field Theories

KW - Topological States of Matter

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