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arXiv · 2109.12097

Study of a lattice 2-group gauge model

Arkadiusz Bochniak·Leszek Hadasz·Piotr Korcyl·Błażej Ruba
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Abstract

Gauge theories admit a generalisation in which the gauge group is replaced by a finer algebraic structure, known as a 2-group. The first model of this type is a Topological Quantum Field Theory introduced by Yetter. We discuss a common generalisation of both the Yetter's model and Yang-Mills theory and in particular we focus on the lattice formulation of such model for finite 2-groups. In the second part we present a particular realization based on a 2-group constructed from $\mathbb Z_4$ groups. In the selected model, independent degrees of freedom are associated to both links and faces of a four-dimensional lattice and are subject to a certain constraint. We present the details of this construction, discuss the expected dynamics in different regions of phase space and show numerical results from Monte Carlo simulations corroborating these expectations.

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Arkadiusz Bochniak, Leszek Hadasz, Piotr Korcyl, Błażej Ruba. 2021-09-24. Study of a lattice 2-group gauge model. https://arxiv.org/abs/2109.12097

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