Mass-deformed ABJM and Black Holes in AdS$_4$

TL;DR

This work establishes a precise holographic match between the topologically twisted index of the mass-deformed ABJM theory (mABJM) and the entropy of new supersymmetric dyonic and magnetic black holes in a four-dimensional maximal gauged supergravity that uplifts to M-theory. By constructing a U(1)^{3}-invariant truncation and analyzing both near-horizon AdS$_2\times\Sigma_g$ geometries and fully interpolating BH solutions, the authors map horizon data to extremal fugacities in the field theory and show that the large-$N$ twisted index reproduces BH entropy. They also demonstrate a duality between ABJM/STU and mABJM/W theories, including the dyonic generalization and the role of the hypermultiplet, providing a unified framework for entropy counting via supersymmetric localization. The results extend the microstate counting program in AdS$_4$ to the Warner vacuum, offering new insights into wrapped M2-brane configurations and hinting at further generalizations and uplifts in M-theory.

Abstract

We find a class of new supersymmetric dyonic black holes in four-dimensional maximal gauged supergravity which are asymptotic to the ${\rm SU(3)}\times {\rm U(1)}$ invariant AdS$_4$ Warner vacuum. These black holes can be embedded in eleven-dimensional supergravity where they describe the backreaction of M2-branes wrapped on a Riemann surface. The holographic dual description of these supergravity backgrounds is given by a partial topological twist on a Riemann surface of a three-dimensional $\mathcal{N}=2$ SCFT that is obtained by a mass-deformation of the ABJM theory. We compute explicitly the topologically twisted index of this SCFT and show that it accounts for the entropy of the black holes.

Figures (7)

• Figure 1: Magnetically charged AdS$_4$ black holes: Formal relations between the free energy, $F_{S^3}$, the twisted topological index, $\mathcal{I}_M$, and the black hole entropy, $S_{\rm BH}$. The operations along the arrows are: MD - mass deformation, TT - topological twist, CE - constrained extremization.
• Figure 2: Dyonic AdS$_4$ black holes. Formal relations between the topological twisted index, $\mathcal{I}_M$, the dyonic twisted index, $\mathcal{I}_D$, and the black hole entropy, $S_{\rm BH}$. The operations along arrows are: MD - mass defomration, LT - Legendre transform, CER - constrained extremization with reality conditions.
• Figure 3: The range of magnetic fluxes giving rise to regular AdS$_2\times\Sigma_{\frak{g}}$ solutions.
• Figure 4: Eigenvalues, $\Lambda_m$, of $M_{nm}$ as a function of $\mathfrak{n}$.
• Figure 5: Examples of scalar profiles for $\frak{n}=1/4$ fine tuned to approach the Warner AdS$_4$ fixed point. The dashed lines correspond to the fixed point values for the scalars given in \ref{['cpwz']}.