An Isomonodromic Approach to Scalar Fields on Sasaki-Einstein Spaces Y^{p, q}

In this study, we investigate the Schrodinger equation equation for scalar particles on the Y-p,Y-q. An equation of general Heun type is obtained for one of the coordinates and its associated Painleve VI equation is derived. Consequently, we take some particular limits of the Y-p,Y-q geometry, which result in a coalescence of singularities of the equation of motion. Finally, the associated isomondromic flows are examined.