Silvio Pallua

We analyse the parity-odd ("type P") surface anomalies of the energy-momentum tensor correlators in conformal field theories, with an emphasis on d=4 and d=3 dimensional spacetimes. Using cohomology analysis we construct the expression for the most general P-type surface trace anomaly on a singular 2-dimensional surface in 4-dimensional bulk spacetimes. As an important example, we specialise to the case when the singular surface is a conical defect and show that the bulk P-type Pontryagin trace anomaly induces such a surface trace anomaly. We show that this conical type P surface trace anomaly is given purely by the outer curvature tensor. In addition, we analyse parity-odd surface contact terms in energy-momentum tensor correlators in the flat spacetime induced by the conical defect by studying two special cases in which the contact terms are induced by, (1) type P trace anomaly in d=4 and, (2) gravitational Chern-Simons Lagrangian term in d=3 spacetime dimensions. In both cases we show that the surface contact terms appear in correlators of the lower rank than the corresponding bulk surface terms.

We consider some general consequences of adding pure gravitational Chern-Simons term to manifestly diff-covariant theories of gravity. Extending the result of a previous paper we enlarge the class of metrics for which the inclusion of a gCS 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.

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 Einstein-Hilbert 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.

We 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.