Oscillator level for black holes and black rings

Microscopic calculations of the Bekenstein–Hawking entropy of supersymmetric black holes in string theory are typically based on the application to a dual 2D CFT of Cardy's formula, , where c is the central charge and is the oscillator level. In the CFT, is non-trivially related to the total momentum. We identify a Komar integral that equals when evaluated at the horizon, and the total momentum when evaluated at asymptotic infinity, thus providing a gravitational dual of the CFT result.