Injecting the UV into the bootstrap: Ising Field Theory

We merge together recent developments in the S-matrix bootstrap program to develop a dual setup in 2 space-time dimensions incorporating scattering amplitudes of massive particles and matrix elements of local operators. In particular, the stress energy tensor allows us to input UV constraints on IR observables in terms of the central charge cUV of the UV Conformal Field Theory. We consider two applications: (1) We establish a rigorous lower bound on cUV of a class of Z(2) symmetric scalar theories in the IR (including phi(4)); (2) We target Ising Field Theory by, first, minimizing cUV for different values of the magnetic field and, secondly, by determining the allowed range of cubic coupling and one-particle form-factor for fixed cUV = 1/2 and magnetic field. [Graphics] [Graphics]

Automated summary

This article presents a dual setup in 2 space-time dimensions that combines scattering amplitudes of massive particles and matrix elements of local operators. By utilizing the stress energy tensor, it is possible to impose UV constraints on IR observables using the central charge cUV of the UV Conformal Field Theory. Two applications are considered, including establishing a lower bound on cUV for Z(2) symmetric scalar theories in the IR and studying Ising Field Theory under different magnetic fields and cubic couplings for fixed cUV = 1/2.