Black Holes from Modular Invariance
River Snively (University of California, Los Angeles)
I lay out surprisingly weak conditions sufficient for a 2d CFT to be a holographic theory of ordinary black holes. I argue that thermal CFT correlation functions are computable by bulk effective field theory as long as zero-temperature ones are, the prescription being to do field theory in the presence of a black hole that influences the bulk fields solely via Hawking radiation (and gravity). The argument, which uses modular invariance to bootstrap powerful analytic bounds on expectation values in black hole microstates, is an extension of Hartman, Keller, and Stoica's analysis of zero-point functions.