Free box^k Scalar Conformal Field Theory

TL;DR

This paper explores generalized free scalar conformal field theories with higher powers of the Laplacian, analyzing their spectra, operator structures, and algebraic properties across various dimensions.

Contribution

It introduces and studies higher-derivative scalar CFTs with box^k operators, revealing novel spectral features and finite operator algebras in certain dimensions.

Findings

Presence of zero norm primary and descendant operators.

Existence of extension operators outside the primary/descendant classification.

Finite single-trace operator algebras in even dimensions d <= 2k.

Abstract

We consider the generalizations of the free U(N) and O(N) scalar conformal field theories to actions with higher powers of the Laplacian box^k, in general dimension d. We study the spectra, Verma modules, anomalies and OPE of these theories. We argue that in certain d and k, the spectrum contains zero norm operators which are both primary and descendant, as well as extension operators which are neither primary nor descendant. In addition, we argue that in even dimensions d <= 2k, there are well-defined operator algebras which are related to the box^k theories and are novel in that they have a finite number of single-trace states.