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We provide a study of the supersymmetric Adler--Bardeen anomaly in the $N=1, d=4,6,10$ super-Yang--Mills theories. We work in the component formalism that includes shadow fields, for which Slavnov--Taylor identities can be independently set for both gauge invariance and supersymmetry. We find a method with improved descent equations for getting the solutions of the consistency conditions of both Slavnov--Taylor identities and finding the local field polynomials for the standard Adler--Bardeen anomaly and its supersymmetric counterpart. We give the explicit solution for the ten-dimensional case.
For all types of N=4 anti-de Sitter (AdS) supersymmetry in three dimensions, we construct manifestly supersymmetric actions for Abelian vector multiplets and explain how to extend the construction to the non-Abelian case. Manifestly N=4 supersymmetri
We use fractional and wrapped branes to describe perturbative and non-perturbative properties of N=1 super Yang-Mills living on their world-volume. (Talk given at the 1st Nordstrom Symposium, Helsinki, August 2003.)
We review a recent progress in constructing low-energy effective action in N=4 super Yang-Mills theories. Using harmonic superspace approach we consider N=4 SYM in terms of unconstrained N=2 superfield and apply N=2 background field method to finding
Integral invariants in maximally supersymmetric Yang-Mills theories are discussed in spacetime dimensions $4leq Dleq 10$ for $SU(k)$ gauge groups. It is shown that, in addition to the action, there are three special invariants in all dimensions. Two
We study the multiplicity of BPS domain walls in N=1 super Yang-Mills theory, by passing to a weakly coupled Higgs phase through the addition of fundamental matter. The number of domain walls connecting two specified vacuum states is then determined