Speaker
Description
We derive the general rules of functional integration in the theories of Schwarzian type,
thus completing the elaboration of Schwarzian functional integrals calculus.
The Schwarzian functional integrals has played a role in many areas of quantum physics.
In recent decades it has appeared in the quantum mechanical model of Majorana fermions with a random interaction (Sachdev-Ye-Kitaev model), the holographic
description of the Jackiw-Teitelboim dilaton gravity, the black hole physics, open string theory and some other models.
Functions
$$
\mathcal {E}_{\sigma }\left(u,\,v\right)
=\left(\frac{2}{\pi\sigma^{2}}\right)^{\frac{3}{2}}\,\frac{1}{\sqrt{uv}}\,\exp\left\{\frac{2}{\sigma^{2}}\left(\pi^{2}-u-v\right) \right\}
$$
$$
\times\int\limits_{0}^{+\infty}\,\exp\left\{-\frac{2}{\sigma^{2}}\left(2\,\sqrt{uv}\,\cosh\theta+\theta^{2}\right) \right\}\,\sin\left(\frac{4\pi\theta}{\sigma^{2}} \right)\,\sinh(\theta)\,d\theta
$$
play a key role in finding Schwarzian functional integrals.
Talk is based on
V.V.Belokurov, E.T. Shavgulidze, (2020) Schwarzian functional integrals calculus. Journal of Physics A: Mathematical and Theoretical, 53 (48) 485201pp. doi:10.1088/1751-8121/abbd52
