Virasoro conformal bootstrap with $c > 1$

TL;DR

This paper develops new analytical and numerical bounds on the spectrum of 2D conformal field theories with central charge greater than one, using the pillow representation and positivity constraints of four-point correlators.

Contribution

It introduces a novel analytic expression for bounds on the first excited Virasoro primary dimension in 2D CFTs with c>1, improving previous bounds.

Findings

Derived explicit bounds on the first excited primary dimension.

Provided analytic formulas and transcendental equations for tighter bounds.

Numerically evaluated bounds for various central charges and operator dimensions.

Abstract

We derive new constraints on the spectrum of two-dimensional conformal field theories with central charge $c>1.$ Employing the pillow representation of the four point correlator of identical scalars with dimension $\Delta_{\mathcal{O}}$ and positivity of the coefficients of its expansion in the elliptic nome we place central charge dependent bounds on the dimension of the first excited Virasoro primary the scalar couples to, in the form $\Delta_1<f(c,\Delta_{\mathcal{O}}).$ We give an analytic expression for $f(c,\Delta_{\mathcal{O}})$ and write down transcendental equations that significantly improve the analytic bound. We numerically evaluate the stronger bounds for arbitrary fixed values of $c$ and $\Delta_{\mathcal{O}}.$