2009/03/31 by Pawel Caputa, Paweł Caputa, Charlotte Kristjansen +1 · 28 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Invariant (physics) #Mathematical physics #Parity (physics) #Physics #Physics of Superconductivity and Magnetism #Planar #Quantum many-body systems #Quantum mechanics #hep-th
paper · pdf · doi:10.1016/j.physletb.2009.05.021
published in Physics Letters B 677(3-4), 197-202 (Elsevier BV) · 11 pages, 1 figure. v2: Typos fixed, minor clarifications
arxiv created 2009/04/14 · openalex publication_date 2009/05/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
While the ABJ Chern–Simons-matter theory and its string theory dual manifestly lack parity invariance, no sign of parity violation has so far been observed on the weak coupling spin chain side. In particular, the planar two-loop dilatation generator of ABJ theory is parity invariant. In this Letter we derive the non-planar part of the two-loop dilatation generator of ABJ theory in its SU(2)×SU(2) sub-sector. Applying the dilatation generator to short operators, we explicitly demonstrate that, for operators carrying excitations on both spin chains, the non-planar part breaks parity invariance. For operators with only one type of excitation, however, parity remains conserved at the non-planar level. We furthermore observe that, as for ABJM theory, the degeneracy between planar parity pairs is lifted when non-planar corrections are taken into account.