Abstract
In this paper we find a host of boost operators for a very general choice of coproducts in AdS3-inspired scattering theories, focusing on the massless sector, with and without an added trigonometric deformation. We find that the boost coproducts are exact symmetries of the R-matrices we construct, besides fulfilling the relations of modified Poincaŕe-type superalgebras. In the process, we discover an ambiguity in determining the boost coproduct which allows us to derive differential constraints on our R-matrices. In one particular case of the trigonometric deformation, we find a non-coassociative structure which satisfies the axioms of a quasi-Hopf algebra.
Highlights
Since neither the massive nor the massless excitations have a relativistic dispersion relation, a natural question arises regarding the existence of any remnant of Poincare symmetry after gauge-fixing the reparameterisation freedom of the string sigma model
In this paper we find a host of boost operators for a very general choice of coproducts in AdS3-inspired scattering theories, focusing on the massless sector, with and without an added trigonometric deformation
We find that the boost coproducts are exact symmetries of the R-matrices we construct, besides fulfilling the relations of modified Poincare-type superalgebras
Summary
In order to better understand the role of the boost JA and how to fix their coproducts, we are going to consider a more general set of allowed coproducts, i.e. Notice that we can perform the redefinitions SL → eiκSpSL, QL → eiκQpQL and HL → ei(κS+κQ)pHL (with κS + κQ = 0 if we want to physically associate the eigenvalue of H directly with the (left) one-particle energy) to fix two of the four components a, b, c, d This is because, by the homomorphism property of the coproduct, ∆(eizpT ) = ∆(eizp)∆(T ) = eizp ⊗ eizp ∆(T ), for any constant z and algebra generator T. The family a + b = c + d = 0, which contains as special cases the trivial braiding a, b, c, d = 0 and the braiding most commonly used in the literature, a = −b = −c = d = −1 We will call this family bosonically unbraided, as we can always get rid of the braiding in the coproduct of the bosonic Cartan element (the energy) via a redefinition of the generator itself. In the rest of this section we construct and study in detail the coproduct of the boost operator for the second and first family, respectively
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