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Branes and Non-Invertible Symmetries

Iñaki García Etxebarria

TL;DR

This work addresses non-invertible symmetries in 4d $ ext{N}=4$ SYM with gauge algebra $ rak{so}(4N)$ and various global structures by leveraging IIB holography on $ ext{AdS}_5 imes ext{RP}^5$ to identify brane realizations of symmetry generators. The authors show that the non-invertible operators arise from branes wrapping torsional cycles (e.g., D3 on $ ext{RP}^1$ and D5/NS5 on higher RP cycles) and that their fusion rules are captured by the worldvolume dynamics and Wess–Zumino couplings, which induce discrete $ ext{Z}_2$ TFTs on the brane worldvolumes. Twisted differential cohomology is employed to model flux backgrounds and to handle torsion, ensuring correct K-theory flux accounting and non-commutativity of electric/magnetic flux operators that underlie non-invertibility. The results provide a unified holographic origin for non-invertible symmetries across $ ext{Sc}(4N)$, $ ext{PO}(4N)$, and $ ext{Pin}^+(4N)$ theories, linking discrete gauging, brane dynamics, and TFT dressing in a concrete geometric framework.

Abstract

$\mathcal{N}=4$ supersymmetric Yang-Mills theories with algebra $\mathfrak{so}(4N)$ and appropriate choices of global structure can have non-invertible symmetries. We identify the branes holographically dual to the non-invertible symmetries, and derive the fusion rules for the symmetries from the worldvolume dynamics on the branes.

Branes and Non-Invertible Symmetries

TL;DR

This work addresses non-invertible symmetries in 4d SYM with gauge algebra and various global structures by leveraging IIB holography on to identify brane realizations of symmetry generators. The authors show that the non-invertible operators arise from branes wrapping torsional cycles (e.g., D3 on and D5/NS5 on higher RP cycles) and that their fusion rules are captured by the worldvolume dynamics and Wess–Zumino couplings, which induce discrete TFTs on the brane worldvolumes. Twisted differential cohomology is employed to model flux backgrounds and to handle torsion, ensuring correct K-theory flux accounting and non-commutativity of electric/magnetic flux operators that underlie non-invertibility. The results provide a unified holographic origin for non-invertible symmetries across , , and theories, linking discrete gauging, brane dynamics, and TFT dressing in a concrete geometric framework.

Abstract

supersymmetric Yang-Mills theories with algebra and appropriate choices of global structure can have non-invertible symmetries. We identify the branes holographically dual to the non-invertible symmetries, and derive the fusion rules for the symmetries from the worldvolume dynamics on the branes.
Paper Structure (6 sections, 42 equations)

This paper contains 6 sections, 42 equations.

Table of Contents

  1. Introduction
  2. 4d $\mathcal{N}=4$ $\mathfrak{spin}(4N)$ SYM and non-invertibles
  3. TQFT stacking from Wess-Zumino couplings
  4. Fluxes and twisted differential cohomology
  5. Non-invertibles in $Sc(4N)$ from D3 branes
  6. 4d $PO(4N)$ and $\mathrm{Pin}^+$ non-invertibles