Exact Results in Quantum Theory

We study the thermodynamics of a (1+1)-dimensional integrable quantum field theory in the planar infinite N limit. Unlike isovector-valued O(N) models, matrix valued field theories in the infinite-N are not solvable by the Hartre-Fock approximation, and are nontrivial interacting theories. By combining the planar limit with integrable bootstrap techniques, one can compute the exact S-matrix, form factors and correlation functions. Thermal expectation values are easily computable as a form factor sum, since many difficult terms are suppressed by powers of 1/N. We also compute out of equilibrium, time dependent correlation functions after a quantum quench, which are also simplified by discarding 1/N suppressed terms. These 1/N suppressions are not related to integrability, and can greatly simplify the computation in other models that are not exactly solvable.