Related papers: Knots as possible excitations of the quantum Yang-…
We perform the dual transformation of the Yang-Mills theory in d=3 dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but embedded into a flat…
It has been argued based on electric-magnetic duality that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four-dimension. And the Euler characteristic of…
Knotted configurations supported by a Yang Mills fluid-field system are suggested as a model for glueballs.
We extend our earlier study of the electroweak interactions of quantum knots to their gravitational and strong interactions. The knots are defined by appropriate quantum groups and are intended to describe all knotted field structures that…
I present a summary of the recent progress made in field and string theory which has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be described in…
Various recently developed connections between supersymmetric Yang-Mills theories in four dimensions and two dimensional integrable systems serve as crucial ingredients in improving our understanding of the AdS/CFT correspondence. In this…
The fundamental problem of knot theory is to know whether two knots are equivalent or not. As a tool to prove that two knots are different, mathematicians have developed various invariants. Knots invariants are just functions that can be…
A complexification of the twisted $\N=2$ theory allows one to determine the N=4 Yang--Mills theory in its third twist formulation. The imaginary part of the gauge symmetry is used to eliminate two scalars fields and create gauge covariant…
We propose that at low energy four dimensional bosonic strings may form bound states where they become bundled together much like the filaments in a cable. We inspect the properties of these bundles in terms of their extrinsic geometry.…
Quantization of two-dimensional Yang-Mills theory on a torus in the gauge where the field strength is diagonal leads to twisted sectors that are completely analogous to the ones that originate long string states in Matrix String Theory. If…
The loop representation of quantum gravity has many formal resemblances to a background-free string theory. In fact, its origins lie in attempts to treat the string theory of hadrons as an approximation to QCD, in which the strings…
We show that two-dimensional SO(N) and Sp(N) Yang-Mills theories without fermions can be interpreted as closed string theories. The terms in the 1/N expansion of the partition function on an orientable or nonorientable manifold M can be…
Continuum reduction and Monte Carlo simulation are used to calculate the heavy quark potential and the string tension in large N Yang-Mills theory in four dimensions. The potential is calculated out to a separation of nine lattice units on…
The massless superfield content of four-dimensional compactifications of closed superstrings with extended (N=2, 3, or 4) supersymmetry is derived by multiplying two (N=0, 1, or 2) Yang-Mills multiplets. In some cases these superfields are…
The classical Yang--Mills equations are analyzed within the geometrical framework of an effective gravity theory. Exact analytical solutions are derived for the cylindrically symmetric configurations of the coupled gauge and isoscalar…
We introduce a novel decomposition of the four dimensional SU(2) gauge field. This decomposition realizes explicitely a symmetry between electric and magnetic variables, suggesting a duality picture between the corresponding phases. It also…
We employ a heat kernel expansion to derive an effective action that describes four dimensional SU(2) Yang-Mills theory in the infrared limit. Our result supports the proposal that at large distances the theory is approximated by the…
I briefly review several important formal theory developments in quantum field theory and string theory that were reported at ICHEP conferences in past decades, and explain how they underlie a new research area referred to as physical or…
Recent progress in string theory has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be understood in topological terms. We describe in detail how to…
The solution of quantum Yang-Mills theory on arbitrary compact two-manifolds is well known. We bring this solution into a TQFT-like form and extend it to include corners. Our formulation is based on an axiomatic system that we hope is…