Topological Manipulations On $\mathbb{R}$ Symmetries Of Abelian Gauge Theory

Abstract

Performing topological manipulations is a fruitful way to understand global aspects of Quantum Field Theory (QFT). Such modifications are typically controlled by the notion of Topological QFT (TQFT) coupling across different codimensions. Motivated by the recent developments involving non-compact TQFTs as the Symmetry Topological Field Theory (SymTFT) for continuous symmetries, we realize topological manipulations on global $\mathbb{R}$ symmetries via TQFT coupling in the simple context of non-compact abelian gauge theory. Namely, by inserting the background fields for $\mathbb{R}$ symmetries into non-compact TQFTs on spacetime, we study the topological gaugings. Furthermore, we explore topological defects in non-compact theories by employing the said manipulations on the half-space, which are analogous to duality defects in compact gauge theories. We examine the action of these defects on the local and extended operators, and discuss their algebra. As opposed to the duality defects, our defects act invertibly on the spectrum. To further understand their role, we discuss the way they mix with other topological defects and the resulting global symmetries. We also comment on possible applications of these ideas to the bosonic String Theory. After studying defects, we provide a detailed inspection of manipulations on ${\mathbb{R}}^{(-1)}$ and ${\mathbb{R}}^{(d-1)}$ symmetries in abelian gauge theory. Notably, we develop a novel deformation tailored for flat gauging subgroups of ${\mathbb{R}}^{(d-1)}$ symmetries, and provide an extension of it for ${\mathbb{R}}^{(p)}$ symmetries. We show that this new simple deformation captures all the topological boundary conditions of the corresponding non-compact SymTFTs as the deformation parameter is varied, which the ordinary non-compact BF coupling cannot do.

arXiv comment61 pages. v4: Matches published version

References in corpus (42)

• Generalized Global Symmetries
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Symmetries and Strings in Field Theory and Gravity
• Two Dimensional Gauge Theories Revisited
• Coupling a QFT to a TQFT and Duality
• Reading between the lines of four-dimensional gauge theories
• Theta, Time Reversal, and Temperature
• Generalized Symmetries in Condensed Matter
• On finite symmetries and their gauging in two dimensions
• On gauging finite subgroups
• 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
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
• AdS/CFT Correspondence And Topological Field Theory
• Topological defects for the free boson CFT
• Cluster decomposition, T-duality, and gerby CFT's
• GLSM's for gerbes (and other toric stacks)
• Non-Invertible Symmetries from Holography and Branes
• Quantum Field Theory of Nonabelian Strings and Vortices
• Modifying the Sum Over Topological Sectors and Constraints on Supergravity
• String compactifications on Calabi-Yau stacks
• Modified instanton sum in QCD and higher-groups
• Non-invertible 1-form symmetry and Casimir scaling in 2d Yang-Mills theory
• Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond $N$-ality
• Sums over topological sectors and quantization of Fayet-Iliopoulos parameters
• Anomalies of Non-Invertible Symmetries in (3+1)d
• Anomalies and gauging of U(1) symmetries
• Quantization of Fayet-Iliopoulos Parameters in Supergravity
• The Sum Over Topological Sectors and $\theta$ in the 2+1-Dimensional $\mathbb{C}{\mathbb{P}}^1$ $\sigma$-Model
• On the Holographic Dual of a Topological Symmetry Operator
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT
• The holography of non-invertible self-duality symmetries
• Holographic duals of symmetry broken phases
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Non-Invertible Symmetry in Calabi-Yau Conformal Field Theories
• Non-Invertible T-duality at Any Radius via Non-Compact SymTFT