Evidence for the Holographic dual of ${\cal N}=3$ Solution in Massive Type IIA

TL;DR

This paper provides evidence supporting the holographic duality between a specific ${ m AdS}_4$ supergravity solution in massive IIA theory and a three-dimensional ${ m N}=3$ superconformal field theory, through spectrum matching and free energy calculations.

Contribution

The authors compute the Kaluza-Klein spectrum and match it with dual operators, confirming the holographic duality for the ${ m N}=3$ solution and SCFT, and also compare free energies for consistency.

Findings

KK spectrum matches dual operators' quantum numbers

Spin-2 mode energies align with SCFT operators

Euclidean action and free energy agree in large N limit

Abstract

We calculate the Kaluza-Klein spectrum of spin-2 fluctuations around the ${\cal N}=3$ warped ${\rm AdS}_4\times M_6$ solution in massive IIA supergravity. This solution was conjectured to be dual to the $D=3$ ${\cal N}=3$ superconformal ${\rm SU}(N)$ Chern-Simons matter theory with level $k$ and 2 adjoint chiral multiplets. The ${\rm SO}(3)_R\times{\rm SO}(3)_D$ isometry of the ${\cal N}=3$ solution is identified with the ${\rm SU}(2)_F\times {\rm SU}(2)_{\cal R}$ global symmetry of the dual ${\cal N}=3$ SCFT. We show that the ${\rm SO}(3)_R\times{\rm SO}(3)_D$ quantum numbers and the ${\rm AdS}$ energies carried by the BPS spin-2 modes match precisely with those of the spin-2 gauge invariant operators in the short multiplets of operators in the ${\cal N}=3$ SCFT. We also compute the Euclidean action of the ${\cal N}=3$ solution and the free energy of the ${\cal N}=3$ SCFT on $S^3$, in the limit $N\gg k$. Remarkably, the results show a complete agreement.