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Conformal perturbation theory and higher spin entanglement entropy on the torus

Shouvik Datta, Justin R. David, Prem Kumar Orcid Logo

Journal of High Energy Physics, Volume: 2015, Issue: 4

Swansea University Author: Prem Kumar Orcid Logo

DOI (Published version): 10.1007/JHEP04(2015)041

Abstract

We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential \mu, the deformation is related at high temperatures to a higher spin black hole in hs[0] theory o...

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Published in: Journal of High Energy Physics
Published: 2015
URI: https://cronfa.swan.ac.uk/Record/cronfa19791
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spelling 2020-07-16T14:30:10.3144431 v2 19791 2014-12-18 Conformal perturbation theory and higher spin entanglement entropy on the torus 087fd097167d724ce1b13cb285741ef5 0000-0003-0867-4213 Prem Kumar Prem Kumar true false 2014-12-18 SPH We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential \mu, the deformation is related at high temperatures to a higher spin black hole in hs[0] theory on AdS_3 spacetime. We calculate the order \mu^2 corrections to the single interval Renyi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order \mu^2 corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Renyi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Renyi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large-N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems. Journal Article Journal of High Energy Physics 2015 4 9 4 2015 2015-04-09 10.1007/JHEP04(2015)041 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2020-07-16T14:30:10.3144431 2014-12-18T15:00:27.6191732 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Shouvik Datta 1 Justin R. David 2 Prem Kumar 0000-0003-0867-4213 3 0019791-27042015193836.pdf JHEP04(2015)041.pdf 2015-04-27T19:38:36.2630000 Output 953031 application/pdf Version of Record true 2015-03-17T00:00:00.0000000 true
title Conformal perturbation theory and higher spin entanglement entropy on the torus
spellingShingle Conformal perturbation theory and higher spin entanglement entropy on the torus
Prem Kumar
title_short Conformal perturbation theory and higher spin entanglement entropy on the torus
title_full Conformal perturbation theory and higher spin entanglement entropy on the torus
title_fullStr Conformal perturbation theory and higher spin entanglement entropy on the torus
title_full_unstemmed Conformal perturbation theory and higher spin entanglement entropy on the torus
title_sort Conformal perturbation theory and higher spin entanglement entropy on the torus
author_id_str_mv 087fd097167d724ce1b13cb285741ef5
author_id_fullname_str_mv 087fd097167d724ce1b13cb285741ef5_***_Prem Kumar
author Prem Kumar
author2 Shouvik Datta
Justin R. David
Prem Kumar
format Journal article
container_title Journal of High Energy Physics
container_volume 2015
container_issue 4
publishDate 2015
institution Swansea University
doi_str_mv 10.1007/JHEP04(2015)041
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str 1
active_str 0
description We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential \mu, the deformation is related at high temperatures to a higher spin black hole in hs[0] theory on AdS_3 spacetime. We calculate the order \mu^2 corrections to the single interval Renyi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order \mu^2 corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Renyi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Renyi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large-N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems.
published_date 2015-04-09T03:23:18Z
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score 11.037056

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