Renormalizable supersymmetric gauge theory in six dimensions

TL;DR

This work constructs a renormalizable six-dimensional ${\cal N}=(1,0)$ supersymmetric gauge theory with a four-derivative action and a dimensionless coupling via harmonic superspace, achieving classical ${\cal N}=(1,0)$ superconformal invariance. At the quantum level, conformal symmetry is broken by a conformal anomaly, yielding a positive beta function and a Landau pole, so the model is not ultraviolet finite. The component action reveals a higher-derivative gauge kinetic term $ (\nabla^M F_{MN})^2$ and dynamical auxiliary fields ${\cal D}^{ik}$, with the degrees of freedom matching between bosons and fermions. The authors discuss extensions to preserve conformal symmetry quantum-mechanically, notably via ${\cal N}=(2,0)$ tensor multiplets or higher-derivative hypermultiplets, aiming toward a UV-finite 6D theory and providing a framework for further superspace-based quantum analyses.

Abstract

We construct and discuss a 6D supersymmetric gauge theory involving four derivatives in the action. The theory involves a dimensionless coupling constant and is renormalizable. At the tree level, it enjoys N = (1,0) superconformal symmetry, but the latter is broken by quantum anomaly. Our study should be considered as preparatory for seeking an extended version of this theory which would hopefully preserve conformal symmetry at the full quantum level and be ultraviolet-finite.

Figures (2)

• Figure 1: Graphs contributing to the renormalization of the kinetic term. Thin solid lines stand for the particle ${\cal D}$, thick solid lines for fermions, and dashed lines for gauge bosons.
• Figure 2: The same for the ${\cal D}^3$ vertex.