Large scalar gaps in 2D CFTs with generalized polynomials

TL;DR

The paper introduces an analytic method for constructing crossing symmetric functions in 2D CFTs, enabling the discovery of large operator gaps for certain scaling dimensions, advancing understanding of conformal bootstrap constraints.

Contribution

It develops a novel analytic approach using generalized polynomials to find large scalar gaps in 2D CFTs, a significant step in conformal bootstrap research.

Findings

Achieved large gaps for operators with integer dimensions up to 18

Developed a new class of crossing symmetric functions called generalized polynomials

Provided analytic expressions for unitary 4-point functions in 2D CFTs

Abstract

We present an analytic way of writing simple crossing symmetric expressions and use them to search for unitary 4-point functions in 2D CFTs. We've applied our method for a class of functions we called generalized polynomials to achieve large gaps for operators with integer scaling dimension less or equal to 18.