A New Class of Conformal Field Theories with Anomalous Dimensions

TL;DR

This paper introduces a new class of 2D ${ m N}=2$ supersymmetric conformal field theories with non-zero anomalous dimensions, constructed via Wilsonian RG, featuring non-Ricci-flat target spaces and explicit models with ${f U}(N)$ symmetry.

Contribution

The authors derive and construct novel conformal field theories with nontrivial anomalous dimensions and non-Ricci-flat target spaces, expanding the landscape of supersymmetric CFTs.

Findings

New conformal theories with positive anomalous dimensions are well-behaved.

Explicit models with ${f U}(N)$ symmetry are constructed and analyzed.

Target space geometry resembles a semi-infinite cigar in the 1D case.

Abstract

The Wilsonian renormalization group (WRG) equation is used to derive a new class of scale invariant field theories with nonvanishing anomalous dimensions in 2-dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. When the coordinates of the target manifolds have nontrivial anomalous dimensions, vanishing of the $\beta$ function suggest the existence of novel conformal field theories whose target space is not Ricci flat. We construct such conformal field theories with ${\bf U}(N)$ symmetry. The theory has one free parameter a corresponding to the anomalous dimension of the scalar fields. The new conformal field theories are well behaved for positive a and have the central charge 3N, while they have curvature singularities at the boundary for a<0. When the target space is of complex 1-dimension, we obtain the explicit form of the Lagrangian, which reduces to two different kinds of free field theories in weak and in strong coupling limit. As a consistency test, the anomalous dimensions are reproduced in these two limits. The target space in this case looks like a semi-infinite cigar with one-dimension compactified to a circle.