Bootstrapping gauge theories

Abstract: 
We consider asymptotically free gauge theories with gauge group SU(N_c) and N_f quarks with mass m_q≪Λ_QCD that undergo chiral symmetry breaking and confinement. We propose a bootstrap method to compute the S-matrix of the pseudo-Goldstone bosons (pions) that dominate the low energy physics. For the important case of N_c=3, N_f=2, a numerical implementation of the method gives the phase shifts of the S₀, P₁ and S₂ waves in good agreement with experimental results. The method incorporates gauge theory information (N_c, N_f, m_q, Λ_QCD) by using the form-factor bootstrap recently proposed by Karateev, Kuhn and Penedones together with a finite energy version of the SVZ sum rules. At low energy we impose constraints from chiral symmetry breaking. The only low energy numerical inputs are the pion mass m_π , and the quark and gluon condensates.

The talk is based on: arXiv:2309.12402 [hep-th]