Rotating particles in AdS: Holography at weak gauge coupling and without conformal symmetry

Abstract

Abstract We consider the gauge/gravity correspondence between maximally supersymmetric Yang–Mills theory in (p + 1) dimensions and superstring theory on the near-horizon limit of the Dp-brane solution. The string-frame metric is AdSp + 2 × S8 − p times a Weyl factor, and there is no conformal symmetry except for p = 3. In a previous paper by one of the present authors, the free-field result of gauge theory has been reproduced from string theory for a particular operator that has angular momentum along S8 − p. In this paper, we extend this result to operators that have angular momenta along AdSp + 2. Our approach is based on a Euclidean formulation proposed by Dobashi et al. [Nucl. Phys. B 665, 94 (2003)] and on the “string bit” picture. We first show that the spinning string solution in Lorentzian AdS, found by Gubser et al. [Nucl. Phys. B 636, 99 (2002)], can be recast in a form that connects two points on the boundary of Euclidean AdS. The transition amplitudes of such strings can be interpreted as gauge theory correlators. We study the case of zero gauge coupling by ignoring interactions among string bits (massless particles in 10D spacetime that constitute a string), and show that the free-field results of gauge theory are reproduced.