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Conformal perturbation theory and higher spin entanglement entropy on the torus

Datta, Shouvik and David, Justin R and Kumar, Prem S (2015) Conformal perturbation theory and higher spin entanglement entropy on the torus. In: JOURNAL OF HIGH ENERGY PHYSICS (4).

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Official URL: http://dx.doi.org/10.1007/JHEP04(2015)041


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 hs0] 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.

Item Type: Journal Article
Publisher: SPRINGER
Additional Information: Copy right for this article belongs to the SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 USA
Keywords: Field Theories in Lower Dimensions; AdS-CFT Correspondence; Conformal and W Symmetry
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 31 Jul 2015 06:09
Last Modified: 31 Jul 2015 06:09
URI: http://eprints.iisc.ac.in/id/eprint/51929

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