1:30 pm MCP 201 - VIA ZOOM
Why Indices Count the Total Number of Black Hole Microstates (at large N).
Understanding why Witten indices reproduce the exponential of the Bekenstein--Hawking entropy of supersymmetric black holes—despite counting bosonic and fermionic states with opposite signs—has remained a long-standing puzzle in string theory and gauge/gravity duality.
In this talk we will address this question in the canonical example of the duality between four-dimensional maximally supersymmetric Yang--Mills theory and ten-dimensional Type IIB supergravity/string theory. Concretely, we will explain why the superconformal index of this gauge theory, after averaging out oscillations, reproduces the semiclassical entropy of the dual supersymmetric black holes in the relevant asymptotic expansions. As a by-product, we will provide a microscopic interpretation of a non-linear constraint among charges that is well known to correspond, on the gravitational side of the duality, to the absence of naked CTCs in the Lorentzian black hole geometry.
Our results indicate that, rather than the superconformal index, the natural observable for counting black-hole microstates at finite $N$ is the Boltzmann partition function over BPS states. The talk will be based on 2512.19946 and on ongoing work.