Theory HEP Seminar

Three tales of crosscaps

Shota Komatsu

CERN

Crosscap states have been studied extensively in two-dimensional conformal field theory in the past, where part of the motivations came from their connection to orientifolds in string theory. Surprisingly however, analogous studies in (massive) integrable theories have been lacking. In this talk, I will fill this gap by presenting a systematic study of crosscap states in integrable field theories and spin chains. First, I derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. I next introduce crosscap states in integrable spin chains and obtain exact determinant expressions for overlaps with energy eigenstates. These states are long-range entangled and provide interesting initial conditions for the quantum quench protocol, which are quite distinct from short-range entangled states corresponding to the boundary states. I will then explain how it is related to certain observables in N=4 super Yang-Mills and present a non-perturbative conjecture for them. Finally, time permitting, I will comment on on-going work on the application to the measurement induced phase transition.