Precision test of AdS$_6$/CFT$_5$ in Type IIB

TL;DR

This work obtains the partition functions and central charges in gauge theory deformations of the SCFTs and extrapolates the results to the conformal fixed points, providing strong support for the proposed dualities of AdS/CFT.

Abstract

Large classes of warped AdS$_6$ solutions were constructed recently in Type IIB supergravity, and identified as holographic duals for five-dimensional superconformal field theories realized by $(p,q)$ five-brane webs. We confront holographic results for the five sphere partition functions obtained from these solutions with computations for the putative dual field theories. We obtain the sphere partition functions and conformal central charges in gauge theory deformations of the superconformal field theories numerically using supersymmetric localization, and extrapolate the results to the conformal fixed points. In the appropriate large $N$ limits, the results match precisely to the supergravity computations, providing strong support for the proposed dualities.

Figures (6)

• Figure 1: Five-brane webs for the $T_N$ theory with $N=3$ on the left hand side and for the $\#_{N,M}$ theory with $N=5$, $M=4$ on the right hand side. The brane webs show relevant deformations of the superconformal field theories.
• Figure 2: The left hand side shows an overlay of the numerical results for the five-sphere partition functions $-F_{\rm S^{5}}^{T_N}$ of the $T_N$ theories with the least-squares fit to a degree four polynomial. The right hand side depicts the same for the conformal central charge $C_T^{T_N}$.
• Figure 3: The curves on the left hand side show the fit to the five-sphere partition functions $-F_{\rm S^{5}}^{\#_{N,M}}$ for the $\#_{N,M}$ theories, (\ref{['eq:hash-fit']}) with (\ref{['eq:hash-fit-parms']}), as functions of $N$ for a representative set of fixed $M$. The numerical results are shown as dots, and the fit functions as dashed curves. The agreement for the remaining values of $M$ is similarly precise. Analogous plots for $C^{\#_{N,M}}_T$ are shown on the right hand side.
• Figure 4: On the left hand side the numerically obtained finite-$N$ results for the five-sphere partition function of the $T_N$ theories as orange points, and the supergravity result as dashed line. On the right hand side the analogous plot for $C_T$.
• Figure 5: On the left hand side the results for $-F_{\rm S^{5}}^{\#_{N,M}}$ discussed in Section \ref{['sec:num-results']} for a selection of fixed $M$. The dashed lines show the supergravity results for the corresponding fixed $M$. The plots for the remaining values of $M$ similarly show precise agreement. On the right hand side we show the same plot for the conformal central charge.