M5-branes probing flux backgrounds

We derive the Symmetry Topological Field Theories (SymTFTs) for 3d supersymmetric quantum field theories (QFTs) constructed in M-theory either via geometric engineering or holography. These 4d SymTFTs encode the symmetry structures of the 3d QFTs, for instance the generalized global symmetries and their ’t Hooft anomalies. Using differential cohomology, we derive the SymTFT by reducing M-theory on a 7-manifold Y7, which either is the link of a conical Calabi-Yau four-fold or part of an AdS4× Y7 holographic solution. In the holographic setting we first consider the 3d $$ \mathcal{N} $$ N = 6 ABJ(M) theories and derive the BF-couplings, which allow the identification of the global form of the gauge group, as well as 1-form symmetry anomalies. Secondly, we compute the SymTFT for 3d $$ \mathcal{N} $$ N = 2 quiver gauge theories whose holographic duals are based on Sasaki-Einstein 7-manifolds of type Y7 = Yp,k($$ \mathbbm{CP} $$ CP 2). The SymTFT encodes 0- and 1-form symmetries, as well as potential ’t Hooft anomalies between these. Furthermore, by studying the gapped boundary conditions of the SymTFT we constrain the allowed choices for U(1) Chern-Simons terms in the dual field theory.

“…has been much recent interest in the holographic literature [24,28,85,88,[90][91][92][93][94][95][96], in particular for AdS 4 /CFT 3 in [92] for 3d N = 6 SCFTs of ABJM type [97].…”

Section: Jhep02(2023)226mentioning

confidence: 99%

Symmetry TFTs for 3d QFTs from M-theory

Beest

Gould

Schäfer‐Nameki

et al. 2023

Non-invertible symmetries of class S theories

Bashmakov

Zotto

Hasan

et al. 2023

We study the non-invertible symmetries of class $$ \mathcal{S} $$ S theories obtained by compactifying the type $$ {\mathfrak{a}}_{p-1} $$ a p − 1 6d (2,0) theory on a genus g Riemann surface with no punctures. After setting up the general framework, we describe how such symmetries can be classified up to genus 5. Of central interest to us is the question of whether a non-invertible symmetry is intrinsic, i.e. whether it can be related to an invertible symmetry by discrete gauging. We then describe the higher-dimensional origin of our results, and explain how the Anomaly and Symmetry TFTs, as well as N-ality defects, of class $$ \mathcal{S} $$ S theories can be obtained from compactification of a 7d Chern-Simons theory. Interestingly, we find that the Symmetry TFT for theories with intrinsically non-invertible symmetries can only be obtained by coupling the 7d Chern-Simons theory to topological gravity.

Disconnected 0-form and 2-group symmetries

Bhardwaj¹,

Gould²

2023

Quantum field theories can have both continuous and finite 0-form symmetries. We study global symmetry structures that arise when both kinds of 0-form symmetries are present. The global structure associated to continuous 0-form symmetries is described by a connected Lie group, which captures the possible backgrounds of the continuous 0-form symmetries the theory can be coupled to. Finite 0-form symmetries can act as outer-automorphisms of this connected Lie group. Consequently, possible background couplings to both continuous and finite 0-form symmetries are described by a disconnected Lie group, and we call the resulting symmetry structure a disconnected 0-form symmetry. Additionally, finite 0-form symmetries may act on the 1-form symmetry group. The 1-form symmetries and continuous 0-form symmetries may combine to form a 2-group, which when combined with finite 0-form symmetries leads to another type of 2-group, that we call a disconnected 2-group and the resulting symmetry structure a disconnected 2-group symmetry. Examples of arbitrarily complex disconnected 0-form and 2-group symmetries in any spacetime dimension are furnished by gauge theories: with 1-form symmetries arising from the center of the gauge group, continuous 0-form symmetries arising as flavor symmetries acting on matter content, and finite 0-form symmetries arising from outer-automorphisms of gauge and flavor Lie algebras.