The free $\sigma$CFTs

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 $d\ge 4$. We use OPE techniques to study their spectrum and show that for $d\to \infty$ 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.

18+10 pages, no figure; v2: references updated, typos corrected, matches JHEP version

References in corpus (4)

• Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies
• $C_T$ for Non-unitary CFTs in Higher Dimensions
• Symplectic critical models in $6+\epsilon$ dimensions
• Higher Spin Fronsdal Equations from the Exact Renormalization Group

Cited by in corpus (11)

• Spinning Witten Diagrams
• Free box^k Scalar Conformal Field Theory
• Generalized Wilson-Fisher critical points from the conformal OPE
• The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
• Partially Massless Higher-Spin Theory
• Large $N_f$ quantum field theory
• $C_T$ for higher derivative conformal fields and anomalies of (1,0) superconformal 6d theories
• Partially Massless Graviton on Beyond Einstein Spacetimes
• Scale and Conformal Invariance in Higher Derivative Shift Symmetric Theories
• Partially Massless Higher-Spin Theory II: One-Loop Effective Actions
• Weyl Covariance and the Energy Momentum Tensors of Higher-Derivative Free Conformal Field Theories