Symplectic critical models in $6+\epsilon$ dimensions

TL;DR

This paper explores nonunitary critical models in 6+epsilon dimensions with symplectic symmetry, providing evidence they can define critical theories in 7 dimensions through large N analysis.

Contribution

It introduces and analyzes nonunitary symplectic scalar models in dimensions above six, extending the understanding of critical theories beyond the well-studied orthogonal cases.

Findings

Models are nonunitary but have positive operator dimensions.

Large N analysis suggests models can define critical theories in 7 dimensions.

Connections to critical Sp(N) theories similar to O(N) models.

Abstract

We consider nontrivial critical models in $d=6+\epsilon$ spacetime dimensions with anticommuting scalars transforming under the symplectic group $\text{Sp}(N)$. These models are nonunitary, but the couplings are real and all operator dimensions are positive. At large $N$ we can take $\epsilon\to1$ consistently with the loop expansion and thus provide evidence that these theories may be used to define critical models in $d=7$. The relation of these theories to critical $\text{Sp}(N)$ theories, defined similarly to the well-known critical $\text{O}(N)$ theories, is examined, and some similarities are pointed out.