Un-twisting the NHEK with spectral flows

TL;DR

This work shows that the six-dimensional uplift of the near-horizon extremal Kerr (NHEK) geometry can be obtained from AdS3 × S3 by a chain of STU-like pseudo-dualities, with three complementary viewpoints: STU transformations, Melvin/T-duality sequences, and generalized spectral flows. It constructs an infinite family of asymptotically flat NHEK embeddings in string theory, parameterized by moduli at infinity, and demonstrates nonperturbative deformations of NHEK spacetimes in which flux wraps nontrivial cycles. The authors provide explicit transformation rules, matchings to Kerr-like data, and show how two generalized spectral flows generate the NHEK IR from D1-D5-p-KK seeds, including axion-ful generalizations. Finally, they discuss the microscopic implications for a dual field theory and outline how spectral-flow-related deformations may realize melvin-twisted D1-D5/D1-D5-pCFTs in the IR, along with bubbling branches of the moduli space.

Abstract

We show that the six-dimensional uplift of the five-dimensional Near-Horizon-Extremal-Kerr (NHEK) spacetime can be obtained from an AdS_3 X S^3 solution by a sequence of supergravity - but not string theory - dualities. We present three ways of viewing these pseudo-dualities: as a series of transformations in the STU model, as a combination of Melvin twists and T-dualities and, finally, as a sequence of two generalized spectral flows and a coordinate transformation. We then use these to find an infinite family of asymptotically flat embeddings of NHEK spacetimes in string theory, parameterized by the arbitrary values of the moduli at infinity. Our construction reveals the existence of non-perturbative deformations of asymptotically-NHEK spacetimes, which correspond to the bubbling of nontrivial cycles wrapped by flux, and paves the way for finding a microscopic field theory dual to NHEK which involves Melvin twists of the D1-D5 gauge theory. Our analysis also clarifies the meaning of the generalized spectral flow solution-generating techniques that have been recently employed in the literature.