AdS/CFT in superspace

TL;DR

This paper establishes a direct relation between the 10D IIB superstring in AdS_5×S^5 and 4D N=4 Yang-Mills theory within superspace, revealing how the internal space and fermionic coordinates correspond in a manifestly symmetric framework.

Contribution

It introduces a novel superspace formulation connecting AdS superstring theory with boundary Yang-Mills theory, preserving SO(3,1)×SO(4) symmetry and clarifying the algebraic structure.

Findings

The sphere becomes the CFT internal space in projective superspace.

The fermionic coordinates map from AdS to the boundary in a spacecone gauge.

The AdS PSU(2,2|4) algebra is represented on the boundary with an extra coordinate.

Abstract

We relate the 10D IIB superstring (primarily free supergravity) expanded about AdS_5\timesS^5 to 4D N=4 Yang-Mills directly in superspace. The sphere becomes the CFT internal space of projective superspace, plus a coordinate counting the number of supergluons. The 32 fermionic coordinates of AdS become the 8 of the CFT in a spacecone gauge that manifestly preserves SO(3,1).SO(4). The PSU(2,2|4) algebra of AdS becomes the projective representation (plus the extra coordinate) on the boundary. (A review of projective superspace and the projective lightcone limit is included for self-containment.)