Integrability and non-perturbative effects in the AdS/CFT correspondence

Abstract We present a non-perturbative resummation of the asymptotic strong-coupling expansion for the dressing phase factor of the AdS 5 × S 5 string S-matrix. The non-perturbative resummation provides a general form for the coefficients in the weak-coupling expansion, in agreement with crossing symmetry and transcendentality. The ambiguities of the non-perturbative prescription are discussed together with the similarities with the non-perturbative definition of the c = 1 matrix model.