On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group

TL;DR

This paper investigates the spectral problem of N=4 SYM with orthogonal and symplectic gauge groups, revealing unique non-planar effects and testing integrability of 1/N corrections via Bethe ansatz, with implications for dual string theories on orientifold backgrounds.

Contribution

It identifies novel non-planar effects in SO(N) and Sp(N) gauge groups and demonstrates the potential for integrability tests of 1/N corrections using Bethe ansatz methods.

Findings

Non-planar 1/N corrections originate from a term acting inside a single spin chain.

Standard Bethe ansatz methods can test the integrability of these corrections.

Dual string theory is on the orientifold AdS5xRP5 background.

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.