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Towards a nonperturbative construction of the S-matrix

Francesco Riva, Matthew Thomas Walters

We present a nonperturbative recipe for directly computing the S-matrix in strongly-coupled QFTs. The method makes use of spectral data obtained in a Hamiltonian framework and can be applied to a wide range of theories, including potentially QCD. We demonstrate the utility of this prescription in the specific example of the 2+1d O(N) model at large N, using energy eigenstates computed with Hamiltonian truncation to reproduce the full 2 -> 2 scattering amplitude for arbitrary (complex) center-of-mass energy.

SPRINGER2023

Thermalization and hydrodynamics of two-dimensional quantum field theories

Matthew Thomas Walters

We consider 2d QFTs as relevant deformations of CFTs in the thermodynamic limit. Using causality and KPZ universality, we place a lower bound on the timescale characterizing the onset of hydrodynamics. The bound is determined parametrically in terms of the temperature and the scale associated with the relevant deformation. This bound is typically much stronger than 1/T, the expected quantum equilibration time. Subluminality of sound further allows us to define a thermodynamic C-function, and constrain the sign of the T(T) over bar term in EFTs.

2022

On the stress tensor light-ray operator algebra

Matthew Thomas Walters

We study correlation functions involving generalized ANEC operators of the form integral dx-x-n+2T--x -> in four dimensions. We compute two, three, and four-point functions involving external scalar states in both free and holographic Conformal Field Theories. From this information, we extract the algebra of these light-ray operators. We find a global subalgebra spanned by n = {-2, -1, 0, 1, 2} which annihilate the conformally invariant vacuum and transform among themselves under the action of the collinear conformal group that preserves the light-ray. Operators outside this range give rise to an infinite central term, in agreement with previous suggestions in the literature. In free theories, even some of the operators inside the global subalgebra fail to commute when placed at spacelike separation on the same null-plane. This lack of commutativity is not integrable, presenting an obstruction to the construction of a well defined light-ray algebra at coincident x-> coordinates. For holographic CFTs the behavior worsens and operators with n not equal -2 fail to commute at spacelike separation. We reproduce this result in the bulk of AdS where we present new exact shockwave solutions dual to the insertions of these (exponentiated) operators on the boundary.

2021