Conformal Fields in Higher Dimensions

TL;DR

This paper extends unitarity bounds and classifies conformal gauge theories across all space-time dimensions, introducing new unitary modules in higher dimensions and proposing a link to tensionless p-branes.

Contribution

It generalizes unitarity bounds for conformal groups in any dimension, classifies invariant gauge theories, and introduces novel unitary modules for $d>4$, suggesting a new perspective on higher-dimensional conformal field theories.

Findings

Classified gauge theories invariant under $so(2,d)$ in all dimensions.

Identified new unitary modules in $d>4$ with no lower-dimensional analogues.

Proposed a connection between higher-dimensional conformal theories and tensionless p-branes.

Abstract

We generalize, to any space-time dimension, the unitarity bounds of highest weight UIR's of the conformal groups with Lie algebras $so(2,d)$. We classify gauge theories invariant under $so(2,d)$, both integral and half-integral spins. A similar analysis is carried out for the algebras $so^*(2n)$. We study new unitary modules of the conformal algebra in $d>4$, that have no analogue for $d\leq 4$ as they cannot be obtained by "squaring" singletons. This may suggest the interpretation of higher dimensional non-trivial conformal field theories as theories of "tensionless" $p$-branes of which tensionless strings in $d=6$ are just particular examples.