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We consider the partition function of the boundary $OSp(2S+2|2S)$ coset sigmamodel on an annulus, based on the lattice regularization introduced in thecompanion paper. Using results for the action of $OSp(2S+2|2S)$ and $B_L(2)$ onthe corresponding spin chain, as well as mini-superspace and small $g_\sigma^2$calculations, we conjecture the full spectrum and set of degeneracies on theentire critical line. Potential relationship with the $OSp(2S+2|2S)$Gross-Neveu model is also discussed.

A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part II: The boundary spectrum