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Non-Invertible Symmetries from Holography and Branes

Fabio Apruzzi, Ibrahima Bah, Federico Bonetti, Sakura Schafer-Nameki

Abstract

We propose a systematic approach to deriving symmetry generators of Quantum Field Theories in holography. Central to this are the Gauss law constraints in the Hamiltonian quantization of Symmetry Topological Field Theories (SymTFTs), which are obtained from supergravity. In turn we realize the symmetry generators from world-volume theories of D-branes in holography. Our main focus is on non-invertible symmetries, which have emerged in the past year as a new type of symmetry in $d\geq 4$ QFTs. We exemplify our proposal in the holographic confinement setup, dual to 4d $\mathcal{N}=1$ Super-Yang Mills. In the brane-picture, the fusion of non-invertible symmetries naturally arises from the Myers effect on D-branes. In turn, their action on line defects is modeled by the Hanany-Witten effect.

Non-Invertible Symmetries from Holography and Branes

Abstract

We propose a systematic approach to deriving symmetry generators of Quantum Field Theories in holography. Central to this are the Gauss law constraints in the Hamiltonian quantization of Symmetry Topological Field Theories (SymTFTs), which are obtained from supergravity. In turn we realize the symmetry generators from world-volume theories of D-branes in holography. Our main focus is on non-invertible symmetries, which have emerged in the past year as a new type of symmetry in QFTs. We exemplify our proposal in the holographic confinement setup, dual to 4d Super-Yang Mills. In the brane-picture, the fusion of non-invertible symmetries naturally arises from the Myers effect on D-branes. In turn, their action on line defects is modeled by the Hanany-Witten effect.
Paper Structure (7 sections, 50 equations, 1 figure)

This paper contains 7 sections, 50 equations, 1 figure.

Table of Contents

  1. Supergravity Analysis and (Non-Invertible) Symmetry Generators
  2. Bulk topological couplings from anomaly inflow and consistent truncation.
  3. Dualization of $c_0$.
  4. Canonical momenta and Gauss constraints.
  5. Symmetry Generators from Gauss law constraints.
  6. D5-brane action and reduction
  7. Review of Myers Effect and Application to D5-branes on $S^3$

Figures (1)

  • Figure 1: Top: Hanany-Witten transition, where the $(x_0, x_3)$-plane is displayed to show the equivalence with the field theory transition. Bottom: 't Hooft loop passing through the non-invertible defect $\mathcal{N}_3^{(1)}$ becomes attached to a topological surface operator.