Worldsheet analysis of gauge/gravity dualities

Abstract Gauge/gravity dualities are investigated from the worldsheet point of view. In [H. Kawai, T. Suyama, AdS/CFT correspondence as a consequence of scale invariance, Nucl. Phys. B 789 (2008) 209, arXiv:0706.1163 [hep-th] ; H. Kawai, T. Suyama, Some implications of perturbative approach to AdS/CFT correspondence, Nucl. Phys. B 794 (2008) 1, arXiv:0708.2463 [hep-th] ], a duality between 4d SYM and supergravity on AdS 5 × S 5 has been partly explained by using an anisotropic scale invariance of worldsheet theory. In this paper, we refine the argument and generalize it to lower dimensional cases. We show the correspondence between the Wilson loops in ( p + 1 ) -d SYM and the minimal surface in the black p -brane background. Although the scale invariance does not exist in these cases, the generalized scale transformation can be utilized. We also find that the energy density of open strings can be related to the ADM mass of the p -brane without relying on this symmetry.