Integrable systems from membranes on AdS 4 × S 7

et al. 2011

J. High Energ. Phys.

Seven-dimensional inhomogeneous Sasaki-Einstein manifolds Y p,k (KE 4 ) present a challenging example of AdS/CFT correspondence. At present, their field theory duals for KE 4 = CP 2 base are proposed only within a restricted range 3p/2 ≤ k ≤ 2p as N = 2 quiver Chern-Simons-matter theories with SU (N ) × SU (N ) × SU (N ) gauge group, nine bifundamental chiral multiplets interacting through a cubic superpotential. To further elucidate this correspondence, we use particle approximation both at classical and quantum level. We setup a concrete AdS/CFT mapping of conserved quantities using geodesic motions, and turn to solutions of scalar Laplace equation in Y p,k . The eigenmodes also provide an interesting subset of Kaluza-Klein spectrum for D = 11 supergravity in AdS 4 ×Y p,k , and are dual to protected operators written in terms of matter multiplets in the dual conformal field theory.

“…Nontrivial classical membrane solutions in AdS 4 × S 7 which are studied in the context of Chern-Simons duals can be found e.g. [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

M-theory and seven-dimensional inhomogeneous Sasaki-Einstein manifolds

et al. 2011

J. High Energ. Phys.

Rotating membranes in AdS 4 × M 1,1,1

Lee

2010

J. High Energ. Phys.

Motivated by the recent progress on gravity duals of supersymmetric Chern-Simons matter theories, we consider classical membrane solutions in AdS 4 × M 1,1,1 . In particular, we present several types of exact solutions rotating in the Sasaki-Einstein 7-manifold whose isometry is SU (3)× SU (2) × U (1). We analyze the limiting behavior of macroscopic membranes and discuss how one can identify the dual operators and the implications of our result on their conformal dimensions.Recently we have seen great progress on our understanding of field theory duals for various AdS 4 backgrounds in string or M-theory. Most notable is the discovery of N = 6 supersymmetric Chern-Simons-matter theories which provide conformal field theory duals for AdS 4 ×S 7 /Z k [1]. This three-dimensional field theory has U (N )×U (N ) gauge symmetry with Chern-Simons (CS) kinetic terms of quantized level (k, −k). The interaction is also described by a quartic superpotential. In fact, as a quiver guage theory the data is exactly the same as the well-known conifold theory in four-dimensions [2], apart from the extra information on CS levels.It is an important issue how to generalize this duality to other backgrounds AdS 4 × Y 7 .In this paper, we are particularly interested in the examples which preserve N = 2, or eight supercharges. Mathematically Y 7 is then required to be Sasaki-Einstein, and we choose the so-called M 1,1,1 space [3]. It is constructed as U (1)-fibration over a six-dimensional Kähler-Einstein manifold CP 2 × CP 1 . The dual field theory is thus expected to enjoy SU (3) × SU (2) × U (1) global symmetry, where the U (1) part is the usual R-symmetry.In order to establish the duality relation, we need the Kaluza-Klein spectrum of 11dimensional supergravity on M 1,1,1 . It is computed in [4], and a three-dimensional quiver gauge theory was proposed as the dual of AdS 4 ×M 1,1,1 in [5], but a consistent superpotential could not be written down. Now with the new insight of Chern-Simons theories without the usual second-order Maxwell-type kinetic terms, we have a more reliable candidate. The CS duals have been given for a general class of the so-called Y p,q (CP 2 ) metrics [6,7]. For our interest here the relevant one has gauge symmetry U (N ) 3 with CS levels (k, k, −2k). The dual geometry is conjectured to be orbifolds AdS 4 × M 1,1,1 /Z k . A cubic superpotential, with conformal dimension two, is written in terms of the nine bifundamental chiral multipelts.The AdS/CFT duality relation implies that the M-theory spectrum in AdS 4 × M 1,1,1 /Z k gives the space of gauge singlet operators on the quiver gauge theory side. Instead of trying to quantize the supermembrane theory in a curved background, one can study classical membrane solutions and compare the result to field theory operators with large conformal dimensions. This is the strategy advocated first in [8] for AdS 5 × S 5 , and has been extensively used in the study of AdS/CFT relations. Quantitative results for non-supersymmetric solutions lead to very non-trivial checks of...

Probing non-toric geometry with rotating membranes

Lee

et al. 2010

Nuclear Physics B

Recently Martelli and Sparks presented the first non-toric AdS 4 /CFT 3 duality relation between M-theory on AdS 4 × V 5,2 /Z k and a class of three-dimensional N = 2 quiver Chern-Simons-matter theories. V 5,2 is a seven-dimensional homogeneneous Sasaki-Einstein manifold with isometry groupThe dual field theory is described by the A 1 quiver, U (N ) k × U (N ) −k gauge group, four bifundamentals, two adjoint chiral multiplets interacting via a cubic superpotential. We explore this proposal by studying various classical membrane solutions moving in V 5,2 . Rotating membrane solutions of folded, wrapped, spike, and giant magnon types are presented with their dispersion relations. We also discuss their dual operators in the Chern-Simons-matter theory.