On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group
arXiv:1005.2611 · doi:10.1007/JHEP10(2010)082
Abstract
We study the spectral problem of N=4 SYM with gauge group SO(N) and Sp(N). At the planar level, the difference to the case of gauge group SU(N) is only due to certain states being projected out, however at the non-planar level novel effects appear: While 1/N-corrections in the SU(N) case are always associated with splitting and joining of spin chains, this is not so for SO(N) and Sp(N). Here the leading 1/N-corrections, which are due to non-orientable Feynman diagrams in the field theory, originate from a term in the dilatation operator which acts inside a single spin chain. This makes it possible to test for integrability of the leading 1/N-corrections by standard (Bethe ansatz) means and we carry out various such tests. For orthogonal and symplectic gauge group the dual string theory lives on the orientifold AdS5xRP5. We discuss various issues related to semi-classical strings on this background.
25 pages, 3 figures. v2: Minor clarifications, section 5 expanded
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- Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
- Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
- Operators, Correlators and Free Fermions for SO(N) and Sp(N)
- A basis for large operators in N=4 SYM with orthogonal gauge group
- Crosscap States in Integrable Field Theories and Spin Chains
- From Schurs to Giants in ABJ(M)
- SO(N) restricted Schur polynomials
- Negative anomalous dimensions in N=4 SYM
- Restricted Schurs and correlators for SO(N) and Sp(N)
- Orthogonal Schurs for Classical Gauge Groups
- Novel charges in CFT's
- Multi-trace Correlators from Permutations as Moduli Space
- Integrability and Conformal Blocks for Surface Defects in SYM