Abstract
Abstract 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.
Highlights
The situation with the entanglement entropy is quite the opposite
We 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
Summary
Where 0 is the covariant Laplace operator acting on scalars (0-form), 0 = ∇α∇α Where in the first line the operators are acting on scalars while in the second they are acting on vectors and the Ricci tensor is viewed as a matrix operator These properties indicate that the determinant of the operator ∆a, defined as product of its non-zero eigen values, reduces to a product of two determinants det ∆a = det ∆T det(a∆L). This representation should be used in (2.8) when we compute the partition function of the Maxwell field
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