I-odd sector of the Klebanov-Strassler theory

The Klebanov-Strassler background is invariant under the ₂ symmetry , which acts by exchanging the bi-fundamental fields A and B, accompanied by the charge conjugation. We study the background perturbations in the -odd sector and find an exhaustive list of bosonic states invariant under the global SU(2) × SU(2) symmetry. In addition to the scalars identified in an earlier publication arXiv: 0712.4404 we find 7 families of massive states of spin 1. Together with the spin 0 states they form 3 families of massive vector multiplets and 2 families of massive gravitino multiplets, containing a vector, a pseudovector and fermions of spin 3/2 and 1/2. In the conformal Klebanov-Witten case these -odd particles belong to the = 1 superconformal Vector Multiplet I and Gravitino Multiplets II and IV. The operators dual to the -odd singlet sector include those without bi-fundamental fields making an interesting connection with the pure = 1 SYM theory. We calculate the mass spectrum of the corresponding glueballs numerically and discuss possible applications of our results.