Higher derivative corrections to non-supersymmetric extremal black holes in N = 2 supergravity Bindusar Sahoo and Ashoke SenHarish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211019, India E-mail: bindusar@mri.ernet.in, sen@mri.ernet.in Abstract: Using the entropy function formalism we compute the entropy of extremal supersymmetric and non-supersymmetric black holes in N = 2 supergravity theories in four dimensions with higher derivative corrections. For supersymmetric black holes our results agree with all previous analysis. However in some examples where the four dimensional theory is expected to arise from the dimensional reduction of a five dimensional theory, there is an apparent disagreement between our results for non-supersymmetric black holes and those obtained by using the five dimensional description. This indicates that for these theories supersymmetrization of the curvature squared term in four dimension does not produce all the terms which would come from the dimensional reduction of a five dimensional action with curvature squared terms.

The entropy of a BTZ black hole in the presence of gravitational Chern-Simons terms has previously been analyzed using Euclidean action formalism. In this paper we treat the BTZ solution as a two dimensional black hole by regarding the angular coordinate as a compact direction, and use Wald's Noether charge method to calculate the entropy of this black hole in the presence of higher derivative and gravitational Chern-Simons terms.The parameters labelling the black hole solution can be determined by extremizing an entropy function whose value at the extremum gives the entropy of the black hole.

We explicitly compute the entropy of an extremal dyonic black hole in heterotic string theory compactified on T 6 or K3 × T 2 by taking into account all the tree level four derivative corrections to the low energy effective action. For supersymmetric black holes the result agrees with the answer obtained earlier 1) by including only the Gauss-Bonnet corrections to the effective action 2) by including all terms related to the curvature squared terms via space-time supersymmetry transformation, and 3) by using general arguments based on the assumption of AdS 3 near horizon geometry and space-time supersymmetry.For non-supersymmetric extremal black holes the result agrees with the one based on the assumption of AdS 3 near horizon geometry and space-time supersymmetry of the underlying theory.

We study giant magnons in the the D1-D5 system from both the boundary CFT and as classical solutions of the string sigma model in AdS 3 × S 3 × T 4 . Re-examining earlier studies of the symmetric product conformal field theory we argue that giant magnons in the symmetric product are BPS states in a centrally extended SU(1|1) × SU(1|1) superalgebra with two more additional central charges. The magnons carry these additional central charges locally but globally they vanish. Using a spin chain description of these magnons and the extended superalgebra we show that these magnons obey a dispersion relation which is periodic in momentum. We then identify these states on the string theory side and show that here too they are BPS in the same centrally extended algebra and obey the same dispersion relation which is periodic in momentum. This dispersion relation arises as the BPS condition for the extended algebra and is similar to that of magnons in N = 4 Yang-Mills

We show that integrability and symmetries of the near horizon geometry of the D1-D5 system determine the S-matrix for the scattering of magnons with polarizations in AdS3 $\times$ S3 completely up to a phase. Using semi-classical methods we evaluate the phase to the leading and to the one-loop approximation in the strong coupling expansion. We then show that the phase obeys the unitarity constraint implied by the crossing relations to the one-loop order. We also verify that the dispersion relation obeyed by these magnons is one-loop exact at strong coupling which is consistent with their BPS nature.Comment: 40 pages, Latex, Role of Virasoro constraints clarified, version matches with published versio