The geometry of decoupling fields

We study the Symmetry Topological Field Theory in holography associated with 4d 𝒩 = 1 Super Yang-Mills theory with gauge algebra 𝔰𝔲(M). From this, all the bulk symmetry operators are computed and matched to various D-brane configurations. The fusion algebra of the operators emerges from brane dynamics. In particular, we show that the symmetry operators are purely determined from the center-of-mass modes of the branes. We identify the TQFT fusion coefficients with the relative motion of the branes. We also establish the origin of condensation defects, arising from fusion of non-invertible operators, as the consequence of tachyon condensation in brane-anti-brane pairs.

Non-invertible symmetries, brane dynamics, and tachyon condensation

Bah,

Leung,

Waddleton

2024

𝒩 = 1 SCFTs from F-theory on Orbifolds

Giacomelli,

Savelli

2023

We study four-dimensional superconformal field theories living on the worldvolume of D3 branes probing minimally-supersymmetric F-theory backgrounds, focusing on the case of orbi-orientifold setups with and without 7-branes. We observe that these theories are closely related to compactifications of six-dimensional 𝒩 = (1, 0) theories on a torus with flux, where the flux quanta is mapped in Type IIB to the defining data of the orbifold group. We analyze the cases of class 𝒮k theories as well as of compactifications of the E-string and of orbi-instanton theories. We also classify 𝒮-fold configurations in F-theory preserving minimal supersymmetry in four dimensions and their mass deformations.

M5-branes probing flux backgrounds

Bah

Bonetti

Leung

et al. 2022

We analyze the global symmetries and anomalies of 4d $$ \mathcal{N} $$ N = 1 field theories that arise from a stack of N M5-branes probing a class of flux backgrounds. These backgrounds consist of a resolved ℂ2/ℤk singularity fibered over a smooth Riemann surface of genus g ≥ 2, supported by a non-trivial G4-flux configuration labeled by a collection of 2(k − 1) flux quanta, {Ni}. For k = 2, this setup defines a non-trivial superconformal field theory (SCFT) in the IR, which is holographically dual to an explicit AdS5 solution first described by Gauntlett, Martelli, Sparks, and Waldram. The generalization to k ≥ 3 is hard to tackle directly within holography. Instead, in this paper we lay the groundwork for a systematic analysis of such a generalization by adopting anomaly inflow methods to identify continuous and discrete global symmetries of the 4d field theories. We also compute the ’t Hooft anomalies for continuous symmetries at leading order in the limit of large N, Ni.