Non-Abelian conformal anomalies are classified via Stora-Zumino descent from the Euler class, placing them on equal footing with perturbative anomalies and enabling WZW terms for anomaly matching.
Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
9 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We give a complete geometric description of conformal anomalies in arbitrary, (necessarily even) dimension. They fall into two distinct classes: the first, based on Weyl invariants that vanish at integer dimensions, arises from finite -- and hence scale-free -- contributions to the effective gravitational action through a mechanism analogous to that of the (gauge field) chiral anomaly. Like the latter, it is unique and proportional to a topological term, the Euler density of the dimension, thereby preserving scale invariance. The contributions of the second class, requiring introduction of a scale through regularization, are correlated to all local conformal scalar polynomials involving powers of the Weyl tensor and its derivatives; their number increases rapidly with dimension. Explicit illustrations in dimensions 2, 4 and 6 are provided.
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Constructs an N=2 Liouville SCFT in 4D, shows no quantum correction to the classical background charge, finds c=0 and negative a depending on the charge, and derives integral expressions for superfield vertex operator correlators.
Closed-form higher-dimensional Euler–Heisenberg Lagrangians for spinor and scalar QED are obtained via extended Schwinger proper-time, with weak-field results in 6, 8, 10D and a d=6 Weyl-anomaly primary.
The replica-energy filter (1 − d^{-1} L ∂_L) on log Z isolates universal subextensive data in thermal QFT: central charges, sphere free energies, topological degeneracies, fracton degeneracies, and the Euler anomaly.
Symmetric teleparallel gravity has the same number of degrees of freedom as general relativity, confirmed via its Hamiltonian formulation after deriving generalized extrinsic geometry relations.
Weyl quadratic gauge gravity is anomaly-free, breaks via Stueckelberg to Einstein-Hilbert plus positive Lambda, and is the leading order of a regulator-free WDBI action that can include the SM.
An auxiliary scalar compensator enables conformal regularization of a vector field model in D ≠ 4, resulting in independent scalar dynamics and interesting properties in the four-dimensional limit.
Anomaly cancellation for specific multiplet numbers in conformal supergravities implies divergences proportional to n_v+2 in 4d PSG and n_T-21 in 6d PSG.
Lecture notes develop semiclassical methods to compute large-n scaling dimensions of composite operators in CFTs, recovering known results in free theory and deriving one-loop corrections at the Wilson-Fisher fixed point.
citing papers explorer
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Non-Abelian and Type-A Conformal Anomalies from Euler Descent
Non-Abelian conformal anomalies are classified via Stora-Zumino descent from the Euler class, placing them on equal footing with perturbative anomalies and enabling WZW terms for anomaly matching.
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$\mathcal{N}=2$ Liouville SCFT in Four Dimensions
Constructs an N=2 Liouville SCFT in 4D, shows no quantum correction to the classical background charge, finds c=0 and negative a depending on the charge, and derives integral expressions for superfield vertex operator correlators.
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Euler-Heisenberg actions in higher dimensions
Closed-form higher-dimensional Euler–Heisenberg Lagrangians for spinor and scalar QED are obtained via extended Schwinger proper-time, with weak-field results in 6, 8, 10D and a d=6 Weyl-anomaly primary.
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Nonadditivity in Quantum Field Theory: Replica Energies, Scaling Filters, and the Renormalization Group
The replica-energy filter (1 − d^{-1} L ∂_L) on log Z isolates universal subextensive data in thermal QFT: central charges, sphere free energies, topological degeneracies, fracton degeneracies, and the Euler anomaly.
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Extrinsic geometry and Hamiltonian analysis of symmetric teleparallel gravity
Symmetric teleparallel gravity has the same number of degrees of freedom as general relativity, confirmed via its Hamiltonian formulation after deriving generalized extrinsic geometry relations.
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The fall and the rise of Weyl gauge theory
Weyl quadratic gauge gravity is anomaly-free, breaks via Stueckelberg to Einstein-Hilbert plus positive Lambda, and is the leading order of a regulator-free WDBI action that can include the SM.
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Conformal anomaly in a vector field model with auxiliary scalar field
An auxiliary scalar compensator enables conformal regularization of a vector field model in D ≠ 4, resulting in independent scalar dynamics and interesting properties in the four-dimensional limit.
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On anomaly free 4d $\mathcal{N}$=4 and 6d (2,0) conformal supergravities and UV finiteness of Poincar\'e supergravities
Anomaly cancellation for specific multiplet numbers in conformal supergravities implies divergences proportional to n_v+2 in 4d PSG and n_T-21 in 6d PSG.
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Lectures on Semiclassical Methods for Composite Operators
Lecture notes develop semiclassical methods to compute large-n scaling dimensions of composite operators in CFTs, recovering known results in free theory and deriving one-loop corrections at the Wilson-Fisher fixed point.