Entanglement entropy of a Maxwell field on the sphere

CASINI, HORACIO; HUERTA, MARINA

PHYSICAL REVIEW D

AMER PHYSICAL SOC

Lugar: New York; Año: 2016

1550-7998

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 c^M_{log}=2(c^S_{log}-c^{S_{l=0}}_{log}) between the logarithmic coefficient in theentropy for a Maxwell field c^M_{log}, the one for a d=4 massless scalarc_{log}^S, and the logarithmic coefficient c^{S_{l=0}}_{log} for a d=2scalar with Dirichlet boundary condition at the origin. Using the acceptedvalues for these coefficients c_{log}^S=-1/90 and c^{S_{l=0}}_{log}=1/6we get c^M_{log}=-16/45, which coincides with Dowker´s calculation, but doesnot match the coefficient -rac{31}{45} in the trace anomaly for a Maxwellfield. We have numerically evaluated these three numbers c^M_{log},c^S_{log} and c^{S_{l=0}}_{log}, verifying the relation, as well aschecked they coincide with the corresponding logarithmic term in mutualinformation of two concentric spheres.