10 research outputs found
From Heun to Painlev\'e on Sasaki-Einstein Spaces and Their Confluent Limits
The aim of this paper is to study the effect of isomonodromic deformations of
the evolution of scalar fields in Sasaki-Einstein spaces in the context of
holography. Here we analyze the monodromy data of the general Heun equation,
resulting from a scalar on Y, thus obtaining the corresponding
Painlev\'e VI equation. Furthermore we have considered limits leading to a
coalescence of singularities, which in turn transform the original Painlev\'e
VI equation, to one of lower rank. The confluent limits we have considered are
Y, T and Y.Comment: 32 pages, three figure