Abstract
The purpose of this contribution is to initiate the study of integrable deformations for different superstring theory formalisms that manifest the property of (classical) integrability. In this paper we choose the hybrid formalism of the superstring in the background AdS_{2}xS^{2} and explore in detail the most immediate consequences of its lambda-deformation. The resulting action functional corresponds to the lambda-model of the matter part of the fairly more sophisticated pure spinor formalism, which is also known to be classical integrable. In particular, the deformation preserves the integrability and the one-loop conformal invariance of its parent theory, hence being a marginal deformation.
Highlights
The second kind of integrable field theory is known as the λ-deformation1 and basically leads to a quantum group q-deformation of its parent σ-model S-matrix [5,6,7] this time with a root-of-unity parameter qN = 1, for some N ∈ Z
The basic goal of this paper is to explore the most direct consequences of the λdeformation for this simpler case keeping in mind the AdS5 × S5 supercoset for a future work as it requires instead the use of the pure spinor formalism [31, 32], which is fairly more complex and where, as we will see below, the introduction of the deformation is more delicate than in the present situation
In this paper we have studied in detail the λ-model of the hybrid formalism of the superstring in the background19 AdS2 × S2 and showed how it preserves most of the main characteristics of the original σ-model except the one related to the maximal isometry group of the target space, a situation that is common to all λ-models
Summary
One of the main properties of the deformation is that it promotes the global Noether symmetry of the parent σ-model associated to the left action of the group F to a global Poisson-Lie group symmetry in the λ-model7 [41]. Generated by the charge QL, i.e. we have that the variation δX f = Xf , X ∈ f can be written in the usual Abelian moment form δX f (x) = X, {QL, f (x)} This action is hidden in the dual field F as can be seen from (2.30) but it can be shown [41] that the infinitesimal right action δΨ(λ±1/2) = Ψ(λ±1/2)X, X ∈ f directly on the wave-function can be written instead in the non-Abelian moment form δX Ψ(±)(x) = ±. Where we have denoted Ψ(λ±1/2) = Ψ(±) This shows that the global left action of F in the σ-model becomes a Poisson-Lie symmetry in the λ-model generated by the non-Abelian Hamiltonian W, which turns out to be the (right) monodromy matrix. The λ-deformation naturally introduces a q-deformation on the hybrid formalism
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
