Integrable Spin Chain in Superconformal Chern-Simons Theory
Jul, 200842 pages
Published in:
- JHEP 10 (2008) 053
e-Print:
- 0807.2063 [hep-th]
Report number:
- SNUST-080701
View in:
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Abstract: (arXiv)
We study integrability of N=6 superconformal Chern-Simons theory proposed as gauge theory dual to Type IIA string theory on AdS4 x CP3 that is inherent to conformal dimension spectrum of single trace operators at planar limit. At strong `t Hooft coupling, the spectrum is obtained from excitation energy of noninteracting superstring on supercoset OSp(6|2,2)/SO(3,1)xSU(3)xU(1). We argue that the worldsheet theory is integrable by utilizing well-known results concerning sigma model on symmetric space. With R-symmetry group SU(4), we also solve relevant Yang-Baxter equation for a spin chain system associated with the single trace operators. From the solution, we construct alternating spin chain Hamiltonian involving three-site interactions between fundamental and antifundamental of SU(4). At weak `t Hooft coupling, we study gauge theory perturbatively, and calculate action of dilatation operator to single trace operators up to two loops. To ensure consistency, we computed all relevant Feynman diagrams contributing to the dilatation opeator. We find that resulting spin chain Hamiltonian matches with the Hamiltonian derived from Yang-Baxter equation. We further study new issues arising from the shortest gauge invariant operators of length 2 with SU(4) quantum numbers (15, 1). We observe that `wrapping interactions' are present and compute the true spectrum. We also find that scaling dimension computed naively from alternating spin chain Hamiltonian coincides with the true spectrum. We solve Bethe ansatz equations for small number of excitations, and find indications of correlation between excitations of fundamentals and anti-fundamentals, and of nonexistence of mesonic bound-state.Note:
- 1+38 pages, 9 .eps figures
- spin: chain
- scaling: dimension
- operator: dilation
- group: SU(4)
- excited state: energy
- integrability
- field theory: conformal
- gauge field theory
- superstring
- string model
References(71)
Figures(8)