Spinning Strings as Small Black Rings

Certain supersymmetric elementary string states with spin can be viewed as small black rings whose horizon has the topology of S 1 × S d−3 in a d-dimensional string theory. By analyzing the singular black ring solution in the supergravity approximation, and using various symmetries of the α ′ corrected effective action we argue that the Bekenstein-Hawking-Wald entropy of the black string solution in the full string theory agrees with the statistical entropy of the same system up to an overall normalization constant. While the normalization constant cannot be determined by the symmetry principles alone, it can be related to a similar normalization constant that appears in the expression for small black holes without angular momentum in one less dimension. Thus agreement between statistical and macroscopic entropy of (d − 1)-dimensional non-rotating elementary string states would imply a similar agreement for a d-dimensional elementary string state with spin. Our analysis also determines the structure of the near horizon geometry and provides us with a geometric derivation of the Regge bound. These studies give more evidences that a ring-like horizon is formed when large angular momentum is added to a small black hole. 1 Introduction and Summary Recently, there has been great deal of progress in computing corrections to black hole entropy due to the effect of higher derivative terms in string theory effective action and comparing the A particularly interesting class of examples is provided by the stringy 'small' black holes. These are singular solutions of the classical supergravity equations of motion since they have vanishing area of the event horizon. However microscopically they are described by BPS states of the fundamental string and hence have non-zero degeneracies. A simple class of such examples is provided by the FP system or the so-called Dabholkar–Harvey (DH) system [14], which is obtained by winding a fundamental heterotic string −w times around a circle S 1 and putting n units of momentum along the same circle. If the right-movers are in the ground state then such a state is BPS but it can carry arbitrary left-moving oscillations. 1 Its microscopic entropy is given by S micro = 4π √ nw. Although in the supergravity approximation the corresponding solution has zero horizon area and hence zero entropy, one expects that the result will be modified by the higher derivative corrections since close to the (singular) horizon the curvature and other field strengths become strong …