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2018

Parity and the modular bootstrap

Anous, Tarek, Mahajan, Raghu, Shaghoulian, Edgar

Understand

We consider unitary, modular invariant, two-dimensional CFTs which are invariant under the parity transformation $P$.

Combining $P$ with modular inversion $S$ leads to a continuous family of fixed points of the $SP$ transformation.
A particular subset of this locus of fixed points exists along the line of positive left- and right-moving temperatures satisfying $\beta_L \beta_R = 4\pi^2$.
We use this fixed locus to prove a conjecture of Hartman, Keller, and Stoica that the free energy of a large-$c$ CFT$_2$ with a suitably sparse low-lying spectrum matches that of AdS$_3$ gravity at all temperatures and all angular potentials.