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arXiv:2604.09126

Lattice Realizations of Flat Gauging and T-duality Defects at Any Radius

Riccardo Argurio, Giovanni Galati, Nathan Godechal

Published Apr 10, 2026• 0 citations
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Abstract

We analyze non-invertible topological interfaces and defects in the two-dimensional compact boson, focusing on the more exotic ones obtained by gauging continuous symmetries with flat connections on a half-space. These include interfaces between mutually irrational radii and T-duality symmetries at arbitrary boson radius. Using the modified Villain discretization on both a Euclidean two-dimensional square lattice and a quantum one-dimensional chain, we show that all these topological interfaces survive discretization and give rise to non-compact edge modes localized at the defect sites. Such non-compact edge modes imply a continuous defect spectrum and an infinite quantum dimension. In the special case of rational radii, we show how the defect action or Hamiltonian can be modified in order to compactify the edge modes and produce more standard defects with finite quantum dimension.

DOI
10.48550/arxiv.2604.09126

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Global symmetries can be generalised to transformations generated by topological operators, including cases in which the topological operator does not have an inverse. A family of such topological operators are intimately related to dualities via the procedure of half-space gauging. In this work we discuss the construction of non-invertible defects based on T-duality in two dimensions, generalising the well-known case of the free compact boson to any Non-Linear Sigma Model with Wess-Zumino term which is T-dualisable. This requires that the target space has an isometry with compact orbits that acts without fixed points. Our approach allows us to include target spaces without non-trivial 1-cycles, does not require the NLSM to be conformal, and when it is conformal it does not need to be rational; moreover, it highlights the microscopic origin of the topological terms that are responsible for the non-invertibility of the defect. An interesting class of examples are Wess-Zumino-Witten models, which are self-dual under a discrete gauging of a subgroup of the isometry symmetry and so host a topological defect line with Tambara-Yamagami fusion. Along the way, we discuss how the usual 0-form symmetries match across T-dual models in target spaces without 1-cycles, and how global obstructions can prevent locally conserved currents from giving rise to topological operators.
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Two different conformal field theories can be joined together along a defect line. We study such defects for the case where the conformal field theories on either side are single free bosons compactified on a circle. We concentrate on topological defects for which the left- and right-moving Virasoro algebras are separately preserved, but not necessarily any additional symmetries. For the case where both radii are rational multiples of the self-dual radius we classify these topological defects. We also show that the isomorphism between two T-dual free boson conformal field theories can be described by the action of a topological defect, and hence that T-duality can be understood as a special type of order-disorder duality.
We study gauging interfaces and their defect descendants in lattice models with generalized symmetries in higher dimensions. We construct explicit interface Hamiltonians for gauging a Z2(0)\mathbb Z_2^{(0)}Z2(0)​ symmetry in (2+1)d(2+1)d(2+1)d and a Z2(1)\mathbb Z_2^{(1)}Z2(1)​ symmetry in (3+1)d(3+1)d(3+1)d. In higher dimensions, and especially in the presence of higher-form symmetries, the topological nature of gauging interfaces is obscured by the fact that the constrained Hilbert space depends on the location of the interface. We resolve this by introducing movement operators acting on a common unconstrained Hilbert space, which transport both the interface Hamiltonians and the associated constraints. As applications, we analyze condensation defects obtained from finite-region gauging and reconstruct the gauging map from movement operators. Finally, we apply the same framework to subgroup gauging, focusing on the example of gauging Z2⊂Z4\mathbb Z_2\subset \mathbb Z_4Z2​⊂Z4​. This produces a dual symmetry carrying a mixed anomaly, which we diagnose on the lattice through symmetry fractionalization on condensation defects. Our results provide an explicit lattice framework for studying topological interfaces, condensation defects, and the associated anomalies arising from gauging in higher-dimensional systems.
We introduce half dualization as a general principle to construct non-invertible duality defects. The construction performs a duality transformation only in a subregion of spacetime, leaving an interface between the original theory and its dual. A non-invertible duality defect can be hosted on this interface. Half dualization is applicable whenever a local duality transformation is available, and does not depend on the spacetime dimension. We demonstrate the construction procedure in the (2+1)-dimensional Villainized charge-nnn XY model on a cubic lattice. Half dualization yields a non-invertible particle-vortex duality defect whose fusion with its orientation reverse produces a (1+1)-dimensional Zn\mathbb{Z}_nZn​ gauge theory on the fusion surface. We then apply half dualization to the Zn\mathbb{Z}_nZn​-gauged XY model relevant to the 3D XY∗^\ast∗ transition. In the gauged model, the half dualization interface hosts a gauge covariant duality wall, rather than a genuine gauge invariant duality defect. It flows to an invertible duality defect in infrared when the Zn\mathbb{Z}_nZn​ gauge theory is confined or Higgsed.