Non-planar ABJ Theory and Parity

Pawel Caputa; Charlotte Kristjansen; Konstantinos Zoubos

doi:10.1016/j.physletb.2009.05.021

Non-planar ABJ Theory and Parity

Pawel Caputa, Charlotte Kristjansen, Konstantinos Zoubos

Theoretical high energy, astroparticle and gravitational physics

19 Citations (Scopus)

30 Downloads (Pure)

Abstract

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.

Original language	English
Journal	Physics Letters B
Volume	677
Issue number	3-4
Pages (from-to)	197-202
ISSN	0370-2693
DOIs	https://doi.org/10.1016/j.physletb.2009.05.021
Publication status	Published - 19 Mar 2009

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title = "Non-planar ABJ Theory and Parity",

abstract = "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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T1 - Non-planar ABJ Theory and Parity

AU - Caputa, Pawel

AU - Kristjansen, Charlotte

AU - Zoubos, Konstantinos

N1 - 11 pages, 1 figure. v2: Typos fixed, minor clarifications

PY - 2009/3/19

Y1 - 2009/3/19

N2 - 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.

AB - 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.

KW - hep-th

U2 - 10.1016/j.physletb.2009.05.021

DO - 10.1016/j.physletb.2009.05.021

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JO - Physics Letters B: Particle Physics, Nuclear Physics and Cosmology

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