Abstract: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 odd dimensions both for purely gravitational CS terms and for mixed gaugegravitational 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.

This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background,

We analyze near horizon behavior of small D-dimensional 2-charge black holes by modifying tree level effective action of heterotic string with all extended Gauss-Bonnet densities. We show that there is a nontrivial and unique choice of parameters, independent of D, for which the black hole entropy in any dimension is given by 4π √ nw, which is exactly the statistical entropy of 1/2-BPS states of heterotic string compactified on T 9−D ×S 1 with momentum n and winding w. This extends the results of Sen [JHEP 0507 (2005) 073] to all dimensions. We also show that our Lovelock type action belongs to the more general class of actions sharing the simmilar behaviour on the AdS 2 × S D−2 near horizon geometry.6 [x] denote integer part of x. 7 [D/2] is the number of extended Gauss-Bonnet terms in D dimensions, including the Einstein term.

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We calculate near-horizon solutions for four-dimensional 4-charge and fivedimensional 3-charge black holes in heterotic string theory from the part of the tendimensional tree-level effective action which is connected to gravitational Chern-Simons term by supersymmetry. We obtain that the entropies of large black holes exactly match the α ′ -exact statistical entropies obtained from microstate counting (D = 4) and AdS/CFT correspondence (D = 5). Especially interesting is that we obtain agreement for both BPS and non-BPS black holes, contrary to the case of R 2 -truncated (four-derivative) actions (D-dimensional N = 2 off-shell supersymmetric or Gauss-Bonnet) were used, which give the entropies agreeing (at best) just for BPS black holes. The key property of the solutions, which enabled us to tackle the action containing infinite number of terms, is vanishing of the Riemann tensor R M N P Q obtained from torsional connection defined with Γ = Γ − 1 2 H. Moreover, if every monomial of the remaining part of the effective action would contain at least two Riemanns R M N P Q , it would trivially follow that our solutions are exact solutions of the full heterotic effective action in D = 10. The above conjecture, which appeared (in this or stronger form) from time to time in the literature, has controversial status, but is supported by the most recent calculations of ). Agreement of our results for the entropies with the microscopic ones supports the conjecture. As for small black holes, our solutions in D = 5 still have singular horizons.