U(1) lattice gauge theory with a topological action

Akerlund, Oscar; Forcrand, Philippe de

doi:10.1007/jhep06(2015)183

Cited by 15 publications

(14 citation statements)

References 18 publications

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“…The fact that Poisson summation interchanges these energy levels with the correctly identified topological sectors was observed in Ref. [56] in a version of the O(2) model where the fluctuations are limited. Note also that it is possible to construct models where the approximations Eqs.…”

Section: Topological Solutions and Semiclassical Approximationsmentioning

confidence: 59%

Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories

Meurice

2020

Phys. Rev. D

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We show that standard identities and theorems for lattice models with Uð1Þ symmetry get reexpressed discretely in the tensorial formulation of these models. We also explain the geometrical analogy between the continuous lattice equations of motion and the discrete selection rules of the tensors. We further construct a gauge-invariant transfer matrix in arbitrary dimensions, show the equivalence with its gaugefixed version in a maximal temporal gauge, and explain how a discrete Gauss's law is always enforced. Moreover, we propose a noise-robust way to implement Gauss's law in arbitrary dimensions, and we reformulate Noether's theorem for global, local, continuous, or discrete Abelian symmetries: for each given symmetry, there is one corresponding tensor redundancy. We discuss semiclassical approximations for classical solutions with periodic boundary conditions in two solvable cases, and we show the correspondence of their weak coupling limit with the tensor formulation after Poisson summation. Finally, we briefly discuss connections with other approaches and implications for quantum computing.

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Section: Topological Solutions and Semiclassical Approximationsmentioning

confidence: 59%

Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories

Meurice

2020

Phys. Rev. D

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“…The gauge action (4) and improved versions of it [2] are presumably the most well known and most used ones in Monte Carlo studies of SU(𝑁) lattice gauge theories. They are, however, not unique and might not be the best choice for the study of lattice gauge theories at strong coupling, as they allow the gauge system to enter a so-called "bulk-phase".…”

Section: Intorductionmentioning

confidence: 99%

Bulk-preventing actions for SU(N) gauge theories

Rindlisbacher,

Rummukainen,

Salami

2021

Preprint

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“…where S[U p ] is any action which is a sum over the individual plaquettes, for example the Wilson action S[U P ] = β P (1 − ReTrU P ), or a topological action [5,6] where the action is constant but the traces of the plaquette variables are limited to a compact region around the identity. The difference to the mean plaquette method is that it is not assumed that the external plaquettes take some average value, but rather that they are distributed according to a mean distribution.…”

Section: B Mean Distribution Theorymentioning

confidence: 99%