The O(N) S-matrix monolith

Abstract

We consider the scattering matrices of massive quantum field theories with no bound states and a global O(N ) symmetry in two spacetime dimensions. In particular we explore the space of two-to-two S-matrices of particles of mass m transforming in the vector representation as restricted by the general conditions of unitarity, crossing, analyticity and O(N ) symmetry. We found a rich structure in that space by using convex maximization and in particular its convex dual minimization problem. At the boundary of the allowed space special geometric points such as vertices were found to correspond to integrable models. The dual convex minimization problem provides a novel and useful approach to the problem allowing, for example, to prove that generically the S-matrices so obtained saturate unitarity and, in some cases, that they are at vertices of the allowed space. arXiv:1909.06495v2 [hep-th]

Two-dimensional O(n) models and logarithmic CFTs

“…In this paper we will touch upon the n 2 theory only briefly, deferring the detailed study to a future publication. Our preliminary investigation suggests a possible relation between these complex CFTs and periodic S-matrices recently discussed in the context of the S-matrix bootstrap program [32,33].…”

“…The energy operator has a null descendant at level 2, ε P = φ 2,1 , as can be seen by expanding the torus partition function [14], and noticing that the partition function contains the term q h 2,1q h 2,1 +2 with multiplicity one. 33 Therefore, its correlation functions satisfy a differential equation similar to (4.8), with the difference that it will be second order this time.…”

S-matrix bootstrap: Supersymmetry, Z2 , and Z4 symmetry

“…In particular, fourfold vertices are equivalent to limits in which the Z 4 or sine-Gordon S-matrix becomes free. The threefold vertices of the dodecahedron are smoothened resembling the prevertices of [11].…”

“…4-are the main results of this paper. Some of the amazing features in these S-matrix spaces-such as unitarity saturation-are now somehow demystified [11] while others-such as emerge of factorization or exotic periodicities in the kinematical variables-remain as elusive as ever. Would be very interesting to explore other setups with different symmetries and space-time dimensions to better shed light over these puzzles and to best understand how universal they really are.…”

Lifting heptagon symbols to functions

“…[1]). One recent incarnation of this program imposes fairly general constraints on scattering (typically 2 → 2 scattering), and leads, for example in two spacetime dimensions, to bounds on couplings and other parameters which are often satisfied by particular known theories [2][3][4][5]. In contrast, the planar N = 4 super-Yang-Mills (SYM) amplitude bootstrap program starts with a fixed theory, the simplest gauge theory in four dimensions, and aims to compute arbitrary scattering amplitudes, typically in perturbation theory but without ever directly inspecting the loop integrand.…”