The unitary subsector of generalized minimal models

TL;DR

This paper proves that global conformal blocks in a key four-point function of generalized minimal models have positive coefficients, advancing understanding of non-unitary conformal theories and their relation to unitarity.

Contribution

It establishes the positivity of global conformal block coefficients in a specific four-point correlator of generalized minimal models using harmonic analysis.

Findings

Proved positivity of conformal block coefficients in the correlator.

Computed coefficients in a mixed correlator system.

Discussed implications for isolating unitary points.

Abstract

We revisit the line of non-unitary theories that interpolate between the Virasoro minimal models. Numerical bootstrap applications have brought about interest in the four-point function involving the scalar primary of lowest dimension. Using recent progress in harmonic analysis on the conformal group, we prove the conjecture that global conformal blocks in this correlator appear with positive coefficients. We also compute many such coefficients in the simplest mixed correlator system. Finally, we comment on the status of using global conformal blocks to isolate the truly unitary points on this line.