6D superconformal theory as the theory of everything

TL;DR

This paper proposes that a 6D superconformal higher-derivative field theory could serve as a fundamental Theory of Everything, with our universe as a 3-brane solution, highlighting the potential of such theories to be renormalizable and ghost-free.

Contribution

It introduces a 6D superconformal higher-derivative model with renormalizable properties and explores its implications as a candidate for the fundamental Theory of Everything.

Findings

A 6D N=(1,0) supersymmetric gauge theory with four derivatives is renormalizable.

Conformal symmetry is broken by quantum anomalies in the model.

Ghosts in conformal higher-derivative theories may be less problematic than previously thought.

Abstract

We argue that the fundamental Theory of Everything is a conventional field theory defined in the flat multidimensional bulk. Our Universe should be obtained as a 3-brane classical solution in this theory. The renormalizability of the fundamental theory implies that it involves higher derivatives (HD). It should be supersymmetric (otherwise one cannot get rid of the huge induced cosmological term) and probably conformal (otherwise one can hardly cope with the problem of ghosts) . We present arguments that in conformal HD theories the ghosts (which are inherent for HD theories) might be not so malignant. In particular, we present a nontrivial QM HD model where ghosts are absent and the spectrum has a well defined ground state. The requirement of superconformal invariance restricts the dimension of the bulk to be D < 7. We suggest that the TOE lives in six dimensions and enjoys the maximum N = (2,0) superconformal symmetry. Unfortunately, no renormalizable field theory with this symmetry is presently known. We construct and discuss an N = (1,0) 6D supersymmetric gauge theory with four derivatives in the action. This theory involves a dimensionless coupling constant and is renormalizable. At the tree level, the theory enjoys conformal symmetry, but the latter is broken by quantum anomaly. The sign of the beta function corresponds to the Landau zero situation.