相关论文: Non-perturbative double scaling limits

Perturbative Symmetry Approach is formulated in symbolic representation. Easily verifiable integrability conditions of a given equation are constructed in the frame of the approach. Generalisation for the case of non-local and non-evolution…

$O(N)$ invariant vector models have been shown to possess non-trivial scaling large $N$ limits, at least perturbatively within the loop expansion, a property they share with matrix models of 2D quantum gravity. In contrast with matrix…

I point out that standard two dimensional, asymptotically free, non-linear sigma models, supplemented with terms giving a mass to the would-be Goldstone bosons, share many properties with four dimensional supersymmetric gauge theories, and…

We argue that for a large class of N=1 supersymmetric gauge theories the effective superpotential as a function of the glueball chiral superfield is exactly given by a summation of planar diagrams of the same gauge theory. This perturbative…

We investigate non-perturbative supersymmetry breaking in various models of quantum mechanics, including an interesting class of $PT$-invariant models, using lattice path integrals. These theories are discretized on a temporal Euclidean…

N=2 gauged non-linear sigma models are examined classically and their D-terms are solved. The variation of the classical Lagrangian in order to solve for the auxiliary fields is identical to integrating these modes functionally. The latter…

An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable…

We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the…

Recently, the author has constructed a series of four dimensional non-critical string theories with eight supercharges, dual to theories of light electric and magnetic charges, for which exact formulas for the central charge of the…

We review two different noncommutative gauge models generalizing approaches which lead to renormalizable scalar quantum field theories. One of them implements the crucial IR damping of the gauge field propagator in the so-called ``soft…

A scaling hypothesis for the n-particle spectral densities of the O(3) nonlinear sigma-model is described. It states that for large particle numbers the n-particle spectral densities are ``self-similar'' in being basically rescaled copies…

The technical problem of deriving the full Green functions of the elementary pion fields of the nonlinear sigma model in terms of ancestor amplitudes involving only the flat connection and the nonlinear sigma model constraint is a very…

This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…

Solutions to scalar theories with derivative self-couplings often have regions where non-linearities are important. Given a classical source, there is usually a region, demarcated by the Vainshtein radius, inside of which the classical…

Various aspects of non-linear sigma models with an $SU(N)\times U(1)$ symmetric target space are considered. In the case $N=2$, three-dimensional topological defects are discussed which are relevant for frustrated magnetic systems and which…

We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…

The wormlike chain model of stiff polymers is a nonlinear $\sigma$-model in one spacetime dimension in which the ends are fluctuating freely. This causes important differences with respect to the presently available theory which exists only…

We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…

We show how non-commutativity arises from commutativity in the double sigma model. We demonstrate that this model is intrinsically non-commutative by calculating the propagators. In the simplest phase configuration, there are two dual…

We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…