Symmetry TFTs from String Theory
Abstract
We determine the $d+1$ dimensional topological field theory, which encodes the higherform symmetries and their 't Hooft anomalies for $d$dimensional QFTs obtained by compactifying Mtheory on a noncompact space $X$. The resulting theory, which we call the Symmetry TFT, or SymTFT for short, is derived by reducing the topological sector of 11d supergravity on the boundary $\partial X$ of the space $X$. Central to this endeavour is a reformulation of supergravity in terms of differential cohomology, which allows the inclusion of torsion in cohomology of the space $\partial X$, which in turn gives rise to the background fields for discrete (in particular higherform) symmetries. We apply this framework to 7d superYang Mills where $X= \mathbb{C}^2/\Gamma_{ADE}$, as well as the SasakiEinstein links of CalabiYau threefold cones that give rise to 5d superconformal field theories. This Mtheory analysis is complemented with a IIB 5brane web approach, where we derive the SymTFTs from the asymptotics of the 5brane webs. Our methods apply to both Lagrangian and nonLagrangian theories, and allow for many generalisations.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 DOI:
 10.48550/arXiv.2112.02092
 arXiv:
 arXiv:2112.02092
 Bibcode:
 2021arXiv211202092A
 Keywords:

 High Energy Physics  Theory
 EPrint:
 61 pages, 3 figures