On Polyakov's basic variational formula for loop spaces

We use the homological algebra context to give a more rigorous proof of Polyakov's basic variational formula for loop spaces.Comment: Latex, 17 pages, no figure

Induced (N,0) supergravity as a constrained Osp(N,2) WZWN model and its effective action

A chiral $(N,0)$ supergravity theory in d=2 dimensions for any $N$ and its induced action can be obtained by constraining the currents of an Osp(N$|$2) WZWN model. The underlying symmetry algebras are the nonlinear SO(N) superconformal algebras of Knizhnik and Bershadsky. The case $N=3$ is worked out in detail. We show that by adding quantum corrections to the classical transformation rules, the gauge algebra on gauge fields and currents closes. Integrability conditions on Ward identities are derived. The effective action is computed at one loop. It is finite, and can be obtained from the induced action by rescaling the central charge and fields by finite Z factors.Comment: 23

Leading Infrared Logarithms from Unitarity, Analyticity and Crossing

We derive non-linear recursion equations for the leading infrared logarithms in massless non-renormalizable effective field theories. The derivation is based solely on the requirements of the unitarity, analyticity and crossing symmetry of the amplitudes. That emphasizes the general nature of the corresponding equations. The derived equations allow one to compute leading infrared logarithms to essentially unlimited loop order without performing a loop calculation. For the implementation of the recursion equation one needs to calculate tree diagrams only. The application of the equation is demonstrated on several examples of effective field theories in four and higher space-time dimensions.Comment: 12 page

On search for the M-Theory Lagrangian

We present a starting point for the search for a Lagrangian density for M-Theory using characteristic classes for flat foliations of bundles.Comment: Latex, 5 pages, no figure

Research of the stress-strain state of rods obtained by porous blank extrusion

The features of the stress-strain state in the cross section of rods under forming are revealed by the finite element modeling of the process of direct extrusion of a porous iron blank. In particular, the nature of porosity distribution and the stress-state stiffness coefficient obtained as a result of calculating the residual stresses field in the rod is studied. The Gurson-Tvergaard-Needleman (GTN) model is used to describe the behavior of the material of a porous blank under plastic deformation. It has been established that, in different cross-section zones of the rod, the values of the stress-state coefficient can be either positive or negative. It is shown that the most unfavorable area of the cross-section in the drawing index range investigated (2.04-4) is the material layer lying in the immediate vicinity of the outer surface of the rod (0.7...0.8R, where R is the rod radius), where the localization of tensile stresses is observed which promotes the emergence and growth of layered annular cracks. © 2017 Author(s)