2D Heisenberg model from rotating membrane

Wen, Wen-Yu

doi:10.1016/j.nuclphysb.2007.09.027

Cited by 5 publications

(2 citation statements)

References 28 publications

(35 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was also established that they can reproduce the continuous limit of the integrable SU(2) spin chain [24]. (See also [25].) Besides, giant magnon (GM) and single spike (SS) like energy-charge relations have been found [26,27,28].…”

Section: Introductionmentioning

confidence: 94%

Finite-size effects of membranes onAdS₄×S₇

Ahn¹,

Bozhilov²

2008

J. High Energy Phys.

View full text Add to dashboard Cite

We consider semi-classical solutions of membranes on the AdS 4 × S 7 background. This is supposed to be dual to the N = 6 super Chern-Simons theory with k = 1 in a planar limit recently proposed by Aharony, Bergmann, Jafferis, and Maldacena (ABJM). We have identified giant magnon and single spike states on the membrane by reducing them to the Neumamm -Rosochatius integrable system. We also connect these to the complex sine-Gordon integrable model. Based on this approach, we find finite-size membrane solutions and obtain their images in the complex sine-Gordon system along with the leading finite-size corrections to the energy-charge relations.

show abstract

Section: Introductionmentioning

confidence: 94%

Finite-size effects of membranes onAdS₄×S₇

Ahn¹,

Bozhilov²

2008

J. High Energy Phys.

View full text Add to dashboard Cite

show abstract

“…Note added: While writing this paper, we learn about the work [57] on the same subject. There, a rotating probe membrane in S 3 inside AdS 4 ×S 7 background of M-theory is studied.…”

Section: Discussionmentioning

confidence: 99%

Spin chain from membrane and the Neumann-Rosochatius integrable system

Bozhilov

2007

Phys. Rev. D

View full text Add to dashboard Cite

We find membrane configurations in AdS_4 x S^7, which correspond to the continuous limit of the SU(2) integrable spin chain, considered as a limit of the SU(3) spin chain, arising in N=4 SYM in four dimensions, dual to strings in AdS_5 x S^5. We also discuss the relationship with the Neumann-Rosochatius integrable system at the level of Lagrangians, comparing the string and membrane cases.Comment: LaTeX, 16 pages, no figures; v2: 17 pages, title changed, explanations and references added; v3: more explanations added; v4: typos fixed, to appear in Phys. Rev.

show abstract

Rotating membranes in AdS 4 × M 1,1,1

Kim

Lee

2010

J. High Energ. Phys.

View full text Add to dashboard Cite

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...

show abstract

2D Heisenberg model from rotating membrane

Cited by 5 publications

References 28 publications

Finite-size effects of membranes onAdS₄×S₇

Finite-size effects of membranes onAdS₄×S₇

Spin chain from membrane and the Neumann-Rosochatius integrable system

Rotating membranes in AdS 4 × M 1,1,1

Contact Info

Product

Resources

About

2D Heisenberg model from rotating membrane

Cited by 5 publications

References 28 publications

Finite-size effects of membranes onAdS4×S7

Finite-size effects of membranes onAdS4×S7

Spin chain from membrane and the Neumann-Rosochatius integrable system

Rotating membranes in AdS 4 × M 1,1,1

Contact Info

Product

Resources

About

Finite-size effects of membranes onAdS₄×S₇

Finite-size effects of membranes onAdS₄×S₇