Integrable spin chain of superconformal U(M) × U(N)} Chern-Simons theory

Dongsu Bak, Dongmin Gang, Soo Jong Rey

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


N = 6 superconformal Chern-Simons theory with gauge group U(M) × U(N)ℳ is dual to N M2-branes and (M-N) fractional M2-branes, equivalently, discrete 3-form holonomy at ℂ 4/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 Yang-Baxter 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 two-parameter family of parity non-invariant, alternating spin chain Hamiltonian involving three-site interactions between 4 and 4ℳ of SU(4) R. At weak 't Hooft coupling, we study the Chern-Simons 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 Yang-Baxter equation, but to the one preserving parity symmetry. We give several intuitive explanations why the parity symmetry breaking is not detected in the Chern-Simons 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.

Original languageEnglish
Article number038
JournalJournal of High Energy Physics
Issue number10
StatePublished - 1 Oct 2008


  • AdS-CFT correspondence
  • Chern-simons theories
  • Integrable field theories


Dive into the research topics of 'Integrable spin chain of superconformal U(M) × U(N)} Chern-Simons theory'. Together they form a unique fingerprint.

Cite this