Backlund Transformations in 10D susy Yang-Mills Theories

This is a continuation of hep-th/9811108, hep-th/9903218, hep-th/9910235, on exact integration technics for modified dynamical equations in ten dimensional supersymmetric gauge theory. A B\"acklund transformation is derived for the Yang type (super) equations previously derived (hep-th/9811108) by M. Saveliev and the author, from the ten dimensional super Yang-Mills field equations in an on-shell light cone gauge. It is shown to be based upon a particular gauge transformation satisfying nonlinear conditions which ensure that the particular form of the equations is retained. These Yang type field equations are shown to be precisely such that they automatically provide a solution of these conditions. This B\"acklund transformation is similar to the one proposed by A. Lesnov for self-dual Yang-Mills in four dimensions. In the introduction a personal recollection on the birth of supersymmetry is given.Comment: 13 pages Latex, Contribution to Y. Golfand Memorial Volum

Lax equations in ten dimensional supersymmetric classical Yang-Mills theories

In a recent paper (hep-th/9811108), Saveliev and the author showed that there exits an on-shell light cone gauge where the non-linear part of the field equations reduces to a (super) version of Yang's equations which may be solved by methods inspired by the ones previously developed for self-dual Yang-Mills equations in four dimensions. Here, the analogy between these latter theories and the present ones is pushed further by writing down a set of super partial linear differential equations whose consistency conditions may be derived from the SUSY Y-M equations in ten dimensions, and which are the analogues of the Lax pair of Belavin and Zakharov. On the simplest example of the two pole ansatz, it is shown that the same solution-generating techniques are at work, as for the derivation of the celebrated multi-instanton solutions carried out in the late seventies. The present Lax representation, however, is only a consequence of (instead of being equivalent to) the field equations, in contrast with the Belavin Zakharov Lax pair.Comment: 8 pages Late

Laundering Money Online: a review of cybercriminals methods

Money laundering is a critical step in the cyber crime process which is experiencing some changes as hackers and their criminal colleagues continually alter and optimize payment mechanisms. Conducting quantitative research on underground laundering activity poses an inherent challenge: Bad guys and their banks do not share information on criminal pursuits. However, by analyzing forums, we have identified two growth areas in money laundering: online gaming and micro laundering.Comment: Industry report, White paper. Tools and Resources for Anti-Corruption Knowledge, June, 01, 2013. United Nations Office on Drugs and Crime (UNODC

Integrable structures in classical off-shell 10D supersymmetric Yang-Mills theory

The superspace flatness conditions which are equivalent to the field equations of supersymmetric Yang-Mills theory in ten dimensions have not been useful so far to derive non trivial classical solutions. Recently, modified flatness conditions were proposed, which are explicitly integrable (hep-th/9811108), and are based on the breaking of symmetry SO(9,1) -> SO(2,1)xSO(7). In this article, we investigate their physical content. To this end, group-algebraic methods are developed which allow to derive the set of physical fields and their equations of motion from the superfield expansion of the supercurl, systematically. A set of integrable superspace constraints is identified which drastically reduces the field content of the unconstrained superfield but leaves the spectrum including the original Yang-Mills vector field completely off-shell. A weaker set of constraints gives rise to additional fields obeying first order differential equations. Geometrically, the SO(7) covariant superspace constraints descend from a truncation of Witten's original linear system to particular one-parameter families of light-like rays.Comment: 43 pages, 4 figures. Improved version for publicatio