The exact or Wilson renormalization group equations can be formulated as a functional Fokker-Planck equation in the infinite-dimensional configuration space of a field theory, suggesting a stochastic process in the space of couplings. Indeed, the ordinary renormalization group differential equations can be supplemented with noise, making them into stochastic Langevin equations. Furthermore, if ...

We review some simple group theoretical properties of BPS states, in relation with the singular homology of level surfaces. Primary focus is on classical and quantum N = 2 supersymmetric Yang-Mills theory, though the considerations can be applied to string theory as well. There has been dramatic recent progress in understanding non-perturbative properties of certain supersymmetric field and str...

Supersymmetry was first applied to high energy physics. In the early eighties, it found a second and very fruitful field of applications in stochastic quantum physics. This relates to Random Matrix Theory, the topic I focus on in this contribution. I review several aspects of more mathematical interest, in particular, supersymmetric extensions of the Itzykson– Zuber and the Berezin–Karpelevich ...

While it is possible to find examples of field theories with a spontaneously broken symmetry at high temperature, in renormalizable supersymmetric models any internal symmetry gets always restored. Recently, a counterexample was suggested in the context of nonrenormalizable supersymmetric theories. We show that non negligible higher loop effects actually restore the symmetry, without compromisi...

We find a class of flat supersymmetric brane-antibrane configurations. They follow from ordinary brane-antibrane systems by turning on a specific worldvolume background electric field, which corresponds to dissolved fundamental strings. We have clarified in detail how they arise and identified their constituent charges as well as the corresponding supergravity solutions. Adopting the matrix the...

We show that many of the recently proposed supersymmetric p-brane solutions of d=10 and d=11 supergravity have the property that they interpolate between Minkowski spacetime and a compactified spacetime, both being supersymmetric supergravity vacua. Our results imply that the effective worldvolume action for small fluctuations of the super p-brane is a supersingleton field theory for (adS) p+2 ...

The one-loop contribution to the superpotential, in particular the VenezianoYankielowicz potential in N = 1 supersymmetric Yang-Mills model is discussed from an elementary field theory method and the matrix model point of view. Both approaches are based on the Renormalization Group variation of the superconformal N = 4 supersymmetric Yang-Mills model. e-mail: [email protected] e-mail...

We construct the cubic interaction vertex and dynamically generated supercharges in lightcone superstring field theory for a large class half-supersymmetric D-branes in the planewave background. We show that these satisfy the plane-wave superalgebra at first order in string coupling. The cubic interaction vertex and dynamical supercharges presented here are given explicitly in terms of oscilato...

I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have little or no prior exposure to supersymmetry. Topics covered include: motivations for supersymmetry; the construction of supersymmetric Lagrangians; supersymmetry-breaking interactions; the Minimal Supersymmetric Stand...