The SymTFT of $u(N)$ Yang-Mills Theory and Holography

TL;DR

This paper introduces a Symmetry Topological Field Theory (SymTFT) for 4d $U(N)$ Yang-Mills theories, exploring their global symmetries and holographic embeddings, revealing limitations in supergravity descriptions of continuous symmetries.

Contribution

It constructs a SymTFT for 4d $U(N)$ Yang-Mills theories and analyzes its holographic realization, highlighting differences from supergravity boundary limits.

Findings

SymTFT reproduces the global one-form symmetry structure.

Continuous symmetries in SymTFT are not always captured by supergravity boundary limits.

The work clarifies the holographic embedding of global symmetries in Yang-Mills theories.

Abstract

We propose a SymTFT for 4d $U(N)$ Yang-Mills theory and its variants. We show that the SymTFT reproduces the structure of the global one-form symmetry in these theories. We consider the holographic embedding of this SymTFT, and observe that SymTFT's containing continuous symmetries are not always obtained as a near boundary limit of the supergravity action.