Fivebranes from gauge theory

TL;DR

This work develops a unified framework for a family of 16-supercharge gauge theories obtained by truncating N=4 SYM, and constructs their gravity duals through a droplet/electrostatic description analogous to LLM. It analyzes BPS and near-BPS sectors, showing how pp-wave limits yield universal plane-wave string dynamics near disk tips while vacuum-dependent details (disk number, spacing, and flux) control the interpolating functions and spectra. A second class of theories with non-central charges arises from compactifying transverse directions, leading to two-dimensional sigma models with H-flux and connections to 2D YM and 3D Chern-Simons theories, with AdS3 x S1 gravity duals in certain limits. The results illustrate a rich vacua structure, interpolate between weak and strong coupling, and reveal concrete matches between gauge theory spectra and string worldsheet dynamics across multiple compactifications and dualities.

Abstract

We study theories with sixteen supercharges and a discrete energy spectrum. One class of theories has symmetry group $SU(2|4)$. They arise as truncations of ${\cal N}=4$ super Yang Mills. They include the plane wave matrix model, 2+1 super Yang Mills on $R \times S^2$ and ${\cal N}=4$ super Yang Mills on $R \times S^3/Z_k$. We explain how to obtain their gravity duals in a unified way. We explore the regions of the geometry that are relevant for the study of some 1/2 BPS and near BPS states. This leads to a class of two dimensional (4,4) supersymmetric sigma models with non-zero $H$ flux, including a massive deformed WZW model. We show how to match some features of the string spectrum with the Yang Mills theory. The other class of theories are also connected to ${\cal N}=4$ super Yang Mills and arise by making some of the transverse scalars compact. Their vacua are characterized by a 2d Yang Mills theory or 3d Chern Simons theory. These theories realize peculiar superpoincare symmetry algebras in 2+1 or 1+1 dimensions with "non-central" charges. We finally discuss gravity duals of ${\cal N}=4$ super Yang Mills on $AdS_3 \times S^1$.

Figures (9)

• Figure 1: Starting from four dimensional ${\cal N}=4$ super Yang Mills and truncating by various subgroups of $SU(2)_L$ we get various theories with ${ \widetilde{SU}}(2|4)$ symmetry. We have indicated the diagrams in the $x_1,x_2$ space that determine their gravity solutions. The $x_1, x_2$ space is a cylinder, with the vertical lines identified for (b) and (c) and it is a torus for (a).
• Figure 2: Translational invariant configurations in the $x_1,x_2$ plane which give rise to various gravity solutions. The shaded regions indicate M2 regions and the unshaded ones indicate M5 regions. The two vertical lines are identified. In (a) we see the configuration corresponding to the vacuum of the 2+1 Yang Mills on $R\times S^2$ with unbroken gauge symmetry. In (b) we consider a configuration corresponding to a vacuum of the plane wave matrix model. In (c) we see a vacuum of the NS5 brane theory on $R \times S^5$. Finally, in (d) we have a droplet on a two torus in the $x_1,x_2$ plane. This corresponds to a vacuum of the ${\cal N}=4$ super Yang Mills on a $R \times S^3/Z_k$.
• Figure 3: Electrostatic problems corresponding to different droplet configurations. The shaded regions (M2 regions) correspond to disks and the unshaded regions map to $\rho =0$. Note that the $x_1$ direction in (a), (c) does not correspond to any variable in (b), (c). The rest of the $\rho, \eta$ plane corresponds to $y>0$ in the $x_2,y$ variables. In (a),(b) we see the configurations corresponding to a vacuum of 2+1 super Yang Mills on $R\times S^2$. In (c),(d) we see a configuration corresponding to a vacuum of ${\cal N}=4$ super Yang Mills on $R\times S^3/Z_k$. In (d) we have a periodic configuration of disks. The fact that it is periodic corresponds to the fact that we have also compactified the $x_2$ direction.
• Figure 4: In (a) we see a configuration which corresponds to a vacuum of 2+1 super Yang Mills on $R\times S^2$. In (b) we see the simplest vacuum of the theory corresponding to the NS5 brane on $R \times S^5$. In this case we have two infinite conducting disks and only the space between them is physically meaningful. In (c) we have another vacuum of the same theory. If the added disk is very small and close to the the top or bottom disks the solution looks like that of (b) with a few D0 branes added. In (d) we see a configuration corresponding to a vacuum of the plane wave matrix model. In this case the disk at $\eta=0$ is infinite and the solution contains only the region with $\eta \geq 0$. In (e) we have another vacuum of the plane wave matrix model with more disks.
• Figure 5: We see a configuration associated to a pair of disks. $d_i$ indicates the distance between the two nearby disks. The dashed line in the $\rho,\eta$ plane, together with the $S^2$ form a three cycle $\Sigma_3$ with the topology of an $S^3$. The dotted line, together with the $S^5$ form a six cycle $\Sigma_6$ with the topology of an $S^6$.