Chiral and Trace Anomalies  

Chiral Anomalies for Spinor Field Theory
$ Def: The anomaly in the chiral current j5a:= ψ* γa γ5 ψ for a spinor field.
* Adler-Bardeen theorem: A result, first proved for QED by Adler and Bardeen in 1969, on the cancellation of anomalies to all orders when they vanish at one loop; It is also known as anomaly non-renormalization, in the sense that it says that the chiral anomaly is given exactly by its lower order contribution.
* Consequences: The \(\pi^0 \to \gamma + \gamma + \gamma\) decay.
@ General references: Zumino in(83); Mañes, Stora & Zumino CMP(86); Banerjee ht/99-ch; Fröhlich & Pedrini ht/00-in [applications]; Ekstrand PLB(00)ht [geometrical interpretation]; Kraus ht/02-conf; Gursoy et al PRD(04)ht/03 [and M-theory]; Adler ht/04-in; Bär & Strohmaier CMP(16)-a1508 [in curved backgrounds].
@ Adler-Bardeen theorem: Mastropietro JMP(07)ht/06 [non-perturbative version]; Anselmi EPJC(14)-a1402.
@ And path integrals: Fujikawa, Ojima & Yajima PRD(86); Gozzi et al IJMPA(05)ht/04 [classical and quantum].
@ And gravity: Dolgov et al NPB(88); Mielke & Kreimer IJMPD(98) [in the Ashtekar approach]; Klebanov et al PRD(02) [gravity dual]; Mielke AIP(08)ht [in gauge theory approaches to gravity].
@ In fuzzy / non-commutative physics: Balachandran & Vaidya IJMPA(01)ht/99; Martin MPLA(01)ht-proc [non-commutative Minkowski spacetime].
@ In Lorentz-violating theories: Arias et al PRD(07)-a0705; Baeta Scarpelli et al IJMPA(16)-a1505 [Lorentz-breaking QED extension].
@ Related topics: Jackiw ht/01-in [and Chern-Simons terms]; Obukhov et al FP(97) [in non-Riemannian spacetime]; Fujikawa IJMPA(08) [vs geometric phase]; Parameswaran et al PRX(14) [transport in topological semimetals].

Conformal / Trace Anomalies > s.a. Bach Tensor [and AdS-cft]; black-hole radiation; conformal invariance [breaking]; cosmological constant; inflation.
* Idea: The non-vanishing of the regularized \(\langle\)T ab\(\rangle\) for theories that are classically conformally invariant.
@ General references: Deser HPA(96)ht [review for relativists]; Cappelli & D'Appollonio PLB(00) [χ and degrees of freedom]; Cappelli et al NPB(01)ht [consequences]; Bastianelli & Dass PRD(01)ht [calculation]; Giannotti & Mottola PRD(09)-a0812 [and massless scalar degrees of freedom]; Donoghue & El-Menoufi a1503 [non-local effective action and infrared physics]; Choy a2007 [and Dirac quantization].
@ And effective action for gravity: Mazur & Mottola PRD(01); Mottola & Vaulin PRD(06)gq; Bardeen a1808 [requirements and proposals].
@ In curved spacetime: Wald PRD(78); Bisabr IJTP(05)ht/04 [thermal radiation in cosmology]; Tsoupros IJMPA(05) [with boundary, interacting scalar]; Spallucci et al PRD(06)ht [quantum spacetime]; Koksma & Prokopec PRD(08)-a0803, Thomas et al JHEP(09)-a0904 [and the cosmological constant]; Koksma a0911-proc [and FLRW cosmology, cosmological constant]; Mottola IJMPA(10)-a1006 [and dynamical vacuum energy in cosmology]; Solodukhin PLB(16)-a1510 [boundary terms].
@ Gravity theories: Dowker CQG(98) [2D dilaton gravity]; Meissner & Nicolai PLB(17)-a1607 [constraints from gravitational wave observations, and viable theories]; > s.a. higher-order gravity; semiclassical gravity; unimodular gravity.
@ Other theories: Nakajima PRD(02) [non-commutative gauge theory]; Czech ht/07 [2D, discrete scalar field model]; Giacosa & Hofmann PRD(07)ht [Yang-Mills theory, linear growth with T]; Andersen et al PRD(11) [QCD]; > s.a. energy-momentum tensor.

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