Homotopy data as part of the lattice field: A first study

Pietro Dall’Olio and José A. Zapata ()
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Pietro Dall’Olio: Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México
José A. Zapata: Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México

International Journal of Modern Physics C (IJMPC), 2022, vol. 33, issue 05, 1-29

Abstract: Fields exhibit a variety of topological properties, like different topological charges, when field space in the continuum is composed by more than one topological sector. Lattice treatments usually encounter difficulties describing those properties. In this work, we show that by augmenting the usual lattice fields to include extra variables describing local topological information (more precisely, regarding homotopy), the topology of the space of fields in the continuum is faithfully reproduced in the lattice. We apply this extended lattice formulation to some simple models with nontrivial topological charges, and we study their properties both analytically and via Monte Carlo simulations.

Keywords: Topological susceptibility; Lattice gauge theory; Sigma models (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0129183122500681

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