Non-perturbative Effects and Unparticle Physics in Generalized Schwinger Models

TL;DR

This paper explores generalized Schwinger models with multiple fermions and gauge fields, revealing non-perturbative effects, unparticle operators, and a transition from free fermions to unparticle and massive particle physics.

Contribution

It introduces a detailed analysis of diagonal color $SU(n)$ and $U(n)$ models, highlighting the emergence of unparticle operators and non-perturbative constraints in these generalized Schwinger models.

Findings

Identification of unparticle operators with non-zero anomalous dimensions.

Discovery of conformal coalescence leading to a single low-energy unparticle type.

Explicit demonstration of the transition from free fermions to unparticles to massive particles.

Abstract

We analyze generalizations of the Schwinger model with more massless fermions and more vector fields. We focus on models with the gauge structure of ``diagonal color $SU(n)$'' but unlike previous investigators, we do not assume that all the gauge boson masses are the same. Unlike the Schwinger model, these are Banks-Zaks models with conformal sectors that survive at long distances. In addition to local operators that go to ``unparticle operators'' with non-zero anomalous dimensions at long distances, they contain local operators like the $\bar\psi_L\psi_R$ operator in the Schwinger model which go to constants at long distances. These operators have calculable vacuum expectation values (up to phases). Cluster decomposition applied to correlation functions involving these operators yields nontrivial and calculable non-perturbative constraints on correlation functions. One consequence is ``conformal coalescence'' in which linear combinations of short distance operators disappear from the long-distance theory, leaving only one kind of unparticle stuff in the low-energy theory. We believe that our detailed analysis of diagonal color $SU(n)$ paints an appealing picture of unparticle operators as the result of an incomplete binding of the massless fermions. We complete the picture (and the binding) by analyzing the diagonal color $U(n)$ model with a very small $U(1)$ coupling and thus a gauge boson with a dynamical mass much smaller than the other masses in the model. This model has a mass gap and we can see explicitly the transition from free-fermion behavior at short distances to unparticle physics at intermediate distances to the physics of massive particles at long distances.