Non-planar ABJ Theory and Parity

Details Non-planar ABJ Theory and Parity Non-planar ABJ Theory and Parity

2009-03-19

arxiv.org/abs/0903.3354v2

Phys.Lett.B677:197-202,2009

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, 1 figure. v2: Typos fixed, minor clarifications

Scientific paper

10.1016/j.physletb.2009.05.021

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)xSU(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.

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