Integral Equation for CFT/String Duality

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.