Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground

TL;DR

This work constructs and leverages a complete $AdS_4\times CP^3$ superspace with 32 fermionic coordinates, enabling gauge-fixing of kappa-symmetry to access regions of the AdS4/CFT3 correspondence beyond the standard coset sigma-model. By choosing a kappa-gauge that projects fermions with $\gamma=\gamma^{012}$, the authors derive simplified, gauge-fixed geometries and superfields, and apply these to obtain explicit, tractable actions for a $D=11$ superparticle in $AdS_4\times S^7/Z_k$, a D0-brane, the fundamental string, and D2-branes in $AdS_4\times CP^3$, including analyses of T-duality and boundary configurations. The gauge-fixed formulations reveal fermionic terms truncated at lower orders (up to 4th–6th order in some cases and up to 8th order in the string action before dualization), enabling detailed studies of $AdS_4/CFT_3$ phenomena and potential integrability beyond the coset sector. The work also provides comprehensive appendices with notation, the full $(10|32)$ superspace construction, and identities needed to manipulate the kappa-projected fermions, together with explicit realizations of the relevant supercoset and superspace constraints.

Abstract

By making an appropriate choice for gauge fixing kappa-symmetry we obtain a relatively simple form of the actions for a D=11 superparticle in AdS(4) x S(7)/Z_k, and for a D0-brane, fundamental string and D2-branes in the AdS(4) x CP(3) superbackground. They can be used to study various problems of string theory and the AdS4/CFT3 correspondence, especially in regions of the theory which are not reachable by the OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In particular, we present a simple form of the gauge-fixed superstring action in AdS(4) x CP(3) and briefly discuss issues of its T-dualization.