ICTS

We consider unitary, modular invariant, two-dimensional CFTs which are invariant under spatial parity flips. Applying parity and modular inversion symmetry to the partition function leads to a continuous family of fixed points of this transformation. We use this fixed locus to prove aconjecture of Hartman, Keller, and Stoica that the free energy of a large-c 2d CFT with a suitably sparse low-lying spectrum matches that of AdS3 gravity at all temperatures and all angular potentials. We also use the fixed locus to generalize the modular bootstrap equations, obtaining novel constraints on the operator spectrum.