Newton constant, contact terms and entropy

We discuss the renormalization of the Newton constant due to fields of various spin $s$. We first briefly review the cases of $s=0, \, 1/2, \, 1,\, 3/2$ already discussed in the literature and notice the appearance of the well-known contact terms for the vector bosons. We then extend this discussion of the contact terms to massive vector fields, $p$-forms and to the case of spin $s=2$ particles (gravitons). We observe that, in general, the contact terms originate from the fields which mediate the interactions (such as vector gauge bosons and gravitons). We then discuss entanglement entropy and the conical entropy and their relation to the renormalized Newton constant. We address the puzzle of the non-analytic terms due to fields of spin $s=2$ and suggest that the resolution of this puzzle comes from the non-equivalence of the orbifold and $n$-fold cover constructions which are used in the entropy calculations. Finally, we propose a mechanism by which the Bekenstein-Hawking entropy is identified with entanglement entropy in any theory which includes both matter fields and the mediators of interactions (vector gauge bosons and gravitons).Comment: 31 pages; new ref. adde

Conformal a-charge, correlation functions and conical defects

In this note we demonstrate that, as we conjectured earlier in [1], the a-charge in the conformal anomaly in dimension $d=2n$ manifests in a $n$-point correlation function of energy momentum tensor of a CFT considered in flat spacetime with a conical defect. We consider in detail dimensions $d=2,\, 4,\, 6$ and give a general formula for arbitrary $n$.Comment: 10 pages; v2: new references added + several remarks on absence of contribution from anomaly of type B adde

How to make the gravitational action on non-compact space finite

The recently proposed technique to regularize the divergences of the gravitational action on non-compact space by adding boundary counterterms is studied. We propose prescription for constructing the boundary counterterms which are polynomial in the boundary curvature. This prescription is efficient for both asymptotically Anti-de Sitter and asymptotically flat spaces. Being mostly interested in the asymptotically flat case we demonstrate how our procedure works for known examples of non-compact spaces: Eguchi-Hanson metric, Kerr-Newman metric, Taub-NUT and Taub-bolt metrics and others. Analyzing the regularization procedure when boundary is not round sphere we observe that our counterterm helps to cancel large $r$ divergence of the action in the zero and first orders in small deviations of the geometry of the boundary from that of the round sphere. In order to cancel the divergence in the second order in deviations a new quadratic in boundary curvature counterterm is introduced. We argue that cancelation of the divergence for finite deviations possibly requires infinite series of (higher order in the boundary curvature) boundary counterterms.Comment: 27 pages, latex, no figure

Metric Redefinition and UV Divergences in Quantum Einstein Gravity

I formulate several statements demonstrating that the local metric redefinition can be used to reduce the UV divergences present in the quantum action for the Einstein gravity in $d=4$ dimensions. In its most general form, the proposal is that any UV divergences in the quantum action can be removed by an appropriate field re-definition and a renormalization of cosmological constant.Comment: 10 pages; v2: minor typos corrected; v3a: more remarks + discussion of S-matrix + 1 new reference added, v3b: more references added, version to appear in PL

Entanglement entropy of round spheres

We propose that the logarithmic term in the entanglement entropy computed in a conformal field theory for a $(d-2)$-dimensional round sphere in Minkowski spacetime is identical to the logarithmic term in the entanglement entropy of extreme black hole. The near-horizon geometry of the latter is $H_2\times S_{d-2}$. For a scalar field this proposal is checked by direct calculation. We comment on relation of this and earlier calculations to the ``brick wall'' model of 't Hooft. The case of generic 4d conformal field theory is discussed.Comment: 11 pages, no figures, minor modificatio

Supersymmetric Topological Quantum Field Theories Of Differential Forms I. Gauge p-forms

We consider the topological theory of Witten type for gauge differential p-forms. It is shown that some topological invariants such as linking numbers appear under quantization of this theory. The non-abelian generalization of the model is discussed.Comment: 12 pages, Late