This paper studies the dual form of Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations in N = 2 supersymmetric Yang-Mills theory by applying a duality transformation to WDVV equations. The dual WDVV equations called in this paper are non-linear differential equations satisfied by dual prepotential and are found to have the same form with the original WDVV equations. However, in contrast with t...

In this thesis, we discuss bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. We begin by finding convergence properties for the models. In the supersymmetric case, we show that the partition function converges when D = 4, 6 and 10, and that correlation functions of degree k < kc = 2(D− 3) are convergent independently of the group. In the bosonic case we s...

Electromagnetism can be generalized to Yang–Mills theory by replacing the group U(1) by a nonabelian Lie group. This raises the question of whether one can similarly generalize 2-form electromagnetism to a kind of ‘higher-dimensional Yang–Mills theory’. It turns out that to do this, one should replace the Lie group by a ‘Lie 2-group’, which is a category C where the set of objects and the set o...

We present a full two-loop O(g6) perturbative field theoretic calculation of the expectation value of two circular Maldacena-Wilson loops in D = 4 N = 4 supersymmetric U(N) gauge theory. It is demonstrated that, after taking into account very subtle cancellations of bulk and boundary divergences, the result is completely finite without any renormalization. As opposed to previous lower order cal...

In generalized Yang-Mills theories scalar fields can be gauged just as vector fields in a usual Yang-Mills theory, albeit it is done in the spinorial representation. The presentation of these theories is aesthetic in the following sense: A physical theory using Yang-Mills theories requires several terms and irreducible representations, but with generalized Yang-Mills theories, only two terms an...