AdS_5 x S^5 Untwisted

TL;DR

This work investigates how the canonical AdS$_5\times S^5$ background can be untwisted via Hopf reductions to yield $AdS_5\times CP^2\times S^1$ and, upon further dualities, $AdS_5\times CP^2\times T^2$ in M-theory. It demonstrates a concrete instance of supersymmetry without supersymmetry: the full string/M-theory spectrum can preserve higher supersymmetry even when the supergravity limit on $AdS_5\times CP^2\times S^1$ appears non-supersymmetric, with winding modes supplying missing fermions and enlarging the gauge symmetry from $SU(3)\times U(1)^3$ to $SO(6)$. The paper then maps a broad web of AdS$_5$ compactifications, including non-maximal cases based on $Q(n_1,n_2)$ and lens spaces $S^5/Z_k$, outlining how T-duality, spin structures, and winding modes shape the resulting supersymmetry and spectrum. Collectively, these results extend the AdS/CFT correspondence to novel untwisted geometries and reveal a rich landscape of AdS$_5$ backgrounds with varied supersymmetry and operator spectra.

Abstract

Noting that T-duality untwists S^5 to CP^2 x S^1, we construct the duality chain: n=4 super Yang-Mills --> Type IIB superstring on AdS_5 x S^5 --> Type IIA superstring on AdS_5 x CP^2 x S^1 --> M-theory on AdS_5 x CP^2 x T^2. This provides another example of supersymmetry without supersymmetry: on AdS_5 x CP^2 x S^1, Type IIA supergravity has SU(3) x U(1) x U(1) x U(1) and N=0 supersymmetry but Type IIA string theory has SO(6) and N=8. The missing superpartners are provided by stringy winding modes. We also discuss IIB compactifications to AdS_5 with N=4, N=2 and N=0.