Fivebranes from gauge theory

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 $AdS_3 \times S^1$.Comment: 50+24 pages, 9 figures, latex. v2: typos corrected, references adde

Phase transitions of largeNorbifold gauge theories

“…Moreover, the Casimir energy does not depend on the indices I, J, and this means that the Casimir energy is the same for all choices of holonomy (n 0 , · · · , n k−1 ). This is consistent with the argument in [6] that the vacua with different holonomy are degenerated at zero temperature. Notice that the Casimir energy…”

“…26 Other interesting theories are the plane wave matrix model [41] and (2+1) dimensional super Yang-Mills theory on R × S 2 , which are obtained by truncating the N = 4 YangMills theory on R × S 3 like our orbifold theory. These models share the same symmetry SU(2|4) at zero temperature, and the gravity dual of these models was studied in [6]. The thermodynamics of plane wave matrix model has been studied in [42,43,44,45,46], and, in particular, the different vacua was compared in [46].…”

“…Our interest is on the orbifold gauge theories with holonomy along the non-trivial cycle, where the existence of the holonomy (n 0 , · · · , n k−1 ) breaks the gauge symmetry into G = k−1 I=0 U(n I ). 6 With respect to the broken gauge group, the states are in the adjoint representation for U(n I ) or in the bi-fundamental representation (n I ,n J ) for U(n I ) × U(n J ).…”

“…The projection into the orbifold invariant modes is 6 The diagonal U (1) parts of each U (n I ) may be decoupled from the rest, but the difference can be ignored when n I are very large. See, however, appendix B for the case of an index.…”

“…22 It was shown in [6] that the dual geometries are also labelled by the integers (n 0 , · · · , n k−1 ) at zero temperature. They discussed how to construct these geometries, where the NS5-branes are replaced by flux and the back-reaction of the flux is taken into account.…”