We analyze the dependence of the effective action and the entanglement entropy in the Maxwell theory on the gauge fixing parameter a in d dimensions. For a generic value of a the corresponding vector operator is nonminimal. The operator can be diagonalized in terms of the transverse and longitudinal modes. Using this factorization we obtain an expression for the heat kernel coefficients of the nonminimal operator in terms of the coefficients of two minimal Beltrami-Laplace operators acting on 0- and 1-forms. This expression agrees with an earlier result by Gilkey et al. Working in a regularization scheme with the dimensionful UV regulators we introduce three different regulators: for transverse, longitudinal and ghost modes, respectively. We then show that the effective action and the entanglement entropy do not depend on the gauge fixing parameter a provided the certain (a-dependent) relations are imposed on the regulators. Comparing the entanglement entropy with the black hole entropy expressed in terms of the induced Newton’s constant we conclude that their difference, the so-called Kabat’s contact term, does not depend on the gauge fixing parameter a. We consider this as an indication of gauge invariance of the contact term.
A. Barvinsky and G. Vilkovisky, The generalized Schwinger-Dewitt technique in gauge theories and quantum gravity, Phys. Rept. 119 (1985) 1 [INSPIRE].
D. Nesterov and S.N. Solodukhin, Gravitational effective action and entanglement entropy in UV modified theories with and without Lorentz symmetry, Nucl. Phys. B 842 (2011) 141 [arXiv:1007.1246] [INSPIRE].
A. Barvinsky, private communication.
P.P. Gilkey, T.P. Branson and S.A. Fulling, Heat equation asymptotics of “nonminimal” operators on differential forms, J. Math. Phys. 32 (1991) 2089.
R. Endo, Gauge dependence of the gravitational conformal anomaly for the electromagnetic field, Prog. Theor. Phys. 71 (1984) 1366 [INSPIRE].
ArXiv ePrint: 1209.2677
About this article
Cite this article
Solodukhin, S.N. Remarks on effective action and entanglement entropy of Maxwell field in generic gauge. J. High Energ. Phys. 2012, 36 (2012). https://doi.org/10.1007/JHEP12(2012)036
- Black Holes
- Renormalization Regularization and Renormalons