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Entanglement entropy of a Maxwell field on the sphere

Dec 18, 2015

11 pages

Published in:

Phys.Rev.D 93 (2016) 10, 105031

Published: May 20, 2016

e-Print:

1512.06182 [hep-th]

DOI:

10.1103/PhysRevD.93.105031

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Abstract: (APS)

We compute the logarithmic coefficient of the entanglement entropy on a sphere for a Maxwell field in d=3+1 dimensions. In spherical coordinates the problem decomposes into one-dimensional ones along the radial coordinate for each angular momentum. We show that the entanglement entropy of a Maxwell field is equivalent to one of two identical massless scalars from which the mode of l=0 has been removed. This shows the relation clogM=2(clogS-clogSl=0) between the logarithmic coefficient in the entropy for a Maxwell field clogM, the one for a d=3+1 massless scalar clogS, and the logarithmic coefficient clogSl=0 for a d=1+1 scalar with a Dirichlet boundary condition at the origin. Using the accepted values for these coefficients clogS=-1/90 and clogSl=0=1/6, we get clogM=-16/45, which coincides with Dowker’s calculation, but does not match the coefficient -3145 in the trace anomaly for a Maxwell field. We have numerically evaluated these three numbers clogM, clogS and clogSl=0, verifying the relation, as well as checked that they coincide with the corresponding logarithmic term in mutual information of two concentric spheres.

Note:

18 pages, 5 figures

entropy: entanglement
dimension: 1
sphere
boundary condition
angular momentum
trace anomaly

References(37)

Figures(5)

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