A deformation of AdS_5 x S^5

TL;DR

Gauntlett, Gutowski, and Suryanarayana study a one-parameter deformation of $AdS_5\times S^5$ within $D=5$ minimal gauged supergravity, yielding a family of solutions that remain locally AdS but develop closed timelike curves for $f^2>1/(4l^2)$. They demonstrate a holographic dual to ${\cal N}=4$ SYM on a non-conformally flat boundary with nonzero $R$-currents, computing a finite holographic energy-momentum tensor across the CTC onset and identifying a boundary curvature structure with vanishing Euler and Weyl invariants. The five-dimensional solution uplifts to Type IIB supergravity preserving exactly two supersymmetries, confirmed by explicit Killing spinor projections, and this persists for uplifted $AdS_5$ black holes, providing insight into holography with CTCs and the microscopic interpretation of supersymmetric AdS$_5$ black hole entropy. The work highlights the interplay between boundary geometry, holographic renormalization, and preserved supersymmetry in deformed AdS/CFT contexts.

Abstract

We analyse a one parameter family of supersymmetric solutions of type IIB supergravity that includes AdS_5 x S^5. For small values of the parameter the solutions are causally well-behaved, but beyond a critical value closed timelike curves (CTC's) appear. The solutions are holographically dual to N=4 supersymmetric Yang-Mills theory on a non-conformally flat background with non-vanishing R-currents. We compute the holographic energy-momentum tensor for the spacetime and show that it remains finite even when the CTC's appear. The solutions, as well as the uplift of some recently discovered AdS_5 black hole solutions, are shown to preserve precisely two supersymmetries.