Quantum Anomaly in a Dirac Fermion System with Spacetime Dependent Mass
© The Physical Society of Japan
This article is on
Anomaly and Superconnection
(PTEP Editors' Choice)
Prog. Theor. Exp. Phys. 2022, 013B02 (2022).
Scientists investigate quantum anomalies in a system of Dirac fermions with spacetime dependent mass and show that the anomaly formulas can be expressed in terms of superconnections.
Quantum anomaly, a situation in which the symmetry of the classical action fails to be a symmetry of the full quantum theory, is a topic of great interest in quantum field theory. This is because it plays various important roles in physics and has beautiful mathematical structures.
In a new study, researchers from Japan explored perturbative anomalies in a system of N Dirac fermions with spacetime dependent mass (or the Higgs field that couples with the fermions through the Yukawa coupling) that included external gauge fields associated with U(N)_{+ }x U(N)_{} chiral symmetry for even dimensions and U(N) flavor symmetry for odd dimensions. Using a technique called “Fujikawa’s method,” they went on to show that the anomalies associated with the chiral and flavor symmetry could be written in terms of a concept called “superconnection” introduced by the mathematician D. Quillen.
Interestingly, their results allowed for a natural string theory interpretation which independently suggests the emergence of superconnections in the anomaly formulas. Moreover, when the team applied these formulas to systems with interfaces and spacetime boundaries, they found that some of the known results for these systems were reproduced in a simple and unified manner.
The formalism developed in this study could be used to describe a broad range of topics in theoretical physics from quantum chromodynamics to topological matter with defects and boundaries, allowing us to explore deeper mathematical structures of physical theories that could lead us to realize new technologies.
Anomaly and Superconnection
(PTEP Editors' Choice)
Prog. Theor. Exp. Phys. 2022, 013B02 (2022).
Share this topic
Fields
Related Articles

Understanding NonInvertible Symmetries in Higher Dimensions Using Topological Defects
Theoretical Particle Physics
2024927
By constructing KramersWannierWegner duality and Z_{2} duality defects and deriving their crossing relations, this study presents the first examples of codimension one noninvertible symmetries in fourdimensional quantum field theories.

Quantum Mechanics of OneDimensional ThreeBody Contact Interactions
Mathematical methods, classical and quantum physics, relativity, gravitation, numerical simulation, computational modeling
Theoretical Particle Physics
2024213
The quantum mechanical description of topologically nontrivial threebody contact interactions in one dimension is not well understood. This study explores the Hamiltonian description of these interactions using the pathintegral formalism.

Investigating Unitarity Violation of Lee–Wick’s Complex Ghost with Quantum Field Theory
Theoretical Particle Physics
2024119
Theories with fourthorder derivatives like Lee–Wick’s quantum electrodynamics model or quadratic gravity result in complex ghosts above a definite energy threshold that violate unitarity.

Investigating Δ and Ω Baryons as Meson–Baryon Bound States in Lattice Quantum Chromodynamics
Theoretical Particle Physics
2023713
We investigate Δ and Ω baryons as meson–baryon bound states in lattice quantum chromodynamics and show that their difference results from the kinematic structure of the two meson–baryon systems, and not their interaction.

Novel Insights Into Bulk Reconstruction in the Antide Sitter/Conformal Field Theory Correspondence
Theoretical Particle Physics
202361
Bulk reconstruction in antide Sitter/conformal field theory is fundamental to our understanding of quantum gravity. We show that contrary to popular belief, bulk reconstruction is rather simple and intuitive.