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The free $\sigma$CFTs
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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.
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Universal relation between $C_{T}$ and the CFT Weyl anomaly
In any even-dimensional CFT, C_T = [d/(d−1)]·[(d+1)!/(d/2−1)!]·c, where c is the coefficient of the quadratic-in-Weyl term in the trace anomaly.
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