HEP Theory Journal Club

Explorations in Non-Orientable 2d CFTs

Yiannis Tsiares

McGill

We will discuss some universal results of two-dimensional conformal field theories (CFTs) defined on non-orientable Riemann surfaces. These theories have been studied extensively in the past mostly in the context of string theories on non-orientable worldsheets, or under the general framework of two-dimensional boundary CFTs in the case where the theory is rational i.e. theories that have a finite number of primary operators. We will extend these results to the case of compact, irrational CFTs with central charge greater than one and a gap in the spectrum of scalar primaries. Our key tool is the implementation of the Virasoro fusion and modular kernels that relate cross-channel conformal blocks on such Riemann surfaces. Using that, one can derive universal expressions for the non-orientable CFT data at large conformal dimension, analogous to the corresponding Cardy formulas in the orientable case. We will discuss the gravitation interpretation of these results, as well as the conformal bootstrap problem on the Klein bottle.