Effective constrained polymeric theories and their continuum limit

Large mass limit of the continuum theories in Kaplan's formulation.

Being inspired by Kaplan’s proposal for simulating chiral fermions on a lattice, we examine the continuum analog of his domain-wall construction for two-dimensional chiral Schwinger models. Adopting slightly unusual dimensional regularization, we explicitly evaluate the one-loop effective action in the limit that the domain-wall mass goes to infinity. For anomaly-free cases, the effective actio...

Wilson Renormalization Group and Continuum Effective Field Theories

This is an elementary introduction to Wilson renormalization group and continuum effective field theories. We first review the idea of Wilsonian effective theory and derive the flow equation in a form that allows multiple insertion of operators in Green functions. Then, based on this formalism, we prove decoupling and heavy-mass factorization theorems, and discuss how the continuum effective fi...

Central and Local Limit Theories in Markov Dependent Random Variables

Effective Field Theories in the Large N Limit

Various effective field theories in four dimensions are shown to have exact non-trivial solutions in the limit as the number N of fields of some type becomes large. These include extended versions of the U(N) Gross–Neveu model, the non-linear O(N) σ-model, and the CP model. Although these models are not renormalizable in the usual sense, the infinite number of coupling types allows a complete c...

The Quenched Continuum Limit

Our increasing ability to carry out unquenched simulations means that the quenched approximation is no longer required. There is an outstanding issue associated with the quenched continuum limit, however, which we address here. At the same time we point out the ingredients that are necessary to obtain an accurate result in the continuum limit, since these ingredients will also be important for ...