Conveners
Mathematical Physics
- Nikolai Iorgov (Bogolyubov Institute for Theoretical Physics)
The behavior of correlation functions in one-dimensional quantum systems at zero temperature is now very well understood in terms of linear and non-linear Luttinger models. The "microscopic" justification of these models consists in the exact accounting for soft-mode excitations around the vacuum state and, at most few high-energy excitations. At finite temperature, or more generically for...
Isomonodromic tau functions have explicit expressions as sums of c=1 conformal blocks (or Nekrasov functions), known as the Kyiv formulas, discovered by Gamayun, Iorgov, and Lisovyy. The zeros of these tau functions are described by classical, or c=∞ conformal blocks, also identified with the Painlevé action on the trajectory. We analyze an expansion of the tau function around its zero and...
The one-dimensional Calogero-Moser model is a well-established integrable model de-
scribing N interacting particles in both classical and quantum frameworks. In their seminal paper, Abanov, Bettelheim, and Wiegmann demonstrated that a collective description of this model gives rise to integrable hydrodynamics similar to the Benjamin-Ono system.
These interacting particle systems can also be...
We recover the predictions of CFT regarding the connection formulae for the family of Heun equations. Two methods of derivation of the connection coefficients are employed: the theorem of Schäfke and Schmidt that allows for a rigorous proof in some cases, as well as the analysis of the asymptotic behavior of the Floquet solutions. Both methods yield closed formulas in terms of continued...
We obtain relativistic Gaussian perturbation equations for osculating elements in Schwarzschild space-time background, for an arbitrary force not restricted to the equatorial plane. As an application, we solve the perturbation equations in linear approximation for force induced by the Kerr space-time as an expansion of the Schwarzschild space-time. For this case in post-Newtonian limit, we...
Abstract is attached as pdf file.
Recently, there were developed notion of irregular conformal blocks in two dimensional conformal field theory. It is believed that the conformal blocks are related to the isomondromic tau functions of Painvleve equations. I will review how it works on the concrete example of Painleve I equation. The main idea is that the isomondromic tau function of Painleve I equation is presented in the form...
Supersymmetric quantum field theories (SQFTs), particularly those with
N=2 supersymmetry in four dimensions, often exhibit intricate behaviors. Yet, their rich structures can be more tractable than those of their non-supersymmetric counterparts. Notably, their BPS sectors are governed by algebraic frameworks reminiscent of those in simpler holomorphic-topological models.
In this talk, I...
The statistical models of dimers belong to the class of so-called free fermionic exactly solvable models. This means, that every correlation function of local operators in this model can be computed by determinant of some matrix, and, moreover, can be expressed using only two-point functions, i.e. the Wick's contraction formula is satisfied. Many other models of statistical physics can be...
