From Heun to Painlev\'e on Sasaki-Einstein Spaces and Their Confluent Limits

V. Avramov; H. Dimov; M. Radomirov; R. C. Rashkov; T. Vetsov

From Heun to Painlev\'e on Sasaki-Einstein Spaces and Their Confluent Limits

High Energy Physics - Theory 2023-02-17 v1 Mathematical Physics math.MP

Authors: V. Avramov , H. Dimov , M. Radomirov , R. C. Rashkov , T. Vetsov

Abstract

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 $^{p,q}$ , 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 $^{p,p}$ , T $^{1,1} / \mathbb{Z}_2$ and Y $^{\infty, q}$ .

Keywords

heun equation painlevé vi sasaki-einstein spaces isomonodromic deformations confluent limits holography

Cite

@article{arxiv.2302.08213,
  title  = {From Heun to Painlev\'e on Sasaki-Einstein Spaces and Their Confluent Limits},
  author = {V. Avramov and H. Dimov and M. Radomirov and R. C. Rashkov and T. Vetsov},
  journal= {arXiv preprint arXiv:2302.08213},
  year   = {2023}
}

Comments

32 pages, three figures

From Heun to Painlev\'e on Sasaki-Einstein Spaces and Their Confluent Limits

Abstract

Keywords

Cite

Comments

Related papers