P. Dominis Prester

Gravitational Chern-Simons Lagrangians and black hole entropy

We analyze the problem of defining the black hole entropy when Chern-Simons terms are present in the action. Extending previous works, we define a general procedure, valid in any dimensions both for purely gravitational CS terms and for mixed gauge-gravitational ones. The final formula is very similar to Wald’s original formula valid for covariant actions, with a significant modification. Notwithstanding an apparent violation of covariance we argue that the entropy formula is indeed covariant.

Gravitational Chern?Simons Lagrangian terms and spherically symmetric spacetimes

We show that for general spherically symmetric configurations, contributions of broad class of gravitational and mixed gauge-gravitational Chern–Simons (CS) terms to the equations of motion vanish identically in D > 3 dimensions. This implies that such terms in the action do not affect Birkhoffs theorem or any previously known spherically symmetric solutions. Furthermore, we investigate the thermodynamical properties using the procedure described in an accompanying paper. We find that in the D > 3 static spherically symmetric case, CS terms do not contribute to the entropy either. Moreover, if one requires only for the metric tensor to be spherically symmetric, letting other fields be unrestricted, the results extend almost completely, with only one possible exception—CS Lagrangian terms in which the gravitational part is just the n = 2 irreducible gravitational CS term.

Stationary rotating black holes in theories with gravitational Chern-Simons Lagrangian term

We study the effects of introducing purely gravitational Chern-Simons Lagrangian terms in ordinary Einstein gravity on stationary rotating black hole solutions and on the associated thermodynamical properties, in a generic number of dimensions which support these terms (i.e. in D = 4k − 1). We analyze the conditions, namely the number of vanishing angular momenta, under which the contributions of the Chern-Simons term to the equations of motion and the black hole entropy vanish. The particular case of a 7-dimensional theory in which a purely gravitational Chern-Simons term is added to the EinsteinHilbert Lagrangian in D = 7 dimensions is investigated in some detail. As we have not been able to find exact analytic solutions in nontrivial cases, we turn to perturbation theory and calculate the first-order perturbative correction to the Myers-Perry metric in the case where all angular momenta are equal. The expansion parameter is a dimensionless combination linear in the Chern-Simons coupling constant and the angular momentum. Corrections to horizon and ergosurface properties, as well as black hole entropy and temperature, are presented.

Symmetries and gravitational Chern-Simons Lagrangian terms

Abstract We consider some general consequences of adding pure gravitational Chern–Simons term to manifestly diff-covariant theories of gravity, focusing essentially on spacetimes with D > 3 . Extending the result of a previous paper we enlarge the class of metrics for which the inclusion of a gravitational Chern–Simons term in the action does not affect solutions and corresponding physical quantities. In the case in which such solutions describe black holes (of general horizon topology) we show that the black hole entropy is also unchanged. We arrive at these conclusions by proving three general theorems and studying their consequences. One of the theorems states that the contribution of the gravitational Chern–Simons to the black hole entropy is invariant under local rescaling of the metric.

Gravitational Chern-Simons terms and black hole entropy. Global aspects

A bstractWe discuss the topological and global gauge properties of the formula for a black hole entropy due to a purely gravitational Chern-Simons term. We study under what topological and geometrical conditions this formula is well-defined. To this end we have to analyze the global properties of the Chern-Simons term itself and the quantization of its coupling. We show that in some cases the coupling quantization may interfere with the well-definiteness of the entropy formula.

Axial gravity, massless fermions and trace anomalies

This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms and using dimensional regularization, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones.

Worldline quantization of field theory, effective actions and L∞ structure

A bstractWe formulate the worldline quantization (a.k.a. deformation quantization) of a massive fermion model coupled to external higher spin sources. We use the relations obtained in this way to show that its regularized effective action is endowed with an L∞ symmetry. The same result holds also for a massive scalar model.

Axial gravity: a non-perturbative approach to split anomalies

In a theory of a Dirac fermion field coupled to a metric-axial-tensor (MAT) background, using a Schwinger-DeWitt heat kernel technique, we compute non-perturbatively the two (odd parity) trace anomalies. A suitable collapsing limit of this model corresponds to a theory of chiral fermions coupled to (ordinary) gravity. Taking this limit on the two computed trace anomalies we verify that they tend to the same expression, which coincides with the already found odd parity trace anomaly, with the identical coefficient. This confirms our previous results on this issue.

Massive Dirac field in 3D and induced equations for higher spin fields

On the example of the free massive Dirac in flat three-dimensional spacetime, we show how the linearised equations of motion for higher spin fields can be obtained from the induced action by coupling higher spin fields to conserved currents. The result is important because a classical analysis leads to many different formulations of free higher spin equations, and not all of them are expected to be a good starting point for introduction of interactions. Our result breaks the degeneracy. We express the results by using a metric-like description for higher spin fields, in which the equations of motion can be elegantly written in generic form that is valid for all spins.

Higher Spins from One-Loop Effective Actions

In this contribution we review the method to obtain information about the classical dynamics of a higher spin field by minimally coupling the field via a conserved current to a simple free fermion, and by integrating out the latter. We consider here the two point correlators of two conserved currents, which allow us to determine the effective action to quadratic order. We show that this gives rise to the classical equation of motion of the Fronsdal type. We point out the importance of the contributions of the tadpole and seagull terms and the ambiguity related to the choice of the conserved currents.