Canonical Coordinates and Meson Spectra for Scalar Deformed N=4 SYM from the AdS/CFT Correspondence

Five supersymmetric scalar deformations of the AdS_5xS^5 geometry are investigated. By switching on condensates for the scalars in the N=4 multiplet with a form which preserves a subgroup of the original R-symmetry, disk and sphere configurations of D3-branes are formed in the dual supergravity background. The analytic, canonical metric for each geometry is formulated and the singularity structure is studied. Quarks are introduced into two of the corresponding field theories using D7-brane probes and the pseudoscalar meson spectrum is calculated. For one of the condensate configurations, a mass gap is found and shown analytically to be present in the massless limit. It is also found that there is a stepped spectrum with eigenstate degeneracy in the limit of small quark masses. In the case of a second, similar deformation, it is necessary to understand the full D3-D7 brane interaction to study the limit of small quark masses. It is seen that simple solutions to the equations of motion for the other three geometries are unlikely to exist.