We apply a recently proposed Kerr/CFT correspondence to extremal supersymmetric five-dimensional charged spinning black holes, constructed by Breckenridge, Myers, Peet and Vafa. By computing the central charge of the dual CFT and Frolov-Thorne temperature, Cardy's formula succeeds in reproducing Bekenstein-Hawking area

We find a 3D flavored N =4 Chern-Simons-matter theory, a kind of N =3 SCFT, has a gravity dual AdS 4 × M 7 (t 1 , t 2 , t 3 ) where three coprime parameters can be read off according to the number and charge of 5-branes in the dual Type IIB string setup. Because M 7 (t 1 , t 2 , t 3 ) has been known in literature as Eschenburg space, we exploit some of its properties to examine the correspondence between two sides.

We find perfect agreements on the genus-one correction to the prepotential of SU (2) Seiberg-Witten theory with N f = 2, 3 between field theoretical and Dijkgraaf-Vafa-Penner type matrix model results.

We investigate closed string tachyon condensation in Misner space, a toy model for big bang universe. In Misner space, we are able to condense tachyonic modes of closed strings in the twisted sectors, which is supposed to remove the big bang singularity. In order to examine this, we utilize D-instanton as a probe. First, we study general properties of D-instanton by constructing boundary state and effective action. Then, resorting to these, we are able to show that tachyon condensation actually deforms the geometry such that the singularity becomes milder. *