The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring

TL;DR

This paper investigates the off-shell symmetry algebra of the light-cone superstring in AdS_5 x S^5, revealing an extension by a central element related to the level-matching operator, aligning with the dual gauge theory's S-matrix conjecture.

Contribution

It demonstrates the extension of the psu(2|2)+psu(2|2) algebra by a central element in the off-shell theory, providing insights into the symmetry structure of the superstring.

Findings

The algebra extends by a central element linked to level-matching.

The off-shell algebra matches the conjectured dual S-matrix symmetry.

Decompactification limit simplifies the algebraic structure.

Abstract

We analyze the psu(2,2|4) supersymmetry algebra of a superstring propagating in the AdS_5 x 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.