A note on D1-D5-J system and 5D small black ring

Abstract

The "small" black ring in 5D obtained by giving angular momentum to the D1-D5 system compactified on S1 × K3 is a very interesting object in the sense that it does not have an event horizon in the supergravity limit whereas it microscopically has a finite entropy. The microscopic origin of this small black ring can be analyzed in detail since it is constructed by adding angular momentum to the well-studied D1-D5 system. On the other hand, its macroscopic, geometrical picture is difficult to study directly. In this note, by duality transformations and the 4D-5D connection, we relate this 5D small black ring to a 4D small non-rotating black hole, where the latter is known to develop a non-vanishing horizon due to stringy R2 corrections to the supergravity action. The entropy of the 4D small black hole agrees with the microscopic entropy of the 5D small black ring, which supports the validity of the 4D-5D connection even for small black objects. These results give an indirect evidence that a non-vanishing horizon is formed for the 5D small black ring.

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