The off-shell symmetry algebra of the light-cone AdS₅×S⁵superstring

Abstract

We analyse the psu(2, 2|4) supersymmetry algebra of a superstring propagating in the AdS 5 × S 5 background in the uniform light-cone gauge. We consider the off-shell theory by relaxing the level-matching condition and take the limit of infinite light-cone momentum, which decompactifies the string world-sheet. We focus on the psu(2|2) ⊕ psu(2|2) subalgebra which leaves the light-cone Hamiltonian invariant and show that it undergoes extension by a central element which is expressed in terms of the level-matching operator. This result is in agreement with the conjectured symmetry algebra of the dynamic S-matrix in the dual N = 4 gauge theory.

Towards the All-Loop WorldsheetSMatrix forAdS3×S3×TBorsato1, Sax2, Sfondrini3 et al. 2014Phys. Rev. Lett.8521750View full textAdd to dashboardCite

“…Unlike what happens in AdS 5 × S 5 [26,27], we cannot use the coset description, since after gauge fixing massless fermions do not have a conventional quadratic kinetic term. Instead we will work with the Green-Schwarz action [28].…”

“…This introduces a nonlocal momentum dependence through the phase ζ [26,27]. In a Hopf-algebra language, this amounts to defining a deformed coproduct [19,27].…”

Quantum deformed magnon kinematics

“…The meaning of this kinematical symmetry must be understood from the structure of the Hopf algebra symmetry [8,9,10,5,11,12]. In [8] the existence of a central Hopf subalgebra was noticed and the spectrum of this center was proposed as the rapidity plane.…”

Factorized world-sheet scattering in near-flat

“…To render our proof mathematically rigorous, one should, however, find the action of the symmetry generators explicitly. Their form is not known for the near-flat-space model to date and taking the corresponding limit of the generators for the full AdS string [49] is not straightforward due to non-local field redefinitions.…”

“…The model (2.1) inherits the symmetries from the AdS 5 × S 5 superstring in light-cone gauge [42]. With relaxed level-matching, the symmetry algebra is psu(2|2) 2 ⋉ Ê 3 [49], where ⋉ symbolizes central extension. The charges of the fields under the bosonic subalgebra su(2) 4 can be made manifest by changing to a double index notation…”