Integrable spin chain of superconformal U(M) × \overline{\mathopU(N)} ChernSimons theory
Abstract
Script N = 6 superconformal ChernSimons theory with gauge group U(M) × \overline{\mathopU(N)} is dual to N M2branes and (MN) fractional M2branes, equivalently, discrete 3form holonomy at Bbb C^{4}/Bbb Z_{k} orbifold singularity. We show that, much like its regular counterpart of M = N, the theory at planar limit have integrability structure in the conformal dimension spectrum of single trace operators. We first revisit the YangBaxter equation for a spin chain system associated with the single trace operators. We show that the integrability by itself does not preclude parity symmetry breaking. We construct twoparameter family of parity noninvariant, alternating spin chain Hamiltonian involving threesite interactions between 4 and bar 4 of SU(4)_{R}. At weak `t Hooft coupling, we study the ChernSimons theory perturbatively and calculate anomalous dimension of single trace operators up to two loops. The computation is essentially parallel to the regular case M = N. We find that resulting spin chain Hamiltonian matches with the Hamiltonian derived from YangBaxter equation, but to the one preserving parity symmetry. We give several intuitive explanations why the parity symmetry breaking is not detected in the ChernSimons spin chain Hamiltonian at perturbative level. We suggest that open spin chain, associated with open string excitations on giant gravitons or dibaryons, can detect discrete flat holonomy and hence parity symmetry breaking through boundary field.
 Publication:

Journal of High Energy Physics
 Pub Date:
 October 2008
 DOI:
 10.1088/11266708/2008/10/038
 arXiv:
 arXiv:0808.0170
 Bibcode:
 2008JHEP...10..038B
 Keywords:

 High Energy Physics  Theory
 EPrint:
 1+21 pages