Integrable spin chain in superconformal Chern-Simons theory

By D. Bak, S. Rey. 2008

178 citations recorded by the source corpus.

N = 6 superconformal Chern-Simons theory was proposed as gauge theory dual to Type IIA string theory on AdS4 ⊗ CP 3 . We study integrability of the theory from conformal dimension spectrum of single trace operators at planar limit. At strong 't Hooft coupling, the spectrum is obtained from excitation energy of free superstring on OSp(6|4; R)/SO(3,1) × SU(3) × U(1) supercoset. We recall that the worldsheet theory is integrable classically 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 con- struct alternating spin chain Hamiltonian involving three-site interactions between 4 and 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 TrY I Y † J = (15,1). We observe that 'wrapping interactions' are present, compute the true spectrum and find that the spectrum agrees with prediction from supersymmetry. We also find that scaling dimension computed naively from alternating spin chain Hamilto- nian coincides with the true spectrum. We solve Bethe ansatz equations for small number of excitations, and find indications of correlation between excitations of 4's and 4's and of nonexistence of mesonic (44) bound-state.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ba1d106dfea5c5f98ad68018b57ed1e1480f100f

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Citations in the corpus

Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal (2008, background): “This is for a good reason, as both the perturbative gauge theory and the dual free string theory appear to be integrable (as was partially verified at two-loop level in gauge theory — namely in the scalar sector [2] (see also [3]) — and at the classical level in string theory [4, 5]).”
Three-dimensional N=6 SCFT's and their membrane dynamics (2008, background): “A notable feature of the string theory limit of the ABJM theory, whose sigma model was studied in [14, 15] and, using a covariant formulation, in [16], is that it appears to be integrable [17, 18] (see also [19, 20]).”
Symmetries of Tree-level Scattering Amplitudes in N = 6 Superconformal Chern{Simons Theory (2010, background): “In the study of the spectrum on both sides of these two correspondences, the discovery of integrability [3–9] in the planar limit has been of crucial importance, and has lead to the belief that the planar theories might be exactly solvable.”
Semiclassical quantization of spinning strings in AdS4 × ℂℙ3 (2008, background): “Complementary, the planar superconformal Chern-Simons theory appears to be integrable at leading order in the weak coupling expansion [8, 9, 10].”
AdS4/CFT3 at one loop (2008, background): “A very interesting aspect of these N = 6 Chern-Simons-matter theories is that they seem to be integrable in the scalar sector [3, 4].”
Spinning strings at one-loop in AdS(4) x P**3 (2008, methodology): “The dilatation operator of the N = 6 Chern-Simons theory was shown [16, 18], to leading order in the scalar sector, to be equivalent to the Hamiltonian of an integrable (alternating) spin chain.”
Wilson loops in superconformal Chern-Simons theory and fundamental strings in Anti-de Sitter supergravity dual (2008, methodology): “In appendix C, we recapitulate the one-loop vacuum polarization in ABJM theory, obtained first in [ 19 ].”