Treelike structure of symmetry topological field theories and multisector QFTs

Three-dimensional Yang-Mills-Chern-Simons theory has the peculiar property that its one-form symmetry defects have nontrivial braiding, namely they are charged under the same symmetry they generate, which is then anomalous. This poses a few puzzles in describing the corresponding Symmetry TFT in a four-dimensional bulk. First, the braiding between lines at the boundary seems to be ill-defined when such lines are pulled into the bulk. Second, the Symmetry TFT appears to be too trivial to allow for topological boundary conditions encoding all the different global variants. We show that both of these puzzles can be solved by including endable (tubular) surfaces in the class of bulk topological operators one has to consider. In this way, we are able to reproduce all global variants of the theory, with their symmetries and their anomalies. We check the validity of our proposal also against a top-down holographic realization of the same class of theories.

On the symmetry TFT of Yang-Mills-Chern-Simons theory

Argurio,

Benini,

Bertolini

et al. 2024

Remarks on geometric engineering, symmetry TFTs and anomalies

Del Zotto,

Meynet,

Moscrop

2024

Geometric engineering is a collection of tools developed to establish dictionaries between local singularities in string theory and (supersymmetric) quantum fields. Extended operators and defects, as well as their higher quantum numbers captured by topological symmetries, can be encoded within geometric engineering dictionaries. In this paper we revisit and clarify aspects of these techniques, with special emphasis on ’t Hooft anomalies, interpreted from the SymTFT perspective as obstructions to the existence of Neumann boundary conditions. These obstructions to gauging higher symmetries are captured via higher link correlators for the SymTFT on spheres. In this work, we give the geometric engineering counterpart of this construction in terms of higher links of topological membranes. We provide a consistency check in the context of 5D SCFTs with anomalous 1-form symmetries, where we give two independent derivations of the anomaly in terms of higher links, one purely field theoretical and the other purely geometrical. Along the way, we also recover the construction of non-invertible duality defects in 4D $$ \mathcal{N} $$ N = 4 SYM from a geometric engineering perspective.

Non-invertible symmetries in SN orbifold CFTs and holography

Gutperle,

Li,

Rathore

et al. 2024

We study non-invertible defects in two-dimensional SN orbifold CFTs. We construct universal defects which do not depend on the details of the seed CFT and hence exist in any orbifold CFT. Additionally, we investigate non-universal defects arising from the topological defects of the seed CFT. We argue that there exist universal defects that are non-trivial in the large-N limit, making them relevant for the AdS3/CFT2 correspondence. We then focus on AdS3×S3 × $$ {\mathcal{M}}_4 $$ M 4 with one unit of NS-NS flux and propose an explicit realization of these defects on the worldsheet.