Improved bounds for CFT's with global symmetries

TL;DR

This paper derives new bounds on operator dimensions in conformal field theories with global SO(N) symmetry, using crossing symmetry constraints on four-point functions, applicable to both non-supersymmetric and superconformal theories.

Contribution

It provides improved bounds on scalar operator dimensions in CFTs with SO(N) symmetry, leveraging the full set of crossing symmetry constraints, including for superconformal theories.

Findings

Bounds for the first scalar singlet operator are established for various N.

Bounds for the first scalar traceless-symmetric operator are computed.

Superconformal bounds improve upon previous results.

Abstract

The four point function of Conformal Field Theories (CFT's) with global symmetry gives rise to multiple crossing symmetry constraints. We explicitly study the correlator of four scalar operators transforming in the fundamental representation of a global SO(N) and the correlator of chiral and anti-chiral superfields in a superconformal field theory. In both cases the constraints take the form of a triple sum rule, whose feasibility can be translated into restrictions on the CFT spectrum and interactions. In the case of SO(N) global symmetry we derive bounds for the first scalar singlet operator entering the Operator Product Expansion (OPE) of two fundamental representations for different value of N. Bounds for the first scalar traceless-symmetric representation of the global symmetry are computed as well. Results for superconformal field theories improve previous investigations due to the use of the full set of constraints. Our analysis only assumes unitarity of the CFT, crossing symmetry of the four point function and existence of an OPE for scalars.