Non-Invertible Symmetries, Brane Dynamics, and Tachyon Condensation

TL;DR

This paper explores the relationship between non-invertible symmetries, brane dynamics, and tachyon condensation in holography, revealing how symmetry operators are derived from brane configurations and their fusion algebra.

Contribution

It provides a detailed analysis of symmetry operators in 4d $ ext{SU}(M)$ Super Yang-Mills, linking them to brane dynamics and tachyon condensation, a novel connection in holographic symmetry studies.

Findings

Symmetry operators are determined by brane center-of-mass modes.

Fusion algebra corresponds to brane relative motion.

Condensation defects originate from tachyon condensation in brane-anti-brane pairs.

Abstract

We study the Symmetry Topological Field Theory in holography associated with 4d $\mathcal{N}=1$ Super Yang-Mills theory with gauge algebra $\mathfrak{su}(M)$. 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.