arXiv:2201.03404

Renyi entropy for monodromy defects of higher derivative free fields on even-dimensional spheres

J. S. Dowker

Published Jan 10, 2022• 0 citations

Abstract

Explicit polynomial forms for Rényi and entanglement entropies are given on even --dimensional spheres which possess a codimension--2 U(1) monodromy defect. Free scalar and Dirac fields are treated and higher-derivative propagation operators employed. The central charge, $C_T$, is also calculated. Comparison with existing results is made and it is shown how these can be obtained from the values here.

DOI: 10.48550/arxiv.2201.03404

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arXiv:2201.03404

Renyi entropy for monodromy defects of higher derivative free fields on even-dimensional spheres

J. S. Dowker

Published Jan 10, 2022• 0 citations

arXiv HTML PDF

Abstract

C_T

, is also calculated. Comparison with existing results is made and it is shown how these can be obtained from the values here.

DOI: 10.48550/arxiv.2201.03404

Related papers

Renyi entropy for spherical monodromy of free scalar fields in even dimensions

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The effect of a co--dimension--2 spherical monodromy defect on the free--field theory of a conformal scalar is investigated. The conformal anomaly is computed (in two ways) and thence the Rényi and entanglement entropies. The $C_T$ central charge is found to be negative for a range of monodromy flux.The calculations are pursued for any even dimensional sphere. A Possible conflict with existing results is raised.The effect of a co--dimension--2 spherical monodromy defect on the free--field theory of a conformal scalar is investigated. The conformal anomaly is computed (in two ways) and thence the Rényi and entanglement entropies. The $C_T$ central charge is found to be negative for a range of monodromy flux.The calculations are pursued for any even dimensional sphere. A Possible conflict with existing results is raised.

arXiv:2112.09031Dec 16, 20211 citation

Entanglement entropy and $C_T$ for monodromy defects of fields on odd-dimensional spheresEntanglement entropy and $C_T$ for monodromy defects of fields on odd-dimensional spheres

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The effect of a spherical monodromy defect on the entanglement entropy and central charge $C_T$ of a free conformal scalar field propagating on an odd-dimensional sphere is investigated. As on even spheres the central charge becomes negative for a range of the flux parameter, $δ$ , with possible implications for reflection positivity. The work is mostly numerical but closed forms are found for the $Z_2$ monodromy ( $δ=1/2$ ) yielding an explicit $d\to\infty$ limit, $C_T\to -6/π$ The effect of a spherical monodromy defect on the entanglement entropy and central charge $C_T$ of a free conformal scalar field propagating on an odd-dimensional sphere is investigated. As on even spheres the central charge becomes negative for a range of the flux parameter, $δ$, with possible implications for reflection positivity. The work is mostly numerical but closed forms are found for the $Z_2$ monodromy ($δ=1/2$) yielding an explicit $d\to\infty$ limit, $C_T\to -6/π$

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C_T

, is also calculated. Comparison with existing results is made and it is shown how these can be obtained from the values here.

C_T

central charge is found to be negative for a range of monodromy flux.The calculations are pursued for any even dimensional sphere. A Possible conflict with existing results is raised.

Entanglement entropy and

C_T

for monodromy defects of fields on odd-dimensional spheres

The effect of a spherical monodromy defect on the entanglement entropy and central charge

C_T

of a free conformal scalar field propagating on an odd-dimensional sphere is investigated. As on even spheres the central charge becomes negative for a range of the flux parameter,

δ

, with possible implications for reflection positivity. The work is mostly numerical but closed forms are found for the

Z_2

monodromy (

δ=1/2

) yielding an explicit

d\to\infty

limit,

C_T\to -6/π

\mathcal{N}

N = 2 hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free d = 4 Maxwell theory and show that their central charges vanish.

Renyi entropy and central charge,

C_T

, are calculated for a coexact p--form on an even sphere with particular reference to the conformally invariant case. It is shown, for example, that the entanglement entropy is minus the standard conformal anomaly with no `shift' being required. The shift necessary for a conformal p--form, when using a hyperbolic technique, is predicted, on a numerical basis, to be (minus) the entanglement entropy of a conformal (p-1)-form. The central charges agree numerically with a general formula of Buchel {\it et al}.