$C_T$ for Non-unitary CFTs in Higher Dimensions

TL;DR

This paper computes the $C_T$ coefficient for various non-unitary and higher-derivative conformal field theories in higher dimensions, matching large-$N$ results and exploring new constructions of the energy-momentum tensor.

Contribution

It provides explicit calculations of $C_T$ for non-unitary scalar CFTs with higher derivatives and for $(n-1)$-form gauge fields, extending known results to general dimensions.

Findings

$C_T$ matches large-$N$ predictions for specific models.

Extended $C_T$ results to non-gauge-invariant $(n-1)$-form theories.

Constructed conformal primaries and alternative energy-momentum tensors for higher-derivative theories.

Abstract

The coefficient $C_T$ of the conformal energy-momentum tensor two-point function is determined for the non-unitary scalar CFTs with four- and six-derivative kinetic terms. The results match those expected from large-$N$ calculations for the CFTs arising from the $O(N)$ non-linear sigma and Gross-Neveu models in specific even dimensions. $C_T$ is also calculated for the CFT arising from $(n-1)$-form gauge fields with derivatives in $2n+2$ dimensions. Results for $(n-1)$-form theory extended to general dimensions as a non-gauge-invariant CFT are also obtained; the resulting $C_T$ differs from that for the gauge-invariant theory. The construction of conformal primaries by subtracting descendants of lower-dimension primaries is also discussed. For free theories this also leads to an alternative construction of the energy-momentum tensor, which can be quite involved for higher-derivative theories.