Chiral and Trace Anomalies| 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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