Supersymmetric Yang-Mills quantum mechanics (SYMQM) results from the dimensional reduction of the Yang-Mills field theory in D space-time dimensions to a single point in the D− 1 dimensional space. It can be also viewed as the effective quantum mechanics of zero momentum modes of the original theory [1]. These systems were first considered in 80’s [2] as simple models with supersymmetry [3]. In...

We propose a new field-theoretic framework for formulating the non-relativistic quantum mechanics of D-particles in a Fock space of U(N) Yang-Mills theories with all different N in a unified way. D-particle field operators, creating and annihilating a D-particle and hence changing N one by one, are defined. The base space of these D-particle fields is a (complex) vector space of infinite dimens...

It is a great honour and pleasure for me to participate in the conference, dedicated to 85 years celebration for Professor C. N. Yang. The influence of C. N. Yang on my own research is very strong. Two of my directions — quantization of the Yang-Mills field and theory of solitons stem from his works. I am proud to remind, that the term “Yang-Baxter equation” was introduced by L. Takhtajan and m...

By constructing a nilpotent extended BRST operator ¯ s that involves the N=2 global supersymmetry transformations of one chirality, we show that the standard N=2 off-shell Super Yang Mills Action can be represented as an exact BRST term ¯ sΨ, if the gauge fermion Ψ is allowed to depend on the inverse powers of supersymmetry ghosts. By using this nonanalytical structure of the gauge fermion (via...

We present intermediate results of an ongoing investigation which attempts a generalization of the well known one-loop Bern Kosower rules of Yang-Mills theory to higher loop orders. We set up a general procedure to extract the field theoretical limit of bosonic open string diagrams, based on the sewing construction of higher loop world sheets. It is tested with oneand two-loop scalar field theo...

We review the application of bosonic string techniques to the calculation of renormalization constants and effective actions in Yang-Mills theory. We display the multiloop string formulas needed to compute Yang-Mills amplitudes, and we discuss how the renormalizations of proper vertices can be extracted in the field theory limit. We show how string techniques lead to the background field method...

We prove the first mathematical result relating the Yang-Mills measure on a compact surface and the Yang-Mills energy. We show that, at the small volume limit, the scaled Yang-Mills measures satisfy a large deviation principle with the Yang-Mills energy as rate function. This gives some rigorous content to the informal description of the Yang-Mills measure as the Gibbs measure of the Yang-Mills...

The paper is a brief review of the works devoted to problem of effective action in N = 2 super Yang-Mills theories in harmonic superspace approach. The formulation of N = 2 superfield models in harmonic superspace is discussed, background field method for N = 2 super Yang-Mills theory is constructed and general structure of effective action in harmonic superspace is investigated. It is shown ho...

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 report on recent progress in the use of string techniques for the computation of field theory amplitudes. We show how one–loop renormalization constants in Yang–Mills theory can be computed using the open spinning string, we review the calculation of two–loop scalar amplitudes with the bosonic string, and we briefly indicate how the technique can be applied to the two–loop vacuum bubbles of ...