Topological Yang-Mills theory with the Belavin-Polyakov-Schwarz-Tyupkin SU (2) instanton is solved completely, revealing an underlying multi-link intersection theory. Link invariants are also shown to survive the coupling to a certain kind of matter (hyperinstantons). The physical relevance of topological field theory and its invariants is discovered. By embedding topological Yang-Mills theory ...

We construct a classical mechanics Hamiltonian which exhibits spontaneous symmetry breaking akin the Coleman-Weinberg mechanism, dimensional transmutation, and asymptotically free self-similarity congruent with the beta-function of four dimensional Yang-Mills theory. Its classical equations of motion support stable periodic orbits and in a three dimensional projection these orbits are self-link...

We examine a double trace deformation of SU(N) Yang-Mills theory which, for large N and large volume, is equivalent to unmodified Yang-Mills theory up to O(1/N2) corrections. In contrast to the unmodified theory, large N volume independence is valid in the deformed theory down to arbitrarily small volumes. The double trace deformation prevents the spontaneous breaking of center symmetry which w...

We study decoupling limits and S-dualities for noncommutative open string/ Yang-Mills theory in a gravity setup by considering an SL(2, Z) invariant super-gravity solutions of the form ((F, D1), D3) bound state of type IIB string theory. This configuration can be regarded as D3-brane solution with both electric and magnetic fields turned on along one of the spatial directions of the brane and p...

We study decoupling limits and S-dualities for noncommutative open string/ Yang-Mills theory in a gravity setup by considering an SL(2, Z) invariant super-gravity solutions of the form ((F, D1), D3) bound state of type IIB string theory. This configuration can be regarded as D3-brane solution with both electric and magnetic fields turned on along one of the spatial directions of the brane and p...

Marchesini showed that the Fokker–Planck Hamiltonian for Yang-Mills theories is the loop operator. Jevicki and Rodrigues showed that the Fokker– Planck Hamiltonian of some matrix models cöıncides with temporal gauge non-critical string field theory Hamiltonians constructed by Ishibashi and Kawai (and their collaborators). Thus the loop operator for Yang–Mills theory is the temporal gauge Hamilt...

In this note we establish the explicit relation between correlation functions in N = 4 SUSY Yang–Mills theory on S3×R in a double scaling limit and scattering amplitudes of the String Theory on the pp-wave background. The relation is found for two– and three– point correlation functions in these theories. As a by product we formulate a dictionary for the correspondence between these theories: i...

By defining an extended BRST operator that includes the chiral part of N=2 global supersymmetry, it is shown that the full N=2 offshell Super Yang Mills Action can be represented as an exact BRST term. The action written in this form suggests that the fields of the Topological Yang Mills theory can be defined in terms of composite fields of supersymmetry ghosts and N=2 fields in a natural way. ...

A solution to Slavnov–Taylor identities in a general four dimensional N=1 supersymmetric Yang-Mills theory containing arbitrary matter superfields is proposed. The solution proposed appears just a simple generalization of an analogous solution in the pure supersymmetric Yang-Mills theory.

From its inception in statistical physics to its role in the construction and in the development of the asymmetric Yang-Mills phase in quantum field theory, the notion of spontaneous broken symmetry permeates contemporary physics. This is reviewed with particular emphasis on the conceptual issues. Contribution to “Fifty years of Yang Mills theory”, editor G. ’t Hooft, World Scientific.