Exact Stringy Microstates from Gauge Theories

We study how the microstates of BPS sectors in string theory are organized in the dual $U(N)$ gauge theory. The microstates take the form of a coherent sum of stacks of branes and their open/closed string excitations. We propose a prescription to holographically construct the indices of string/brane configurations by analyzing the modifications of determinant operators in gauge theory. The string/brane configurations should be interpreted in the tensionless limit, but their indices are well-defined at finite $N$. In various examples, we provide evidence that a sum, of the giant graviton-type recently proposed in the literature, over all such configurations gives the finite $N$ gauge theory index. Finally, we discuss how these microstates assemble in the BPS Hilbert space and in what circumstances the branes can form bound states to produce black hole degeneracies.