Remote Nordic HET seminar: Eric Perlmutter

Speaker: Eric Perlmutter

Title: Discreteness and Integrality in Conformal Field Theory

Abstract: Familiar observables in compact CFTs, such as the partition function, are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but there is poor understanding of the abstract implications of discreteness and integrality for the space of CFTs. We study these constraints in 2D CFTs and demonstrate their power to produce rigorous bootstrap-type results *without* the need for positivity. For curious reasons which we explain, CFTs with marginal operators admit special bounds. We also derive surprising results on questions of spectral determinacy -- that is, whether certain parts of the spectrum are uniquely fixed by their complement -- in non-holomorphic CFT, which go against conventional folklore. Our conclusions follow from two new mathematical results: one on holomorphic vector-valued modular forms, and the other on non-holomorphic cusp forms. The obligation to discuss 3D gravity is fulfilled. Based on 2008.02190.