$C_T$ for Non-unitary CFTs in Higher Dimensions

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.

arXiv comment19 pages. v2: References added, discussion expanded, typos fixed. v3: Note added including a derivation of eq. (2.13). v4: Minor clarifications, version to appear in JHEP

References in corpus (24)

• New Developments in FeynCalc 9.0
• Implications of Conformal Invariance in Field Theories for General Dimensions
• The Uses of Conformal Symmetry in QCD
• Holographic GB gravity in arbitrary dimensions
• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• Unitarity and the Holographic S-Matrix
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Notes On Higher Spin Symmetries
• Conserved Currents, Consistency Relations and Operator Product Expansions in the Conformally Invariant O(N) Vector Model
• Conformally invariant powers of the Laplacian, Q-curvature, and tractor calculus
• What Maxwell Theory in D<>4 teaches us about scale and conformal invariance
• Conformally Covariant Differential Operators: Properties and Applications
• C_{T} and C_{J} up to next-to-leading order in 1/N in the Conformally Invariant O(N) Vector Model for 2<d<4
• Weyl vs. Conformal
• Renormalization Theory for Interacting Crumpled Manifolds
• Structures on the Conformal Manifold in Six Dimensional Theories
• On $C_J$ and $C_T$ in the Gross-Neveu and $O(N)$ Models
• Six dimensional QCD at two loops
• Conformal anomaly c-coefficients of superconformal 6d theories
• Renormalization of Crumpled Manifolds
• Two-loop renormalization of multiflavor ${\varphi }^3$ theory in six dimensions and the trace anomaly
• Symplectic critical models in $6+\epsilon$ dimensions
• Conformal symmetry in non-local field theories
• Classification of Perturbations for Membranes with Bending Rigidity

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• Boundaries in Free Higher Derivative Conformal Field Theories
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• Higher Derivative Gauge theory in $d=6$ and the $\mathbb{C}{\mathbb{P}}^{(N_f-1)}$ NLSM
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