Entanglement entropy of a Maxwell field on the sphere

CASINI, HORACIO; HUERTA, MARINA

PHYSICAL REVIEW D - PARTICLE AND FILDS

APS

Año: 2016

0556-2821

We compute the logarithmic coefficient of the entanglement entropy on asphere for a Maxwell field in d=4 dimensions. In spherical coordinates theproblem decomposes into one dimensional ones along the radial coordinate foreach angular momentum. We show the entanglement entropy of a Maxwell field isequivalent to the one of two identical massless scalars from which the mode ofl=0 has been removed. This shows the relation cMlog=2(cSlog−cSl=0log) between the logarithmic coefficient in theentropy for a Maxwell field cMlog, the one for a d=4 massless scalarcSlog, and the logarithmic coefficient cSl=0log for a d=2scalar with Dirichlet boundary condition at the origin. Using the acceptedvalues for these coefficients cSlog=−1/90 and cSl=0log=1/6we get cMlog=−16/45, which coincides with Dowker's calculation, but doesnot match the coefficient −3145 in the trace anomaly for a Maxwellfield. We have numerically evaluated these three numbers cMlog,cSlog and cSl=0log, verifying the relation, as well aschecked they coincide with the corresponding logarithmic term in mutualinformation of two concentric spheres.