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

Abstract

We consider the 2D S-matrix bootstrap in the presence of supersymmetry, Z 2 , and Z 4 symmetry. At the boundary of the allowed S-matrix space we encounter well-known integrable models such as the supersymmetric sine-Gordon and restricted sine-Gordon models, novel elliptic deformations thereof, as well as a two parameter family of Z 4 elliptic S-matrices previously proposed by Zamolodchikov. We highlight an intricate web of relations between these various S-matrices.

Dual S-matrix bootstrap. Part I. 2D theory

“…Above s = (m 1 +m 2 ) 2 we are at physical energies and the extended unitarity relation is replaced by regular unitarity which is now nothing but the statement that U is a positive semi-definite matrix U 0 for s > (m 1 + m 2 ) 2 . 18 Finally we have poles. These correspond to the single particle exchanges when s or t or u are equal to either m 1 or m 2 .…”

“…The blue and green dots mark respectively the well known integrable 3-states Potts and supersymmetric Sine-Gordon. We recall that starting at θ = π/4, the yellow dot, and all the way to θ = π/2 the S-matrix saturating the boundary is known analytically and correspond to the elliptic deformation of supersymmetric Sine-Gordon -see [17,18] for details. For the objective functional (D.18) we must require that W a ∼ s −3/2 for s → ∞.…”

Dual EFT bootstrap: QCD flux tubes

“…We know that adding fermionic degrees of freedom and supersymmetry on the worldsheet of confining strings leads to a series of predictions for the low energy flux-tube dynamics and its S-matrix [75]. The scattering of supersymmetric gapped particles in two dimensions was studied in [76] and the bound of allowed space of couplings showed interesting geometric structures in that case. It could happen that supersymmetric world-sheet theories lies at a special point in the space of feasible Wilson coefficients.…”

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.…”