Integral Equation for CFT/String Duality

TL;DR

This paper derives an explicit equation for the mass spectrum in confining conformal field theories, including QCD, by relating it to the OPE expansion, and shows that the resulting spectrum converges under certain conditions.

Contribution

It introduces a novel method to compute the mass spectrum of confining CFTs using OPE expansion, applicable to theories like QCD and AdS models.

Findings

Derived a convergent expansion for the mass spectrum

Applied the method to QCD with good agreement to Regge trajectories

Extended previous work on CFT/string duality to include confinement effects

Abstract

We reinterpret and extend some old work on CFT/string duality. We consider some asymptotically conformal field theory in large N limit, with conformal symmetry broken by VEV's of infinite number of operators. Assuming that this theory confines (i.e. is dual to infinite number of free composite particles) we derive explicit equation for the mass spectrum operator Q of the theory, relating this operator to terms OPE expansion of CFT. Under some general assumptions about growth of OPE coefficients (less than double factorial growth) the resulting expansion for the mass spectrum is convergent. This method applies to confining CFT of ADS family as well as any asymptotically CFT with confinement. This includes the ordinary QCD. In the latter case the first terms of our perturbation expansion have good correspondence with experimental Regge trajectories at low angular momentum.