Supersymmetric phases of AdS$_4$/CFT$_3$

TL;DR

This paper identifies an infinite family of supersymmetric phases in ABJM theory and their dual gravity solutions, revealing new partially deconfined states and matching free energies through large-N analysis.

Contribution

It introduces a novel family of supersymmetric phases in ABJM theory and constructs their dual gravitational solutions, extending the understanding of AdS4/CFT3 correspondence.

Findings

Found saddle-points labeled by roots of unity in superconformal index.

Calculated free energies matching gravitational solutions.

Discovered two saddles with same entropy as black hole causing oscillations.

Abstract

We exhibit an infinite family of supersymmetric phases in the three-dimensional ABJM superconformal field theory and the dual asymptotically AdS$_4$ gravity. They are interpreted as partially deconfined phases which generalize the confined/pure AdS phase and deconfined/supersymmetric black hole phase. Our analysis involves finding a family of saddle-points of the superconformal index labelled by rational points (equivalently, roots of unity), separately in the bulk and boundary theories. In the ABJM theory we calculate the free energy of each saddle by the large-$N$ asymptotic expansion of the superconformal index to all orders in perturbation theory near the saddle-point. We find that this expansion terminates at finite order. In the gravitational theory we show that there is a corresponding family of solutions, constructed by orbifolding the eleven-dimensional uplift of the supersymmetric black hole. The on-shell gravitational action of each orbifold agrees with the free energy of the corresponding saddle in the SCFT. We find that there are two saddles in the ABJM theory with the same entropy as the supersymmetric black hole, corresponding to the two primitive fourth-roots of unity, which causes macroscopic oscillations in the microcanonical index.