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Twenty Years of the Weyl Anomaly
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abstract
In 1973 two Salam prot\'{e}g\'{e}s (Derek Capper and the author) discovered that the conformal invariance under Weyl rescalings of the metric tensor $g_{\mu\nu}(x)\rightarrow\Omega^2(x)g_{\mu\nu}(x)$ displayed by classical massless field systems in interaction with gravity no longer survives in the quantum theory. Since then these Weyl anomalies have found a variety of applications in black hole physics, cosmology, string theory and statistical mechanics. We give a nostalgic review. (Talk given at the {\it Salamfest}, ICTP, Trieste, March 1993.)
Forward citations
Cited by 19 Pith papers
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Six-dimensional $\mathcal{N}=(2,0)$ Conformal Superspace
A new off-shell 6D N=(2,0) conformal superspace is constructed, and its unique Bach tensor superfield is derived up to overall scaling.
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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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Symmetry TFTs for Continuous Spacetime Symmetries
Continuous spacetime symmetries can be encoded in a (d+1)-dimensional BF/Chern-Simons topological field theory, whose boundary reproduces symmetry generators, symmetry breaking, and anomalies.
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On the Renormalization in Conformal Quantum Gravity
A formal BRST proof that one-loop divergences in conformal quantum gravity, pure or with matter, are invariant under local conformal transformations.
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Four-Fermion Condensates in Curved Spacetimes: A Functional Approach
A one-loop functional derivation gives the local effective action and FLRW energy-momentum tensor for a scalar-channel NJL condensate in curved spacetime, reproducing flat-space mean-field results in the constant-cond...
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Conformally Invariant Corrections to the Anomaly-Induced Effective Action and Black Hole Evaporation in Four Dimensions
Conformally invariant corrections to the anomaly-induced effective action produce a one-parameter family of quantum hair for Schwarzschild black holes that modifies the near-horizon stress tensor in a static approximation.
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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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The One-Loop QCD $\beta$-Function as an Index
The one-loop QCD beta-function coefficient b and the Weyl anomaly difference a-c are computed as the first Chern class of a determinant line bundle via Grothendieck-Riemann-Roch on twistor space.
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One loop analysis of the cubic action for gravity
The cubic Palatini gravity action is BRST-consistent at one loop around flat space only after finite counterterms beyond minimal subtraction are added.
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Analyticity Constraints and Trace Anomaly Matching
Type A and type B trace anomalies are shown to match between the unbroken and spontaneously broken phases of conformal field theories, with new dispersive sum rules constraining dilaton couplings to massive states.
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Inner horizon instability via the trace anomaly effective action
The anomaly-induced effective action can reproduce the Hartle-Hawking stress-energy divergence at the Cauchy horizon of Reissner-Nordström, but lacks enough freedom to describe the Unruh state.
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Emergent gravitational action from non-local $T\bar T$-like deformations
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Nonadditivity in Quantum Field Theory: Replica Energies, Scaling Filters, and the Renormalization Group
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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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From minimal-length quantum theory to modified gravity
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Semi-classical spacetime thermodynamics
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Conformal anomaly in a vector field model with auxiliary scalar field
An auxiliary scalar compensator in a vector field model allows conformal formulation in D≠4 and yields independent scalar dynamics after the 4D limit.
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Inside astronomically realistic black holes
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Progress in Einstein-Cartan gravity
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