Spinning Strings as Small Black Rings

TL;DR

This work analyzes spinning string states as small black rings in $d$-dimensional string theory, showing that the macroscopic Bekenstein-Hawking-Wald entropy of rotating ring solutions matches the microscopic degeneracy of spinning fundamental strings up to a universal normalization constant. Through a scaling analysis of the singular supergravity ring and a near-horizon entropy-function treatment, the authors derive the entropy form $S_{BH}=C\sqrt{nw-JQ}$ and identify a Regge bound $JQ\le nw$ tied to causality. They relate the constant $C$ to the corresponding coefficient for non-rotating small black holes in $(d-1)$ dimensions, implying that microscopic-macroscopic agreement in the lower dimension extends to the higher-dimensional rotating case. However, $C$ remains undetermined in general, with $C=4π$ established in four dimensions via independent Chern–Simons arguments, highlighting a key open problem and guiding future higher-dimensional analyses.

Abstract

Certain supersymmetric elementary string states with spin can be viewed as small black rings whose horizon has the topology of S^1 \times 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 further evidence that a ring-like horizon is formed when large angular momentum is added to a small black hole.