arXiv subjects

Yuta Nagoya

Publications and source records attributed to Yuta Nagoya.

5 recordsLinked to original sources

arXiv2024

Non-invertible duality defect and non-commutative fusion algebra

We study non-invertible duality symmetries by gauging a diagonal subgroup of a non-anomalous U(1) $\times$ U(1) global symmetry. In particular, we employ the half-space gauging to $c=2$ bosonic torus conformal field theory (CFT) in two dimensions and pure U(1) $\times$ U(1) gauge theory in four dimensions. In $c=2$ bosonic torus CFT, we show that the non-invertible symmetry obtained from the diagonal gauging becomes emergent on an irrational CFT point. We also calculate the fusion rules concerning the duality defect. We find out that the fusion algebra is non-commutative. We also obtain a similar result in pure U(1) $\times$ U(1) gauge theory in four dimensions.

hep-th↗

arXiv2024

Higher-group structure in lattice Abelian gauge theory under instanton-sum modification

We consider the $U(1)$ gauge theory on a four-dimensional torus, where the instanton number is restricted to an integral multiple of $p$. This theory possesses the nontrivial higher-group structure, which can be regarded as a generalization of the Green--Schwarz mechanism, between $\mathbb{Z}_q$ $1$-form and $\mathbb{Z}_{pq}$ $3$-form symmetries. Here, $\mathbb{Z}_q$ is a subgroup of the center of~$U(1)$. Following the recent study of the lattice construction of the $U(1)/\mathbb{Z}_q$ principal bundle, we examine how such a structure is realized on the basis of lattice regularization.

hep-th↗

arXiv2023

Higher-group symmetry in lattice gauge theories with restricted topological sectors

In this paper, we give a brief overview of generalized symmetries from the point of view of the lattice regularization as a fully regularized framework. At first, we illustrate the generalization of 't~Hooft anomaly matching for higher-form symmetries. Furthermore the main interest goes to the higher-group symmetry. In particular, we find that the so-called $4$-group appears in the lattice Yang--Mills theory under modification of instanton sum.

hep-lat↗

arXiv2023

Non-invertible symmetries and boundaries in four dimensions

We study quantum field theories with boundary by utilizing non-invertible symmetries. We consider three kinds of boundary conditions of the four dimensional $\mathbb{Z}_2$ lattice gauge theory at the critical point as examples. The weights of the elements on the boundary is determined so that these boundary conditions are related by the Kramers-Wannier-Wegner (KWW) duality. In other words, it is required that the KWW duality defects ending on the boundary is topological. Moreover, we obtain the ratios of the hemisphere partition functions with these boundary conditions; this result constrains the boundary renormalization group flows under the assumption of the conjectured g-theorem in four dimensions.

hep-th↗

arXiv2021

Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

We explore topological defects in the 4-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. This theory has 1-form $\mathbb{Z}_{2}$ center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We construct the KWW duality topological defects in the similar way to that constructed by Aasen, Mong, Fendley arXiv:1601.07185 for the 2-dimensional Ising model. These duality defects turn out to be non-invertible. We also construct the 1-form $\mathbb{Z}_{2}$ symmetry defects as well as the junctions among KWW duality defects and 1-form $\mathbb{Z}_{2}$ center symmetry defects. The crossing relations among these defects are derived. The expectation values of some configurations of these topological defects are calculated by using these crossing relations.

hep-th↗