Abstract:

In this talk, I will discuss how quasinormal modes of certain black holes can be studied utilising the two-dimensional conformal field theory (2D CFT) and their connection to four-dimensional N=2 supersymmetric field theories. This serves as an example of the interesting interplay between black hole physics, 2D CFTs, and 4D N=2 theories, where insights from one domain illuminate the others. We will review the correspondences and the dictionaries. I will show how to solve the connection problem of second-order linear ODEs of Fuchsian type coming from quiver gauge theories or corresponding black hole perturbation theories in terms of the crossing symmetry of the 2d CFT. This is a generalization of the Heun case studied in Bonelli-Iossa-Lichtig-Tanzini. In particular, the connection coefficients are expressed in terms of a special function defined in 4D N=2 theories, which is the Nekrasov-Shatashvili function. We will show an example of the 2nd order ODE with 5 regular singularities and its application to scalar perturbations Schwarzschild-AdS7 black hole.