More on integrable structures of superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds

TL;DR

This paper extends the classical integrability analysis of superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) backgrounds by explicitly incorporating non-coset fermions into the Lax connection, preserving key symmetries crucial for Bethe-ansatz methods.

Contribution

It provides explicit all-order expressions for the Lax connection including non-coset fermions, maintaining Z_4-symmetry, and derives the complete superspace geometry for AdS(2) x S(2) x T(6).

Findings

Lax connection extended to all orders in coset fermions and second order in non-coset fermions.

Z_4-symmetry preserved despite non-coset fermion contributions.

Derived the complete superspace geometry for AdS(2) x S(2) x T(6).

Abstract

In this paper we continue the study, initiated in arXiv:1009.3498 and arXiv:1104.1793, of the classical integrability of Green-Schwarz superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds whose spectrum contains non-supercoset worldsheet degrees of freedom corresponding to broken supersymmetries in the bulk. We derive an explicit expression, to all orders in the coset fermions and to second order in the non-coset fermions, which extends the supercoset Lax connection in these backgrounds with terms depending on the non-coset fermions. An important property of the obtained form of the Lax connection is that it is invariant under Z_4-transformations of the superisometry generators and the spectral parameter. This demonstrates that the contribution of the non-coset fermions does not spoil the Z_4-symmetry of the super-coset Lax connection which is of crucial importance for the application of Bethe-ansatz techniques. The expressions describing the AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superstring sigma--models and their Lax connections have a very similar form. This is because their amount of target-space supersymmetries complement each other to 32=24+8, the maximal number of 10d type II supersymmetries. As a byproduct, this similarity has allowed us to obtain the form of the geometry of the complete type IIA AdS(2) x S(2) x T(6) superspace to all orders in the coset fermions and to the second order in the non-coset ones.