Supersymmetric States in Large N Chern-Simons-Matter Theories

TL;DR

The paper investigates the spectrum of supersymmetric (BPS) states in large-N ${\cal N}=2$ and ${\cal N}=3$ Chern-Simons-matter theories with adjoint chiral multiplets, using ${\cal Z}$-minimization via localization and the superconformal index to map $R$-charges and single-trace spectra as functions of $\lambda$. It finds a rich set of fixed points with and without superpotential, including lines of fixed points for a single adjoint where high-spin towers appear, suggesting higher-spin or stringy duals; some theories (notably the ${\cal N}=3$ cases and certain ${\cal N}=2$ deformations) exhibit spectra compatible with supergravity KK towers, while others point to more exotic duals. The study also derives comprehensive decompositions of ${\cal N}=3$ into ${\cal N}=2$ representations and provides conjectured cohomology-based spectra tied to the computed indices, including explicit results for specific $g$ and superpotentials. Overall, the work maps how BPS spectra and $R$-charges evolve with coupling, clarifying when traditional gravity duals might arise and when higher-spin or stringy descriptions are required. Its results illuminate the landscape of AdS4/CFT3 dualities in theories with minimal matter content and set the stage for further construction of explicit holographic duals.

Abstract

In this paper we study the spectrum of BPS operators/states in N=2 superconformal U(N) Chern-Simons-matter theories with adjoint chiral matter fields, with and without superpotential. The superconformal indices and conjectures on the full supersymmetric spectrum of the theories in the large N limit with up to two adjoint matter fields are presented. Our results suggest that some of these theories may have supergravity duals at strong coupling, while some others may be dual to higher spin theories of gravity at strong coupling. For the N=2 theory with no superpotential, we study the renormalization of R-charge at finite 't Hooft coupling using "Z-minimization". A particularly intriguing result is found in the case of one adjoint matter.

Figures (14)

• Figure 1: $h$ vs. $\lambda$ for $g=3$, $Ne=20$ and $Ne=30$. In the figure on the left, $\lambda$ varies from $0$ to $2$. In the figure on the right $\lambda$ varies from 2 to 7. Note that $h(\lambda)$ scale is different in the two figures. $R$-charge saturates to around $0.354$. While we have not performed a serious error estimate, it seems unlikely to us that the error in this asymptote value exceeds $\pm 0.01$.
• Figure 2: $h$ vs. $\lambda$ for $g=2$, $Ne=20$ and $Ne=30$. In the figure on the left, $\lambda$ varies from $0$ to $2$. In the figure on the right $\lambda$ varies from $2$ to $7$. Note that $h(\lambda)$ scale is different in the two figures. $R$-charge saturates to around $0.274$.While we have not performed a serious error estimate, it seems unlikely to us that the error in this asymptote value exceeds $\pm 0.01$.
• Figure 3: $h$ vs. $\lambda$ for $g=3$ and $Ne=30$. The blue line is large g perturbation theory prediction. $R$-charge saturates to around $0.354$. While we have not performed a serious error estimate, it seems unlikely to us that the error in this asymptote value exceeds $\pm 0.01$.
• Figure 4: $h$ vs. $\lambda$ for $g=1$. Blue line is best fit of the data points to the form $\frac{\alpha}{\beta+\lambda}$. The red curve is $\frac{1}{2(1+\lambda)}$.
• Figure 5: Eigenvalue distribution for Ne=90 at $\lambda=11$.