Classical irregular block, N=2 pure gauge theory and Mathieu equation

Combining the semiclassical/Nekrasov-Shatashvili limit of the AGT conjecture and the Bethe/gauge correspondence results in a triple correspondence which identifies classical conformal blocks with twisted superpotentials and then with Yang-Yang functions. In this paper the triple correspondence is studied in the simplest, yet not completely understood case of pure SU(2) super-Yang-Mills gauge theory. A missing element of that correspondence is identified with the classical irregular block. Explicit tests provide a convincing evidence that such a function exists. In particular, it has been shown that the classical irregular block can be recovered from classical blocks on the torus and sphere in suitably defined decoupling limits of classical external conformal weights. These limits are "classical analogues" of known decoupling limits for corresponding quantum blocks. An exact correspondence between the classical irregular block and the SU(2) gauge theory twisted superpotential has been obtained as a result of another consistency check. The latter determines the spectrum of the 2-particle periodic Toda (sin-Gordon) Hamiltonian in accord with the Bethe/gauge correspondence. An analogue of this statement is found entirely within 2d CFT. Namely, considering the classical limit of the null vector decoupling equation for the degenerate irregular block a celebrated Mathieu's equation is obtained with an eigenvalue determined by the classical irregular block. As it has been checked this result reproduces a well known weak coupling expansion of Mathieu's eigenvalue. Finally, yet another new formulae for Mathieu's eigenvalue relating the latter to a solution of certain Bethe-like equation are found.Comment: 47 pages, 3 figure

Solving Heun's equation using conformal blocks

It is known that the classical limit of the second order BPZ null vector decoupling equation for the simplest two 5-point degenerate spherical conformal blocks yields: (i) the normal form of the Heun equation with the complex accessory parameter determined by the 4-point classical block on the sphere, and (ii) a pair of the Floquet type linearly independent solutions. A key point in a derivation of the above result is the classical asymptotic of the 5-point degenerate blocks in which the so-called heavy and light contributions decouple. In the present work the semi-classical heavy-light factorization of the 5-point degenerate conformal blocks is studied. In particular, a mechanism responsible for the decoupling of the heavy and light contributions is identified. Moreover, it is shown that the factorization property yields a practical method of computation of the Floquet type Heun's solutions. Finally, it should be stressed that tools analyzed in this work have a broad spectrum of applications, in particular, in the studies of spectral problems with the Heun class of potentials, sphere-torus correspondence in 2d CFT, the KdV theory, the connection problem for the Heun equation and black hole physics. These applications are main motivations for the present work.Comment: 28 pages, revised and extended versio

Drugged Paranoia and Warlust

Drugged Paranoia and Warlust are stories of human depravity and violence that happened on an abandoned U.S. military base in the rural world of Indiana. These tales are told through a series of prints, drawings, animation and a comic. Scenes of bombings, mass graves, and drug overdoses are presented as humorous cartoons in playful colors to subvert the viewer into exploring imagery that discusses serious and somewhat bleak issues. The work in this exhibition is both satire of absurd events and trying to find meaning amongst madness

SIMULATION STUDY OF HYDRODYNAMIC CAVITATION IN THE ORIFICE FLOW

Hydrodynamic cavitation is a phenomenon that can be used in the water treatment process. For this purpose, venturis or orifices varying in geometry are used. Studying this phenomenon under experimental conditions is challenging due to its high dynamics and difficulties in measuring and observing the phase transition of the liquid. For this reason, the CFD method was used to study the phenomenon of hydrodynamic cavitation occurring in water flow through the orifice and then analyze flow parameters for different boundary conditions. The research was performed for four different orifice geometries and two defined fluid pressure values at the inlet, based on a computational 2D model of the research object created in Ansys Fluent software. As a result of the numerical simulation, the distribution of fluid velocity and pressure and volume fraction of the gas phase were obtained. A qualitative and quantitative analysis of the phenomenon of hydrodynamic cavitation under the considered flow conditions was conducted for the defined orifice geometries. The largest cavitation zone and thus the largest volume fraction of the gas phase was obtained for the orifice diameter of 2 mm with a sharp increase in diameter. However, the geometry with a linear change in diameter provided the largest volume fraction of the gas phase per power unit

Absence of gravitational contributions to the running Yang-Mills coupling

The question of a modification of the running gauge coupling of (non-) abelian gauge theories by an incorporation of the quantum gravity contribution has recently attracted considerable interest. In this letter we perform an involved diagrammatical calculation in the full Einstein-Yang-Mills system both in cut-off and dimensional regularization at one loop order. It is found that all gravitational quadratic divergencies cancel in cut-off regularization and are trivially absent in dimensional regularization so that there is no alteration to asymptotic freedom at high energies. The logarithmic divergencies give rise to an extended effective Einstein-Yang-Mills Lagrangian with a counterterm of dimension six. In the pure Yang-Mills sector this counterterm can be removed by a nonlinear field redefinition of the gauge potential, reproducing a classical result of Deser, Tsao and van Nieuwenhuizen obtained in the background field method with dimensional regularization.Comment: 4 pages, 1 figure, uses revtex and feynmf. v2: references adde