The free $\sigma$CFTs

TL;DR

This paper introduces a new class of free conformal field theories called $\sigma$CFTs, describing shadows of composite operators made from free scalars and fermions, and explores their properties across various dimensions.

Contribution

It defines $\sigma$CFTs as consistent free theories in even dimensions and analyzes their spectra and central charges, extending understanding of shadow CFTs in higher dimensions.

Findings

$\sigma$CFTs are consistent free theories in even $d \\geq 4$

Spectrum matches free bosonic CFTs as $d \\to \\infty$

Calculated $c_T$ in multiple dimensions, confirming theoretical predictions

Abstract

We introduce the conformal field theories that describe the shadows of the lowest dimension composites made out of massless free scalars and fermions in $d$ dimensions. We argue that these theories can be consistently defined as free CFTs for even $d\geq 4$. We use OPE techniques to study their spectrum and show that for $d\rightarrow\infty$ it matches that of free bosonic CFTs in $d=6$ and $d=4$ dimensions. For these $\sigma$CFTs we calculate $c_T$ in $d=6,8,10$ and $12$ dimensions using the OPE and also a direct construction of their higher-derivative energy momentum tensors. Our results agree with the general proposal of arXiv:1601.07198.