  Symplectic potentials are presented for a wide class of five dimensional
toric Sasaki-Einstein manifolds, including L^{a,b,c} which was recently
constructed by Cvetic et al. The spectrum of the scalar Laplacian on L^{a,b,c}
is also studied. The eigenvalue problem leads to two Heun's differential
equations and the exponents at regular singularities are directly related to
toric data. By combining knowledge of the explicit symplectic potential and the
exponents, we show that the ground states, or equivalently holomorphic
functions, have one-to-one correspondence with integral lattice points in the
convex polyhedral cone. The scaling dimensions of the holomorphic functions are
simply given by scalar products of the Reeb vector and the integral vectors,
which are consistent with R-charges of BPS states in the dual quiver gauge
theories.

High Energy Physics - Theory