In
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
, a chiral gauge theory is a quantum field theory with charged chiral (i.e.
Weyl
Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...
) fermions. For instance, the
Standard Model
The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...
is a chiral gauge theory. For topological reasons, chiral charged fermions cannot be given a mass without breaking the gauge symmetry, which will lead to inconsistencies unlike a global symmetry. It is notoriously difficult to construct a chiral gauge theory from a theory which does not already contain chiral fields at the fundamental level.
A consistent chiral gauge theory must have no
gauge anomaly
In theoretical physics, a gauge anomaly is an example of an anomaly: it is a feature of quantum mechanics—usually a one-loop diagram—that invalidates the gauge symmetry of a quantum field theory; i.e. of a gauge theory.
All gauge anomalie ...
(or
global anomaly
Primary Examples
In theoretical physics, a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformation that would otherwise be preserved in the classical theory. This lea ...
). Almost by necessity,
regulators will have to break the gauge symmetry. This is responsible for gauge anomalies in the first place.
Fermion doubling on a lattice
Lattice regularizations suffer from
fermion doubling
In lattice field theory, fermion doubling occurs when naively putting fermionic fields on a lattice (group), lattice, resulting in more fermionic states than expected. For the naively discretized Dirac fermions in d Euclidean space, Euclidean dime ...
s leading to a loss of chirality.
See also
*
Chiral anomaly
In theoretical physics, a chiral anomaly is the anomalous nonconservation of a chiral current. In everyday terms, it is analogous to a sealed box that contained equal numbers of left and right-handed bolts, but when opened was found to have mor ...
References
External links
*
273. Lattice Chiral Gauge Theories: What’s the Problem?, Yanwen Shang, Department of Physics, University of Toronto, February 19, 2009
Gauge theories
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