The holography of non-invertible self-duality symmetries

Abstract

We study how non-invertible self-duality defects arise in theories with a holographic dual. We focus on the paradigmatic example of $\mathfrak{su}(N)$ $\mathcal{N}=4$ SYM. The theory is known to have non-invertible duality and triality defects at $\tau =i$ and $\tau =e^{2\pi i/3}$, respectively. At these points in the gravitational moduli space, the gauged $SL(2,\mathbb{Z})$ duality symmetry of type IIB string theory is spontaneously broken to a finite subgroup $G$, giving rise to a discrete emergent $G$ gauge field. After reduction on the internal manifold, the low-energy physics is dominated by an interesting 5d Chern-Simons theory, further gauged by $G$, that we analyze and which gives rise to the self-duality defects in the boundary theory. Using the five-dimensional bulk theory, we compute the fusion rules of those defects in detail. The methods presented here are general and may be used to investigate such symmetries in other theories with a gravity dual.

56 pages plus appendices

References in corpus (31)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• Duality and defects in rational conformal field theory
• Kramers-Wannier-like duality defects in (3+1)d gauge theories
• Non-Invertible Duality Defects in 3+1 Dimensions
• Symmetries and Strings of Adjoint QCD${}_2$
• Higher Gauging and Non-invertible Condensation Defects
• Orbifold groupoids
• Topological boundary conditions in abelian Chern-Simons theory
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Non-Invertible Higher-Categorical Symmetries
• Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
• Universal Non-Invertible Symmetries
• Asymptotic density of states in 2d CFTs with non-invertible symmetries
• Non-Invertible Symmetries from Holography and Branes
• Non-Invertible Symmetries of $\mathcal{N}=4$ SYM and Twisted Compactification
• The Branes Behind Generalized Symmetry Operators
• Construction of two-dimensional topological field theories with non-invertible symmetries
• Non-invertible Time-reversal Symmetry
• Branes and Non-Invertible Symmetries
• Exploring Non-Invertible Symmetries in Free Theories
• On Continuous 2-Category Symmetries and Yang-Mills Theory
• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond $N$-ality
• Non-invertible Symmetries and Higher Representation Theory I
• Non-Invertible Defects in 5d, Boundaries and Holography
• Decomposition, condensation defects, and fusion
• Symmetry TFTs for 3d QFTs from M-theory
• Non-Invertible Symmetries from Discrete Gauging and Completeness of the Spectrum
• The holography of duality in $\mathcal{N}=4$ Super-Yang-Mills theory
• Fermionization of fusion category symmetries in 1+1 dimensions

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