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

The ``small'' black ring in 5D obtained by giving angular momentum to theD1-D5 system compactified on S^1 x K3 is a very interesting object in the sensethat it does not have an event horizon in the supergravity limit whereas itmicroscopically has a finite entropy. The microscopic origin of this smallblack ring can be analyzed in detail since it is constructed by adding angularmomentum to the well-studied D1-D5 system. On the other hand, its macroscopic,geometrical picture is difficult to study directly. In this note, by dualitytransformations and the 4D-5D connection, we relate this 5D small black ring toa 4D small non-rotating black hole, where the latter is known to develop anon-vanishing horizon due to stringy R^2 corrections to the supergravityaction. This gives an indirect evidence that a non-vanishing horizon is formedfor the 5D small black ring. We also show that the entropy of the 4D smallblack hole agrees with the microscopic entropy of the 5D small black ring,which supports that the 4D-5D connection is indeed valid even for small blackobjects.Comment: 12 pages, LaTeX. v2: minor correction