Spiky Strings on AdS (4) X CP** 3

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Spiky Strings on AdS (4) X CP** 3

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Nov 7, 2008 - We consider rigid rotating fundamental string in the SU(2)×SU(2) .... When ψ = constant, θ1 = θ2 and φ1 = φ2 gives Γα = 0, which satisfies the second equation .... where we replace the string tension T with the 't Hooft coupling λ. .... Note that for the infinite size limit, zmin → 0, the second term in the right.

0807.2559

arXiv:0807.2559v3 [hep-th] 7 Nov 2008

Preprint typeset in JHEP style - HYPER VERSION

Spiky Strings on AdS4 × CP3

Bum-Hoon Lee a , Kamal L. Panigrahi

b

and Chanyong Park

a,c

a

Center for Quantum Spacetime (CQUeST), Sogang University, Seoul 121-742, Korea

b

Department of Physics, Indian Institute of Technology Guwahati, Guwahati-781 039, India

c

National Institute for Mathematical Sciences, Daejeon 305-340, Korea

E-mail: [email protected], [email protected], [email protected]

Abstract: We study a giant magnon and a spike solution for the string rotating on AdS4 ×CP3 geometry. We consider rigid rotating fundamental string in the SU (2)×SU (2) sector inside the CP3 and find out the general form of all the conserved charges. We find out the dispersion relation corresponding to both the known giant magnon and the new spike solutions. We further study the finite size correction in both cases. Keywords: AdS-CFT Correspondence.

Contents 1. Introduction and Summary

1

2. Rotating strings on R × S 2 × S 2

2

3. Giant magnon and Spike solutions 3.1 Giant magnon solution 3.2 Spike solution

6 7 7

4. Finite Size effects

8

5. Discussions

11

1. Introduction and Summary The AdS/CFT duality [1] relates type IIB string theory on AdS5 × S5 with N = 4 superconformal Yang-Mills (SYM) theory, and it has been celebrated in the last decade as one of the exact duality between string and gauge theory. Recently there has been a lot of works devoted towards the understanding of the worldvolume dynamics of multiple M2-branes, initiated by Bagger, Lambert and Gustavsson [2] based on the structure of Lie 3-algebra. In this new development of understanding of the worldvolume theory of coincident M-branes in M-theory, a new class of conformal invariant 2+1 dimensional field theories has been found out. Based on this Aharony, Bergman, Jafferis and Maldacena (ABJM) [3] proposed a new gauge-string duality between N = 6 Chern-Simons theory and type IIA string theory on AdS4 ×CP3 . More precisely, ABJM theory has been conjectured to be dual to M-theory on AdS4 × S 7 /Zk with N units of four-form flux which for k