In the realm of theoretical physics, researchers Zheyan Wan and Juven Wang from the Massachusetts Institute of Technology have been delving into the intricacies of topological quantum field theories (TQFTs) and their implications for global symmetries. Their recent work, published in the journal Physical Review D, explores the concept of ‘t-Hooft anomalies in discrete finite-group global symmetries and their potential cancellation through anomalous symmetry-preserving TQFTs.
The researchers focus on mixed gauge-gravitational nonperturbative global anomalies of Weyl fermions, which are particles that exhibit Weyl symmetry, in four-dimensional spacetime. These fermions are charged under discrete Abelian internal symmetries, and the researchers consider spacetime-internal fermionic symmetry groups that include fermion parity.
In their study, Wan and Wang determine the minimal finite gauge group K of anomalous G-symmetric TQFTs that can match the fermionic anomaly via a symmetry-extension construction. This construction allows the anomaly in the original symmetry group G to be trivialized upon pullback to a larger group G_Tot. The researchers compute this using the Atiyah-Patodi-Singer eta invariant, a mathematical tool used in the study of elliptic operators on manifolds with boundary.
The practical application of this research lies in the potential to replace a G-symmetric four-dimensional Weyl fermion with an anomalous G-symmetric discrete-K-gauge TQFT as an alternative low-energy theory within the same deformation class. This could have significant implications for the energy sector, particularly in the development of topological quantum computing and the understanding of exotic states of matter.
One of the most intriguing applications of this research is in the context of the Standard Model of particle physics. The researchers demonstrate that the four-dimensional Standard Model with 15 Weyl fermions per family, in the absence of a sterile right-handed neutrino, exhibits mixed gauge-gravitational global anomalies between baryon and lepton number symmetries and spacetime diffeomorphisms. They identify the corresponding minimal K-gauge fermionic TQFT that cancels these anomalies, suggesting that this TQFT could be interpreted as a gapped, topologically ordered dark sector replacing missing Weyl fermions via symmetry extension, without invoking conventional Anderson-Higgs symmetry breaking.
While the immediate practical applications for the energy industry may not be apparent, the underlying principles of this research could contribute to the development of new materials and technologies based on topological quantum field theories. These could potentially revolutionize areas such as energy storage, quantum computing, and the understanding of fundamental physical processes. The research was published in Physical Review D, a peer-reviewed scientific journal published by the American Physical Society.
This article is based on research available at arXiv.