Korkut Bardakci

Parafermions from coset models

Conformally invariant coset models in two dimensions can be described by the gauged Wess-Zumino-Witten lagrangian. We present a semi-classical treatment of these theories in a unitary gauge. In particular, we give an explicit construction of the conserved parafermion fields in the case of an abelian gauge group, and also show that the Poisson brackets between these field close in a simple fashion. We make use of these results to find a free field realization of this Poisson structure.

Dual models and spontaneous symmetry breaking

Abstract The stability of the vacuum of the orbital dual model with zero intercept with respect to spurion emission is investigated. Although the model is not fully satisfactory because of the presence of negative norm states, it serves as a simplified laboratory for the more realistic (and more complicated) models. Feynman rules for the calculation of the effective potential are developed, and the problem of finding the Goldstone minimum is reduced to a non-linear integral equation. The propagator of the model is also determined, and trajectories are shown to remain linear.

A construction of the

Decomposition theorems for certain representations of Kac-Moody algebras which are needed for the construction of modular invariant unitary conformal models are proved. It is shown that allc<1 modular invariant models can then be recovered from gauged free fermionic models, including the exceptional cases.

c<1

Abstract For various models of increasing complexity, it is shown that the large- N limit is dominated by solutions to the classical equations of motion, supplemented by boundary conditions that follow from canonical commutation relations. The basic idea is to focus on ordered invariant equal-time Green functions, and to classify the intermediate states that contribute according to the group of invariance. It is then possible to define reduced matrix elements and their classical limits for large N systematically. The method is also applied to the hamiltonian version of the lattice gauge theory, and the relevant boundary conditions on the classical solutions are deduced.

modular invariant partition functions

Abstract We generalize an earlier work on conformal coset models to the case of a non-abelian factor group. Starting with the gauged Wess-Zumino-Witten lagrangian, we derive the associated parafermion fields and deduce their Poisson brackets. We then present an explicit classical realization of these fields in terms of path ordered exponentials of free currents that satisfy an affine Lie algebra. This construction can be viewed as a non-abelian generalization of the standard free field representation of parafermions. Finally, we extended the classical construction to the full quantum mechanical case.

Classical solutions and the large-N limit

Abstract We develop an approximation scheme for our worldsheet model of the sum of planar diagrams based on mean field theory. At finite coupling the mean field equations show a weak coupling solution that resembles the perturbative diagrams and a strong coupling solution that seems to represent a tensionless soup of field quanta. With a certain amount of fine-tuning, we find a solution of the mean field equations that seems to support string formation.

Parafermions from non-abelian coset models☆

Abstract We show that to leading order in the quark number N , the Skyrme model, the strong coupling theory and the static quark model share a common underlying symmetry group.

A mean field approximation to the worldsheet model of planar φ3 field theory

The present article is based on a previous one, where a second quantized field theory on the world sheet for summing the planar graphs of 3 theory was developed. In this earlier work, the ground state of the model was determined using a variational approximation. Here, starting with the same world sheet field theory, we instead use the mean field method to compute the ground state, and find results that are in agreement with the variational calculation. Apart from serving as a check on the variational calculation, the mean field method enables us to go beyond the ground state to compute the excited states of the model. The spectrum of these states is that of a string with linear trajectories, plus a continuum that starts at higher energy. We show that, by appropriately tuning the parameters of the model, the string spectrum can be cleanly seperated from the continuum.

The Skyrme model, the strong coupling theory and the static quark model

Abstract We present an improved version of our earlier work on summing the planar graphs in φ3 field theory. The present treatment is also based on our world sheet formalism and the mean field approximation, but it makes use of no further approximations. We derive a set of equations between the expectation values of the world sheet fields, and we investigate them in certain limits. We show that the equations can give rise to (metastable) string forming solutions.

Mean field method applied to the new world sheet field theory: string formation

Abstract We continue and extend earlier work on the summation of planar graphs in φ 3 field theory, based on a local action on the world sheet. The present work employs a somewhat different version of the self consistent field (meanfield) approximation compared to the previous work on the same subject. Using this new approach, we are able to determine in general the asymptotic forms of the solutions, and in the case of one solution, even its exact form. This solution leads to formation of an unstable string, in agreement with the previous work. We also investigate and clarify questions related to Lorentz invariance and the renormalization of the solution.