Eschenburg space as gravity dual of flavored N=4 Chern-Simons-matter theory

TL;DR

The paper identifies a gravity dual for a flavored 3D ${\mathcal N}=4$ Chern-Simons-matter theory as $AdS_4\times \tilde{\mathcal M}_7$ Eschenburg space, with the triple $(t_1,t_2,t_3)=(qN_F,pN_F,kpq)$ encoding flavor and brane data. It develops two parallel channels to probe the duality: field-theoretic entropy via a unitary matrix model and gravity-based entropy via M-theory (AdS-Schwarzschild) and IIA (flavor D6-branes) setups, revealing flavor-induced corrections scaling with the 't Hooft coupling as $\sqrt{\lambda}$ and confirming leading $N^{3/2}$ behavior in the gravity description. The work also examines KK spectra through the ${\mathcal N}=3$ superconformal index and analyzes mesonic and baryonic operators, using Eschenburg-space volumes to match operator dimensions and highlighting an outstanding di-baryon degeneracy issue. Overall, the results provide strong evidence that Eschenburg space serves as a valid gravity dual for the flavored ${\mathcal N}=4$ CSM theory and lay out concrete avenues for further tests via KK spectra and di-baryon counting.

Abstract

We find 3D flavored N=4 Chern-Simons-matter theory, a kind of N=3 SCFT, has a gravity dual AdS4xM7(t1,t2,t3) where three coprime parameters can be read off according to the number and charge of 5-branes in Type IIB setup. Because M7(t1,t2,t3) has been known in literatures as Eschenburg space, we exploit some of its properties to examine the correspondence between two sides.