Non-planar ABJ Theory and Parity
arXiv:0903.3354 · doi:10.1016/j.physletb.2009.05.021
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.
11 pages, 1 figure. v2: Typos fixed, minor clarifications
References in corpus (20)
- N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
- The Bethe-Ansatz for N=4 Super Yang-Mills
- The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
- Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
- Fractional M2-branes
- Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence
- A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
- A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
- N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds
- The Bethe ansatz for superconformal Chern-Simons
- BMN Correlators and Operator Mixing in N=4 Super Yang-Mills Theory
- BMN Gauge Theory as a Quantum Mechanical System
- Integrable Spin Chain in Superconformal Chern-Simons Theory
- Two loop integrability for Chern-Simons theories with N=6 supersymmetry
- Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory
- Integrable Spin Chain of Superconformal U(M)xU(N) Chern-Simons Theory
- Splitting spinning strings in AdS/CFT
- BMN operators and string field theory
- Non-planar ABJM Theory and Integrability
- Quasilocality of joining/splitting strings from coherent states
Cited by in corpus (20)
- Summing Up All Genus Free Energy of ABJM Matrix Model
- Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
- Multiple Membranes in M-theory
- Chern-Simons-Matter Theory
- Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories
- Magnon dispersion to four loops in the ABJM and ABJ models
- Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
- Nonplanar Integrability: Beyond the SU(2) Sector
- From Schurs to Giants in ABJ(M)
- Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond
- Beyond the Planar Limit in ABJM
- Aspects of ABJ Theory
- On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group
- Non-anticommutative ABJ Theory
- Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds
- Note on Integrability of Marginally Deformed ABJ(M) Theories
- Nonplanar Integrability and Parity in ABJ Theory
- Wilson Loops from D-branes in AdS(4) X CP**3 with B-NS Holonomy
- Heavy Operators in Superconformal Chern-Simons Theory
- Polyakov Loops for the ABJ Theory