Noncompact chiral U(1) gauge theories on the lattice

Abstract

A new, adiabatic phase choice is adopted for the overlap in the case of an infinite volume, noncompact abelian chiral gauge theory. This gauge choice obeys the same symmetries as the Brillouin-Wigner (BW) phase choice, and, in addition, produces a Wess-Zumino functional that is linear in the gauge variables on the lattice. As a result, there are no gauge violations on the trivial orbit in all theories, consistent and covariant anomalies are simply related and Berry's curvature now appears as a Schwinger term. The adiabatic phase choice can be further improved to produce a perfect phase choice, with a lattice Wess-Zumino functional that is just as simple as the one in continuum. When perturbative anomalies cancel, gauge invariance in the fermionic sector is fully restored. The lattice effective action describing an anomalous abelian gauge theory has an explicit form, close to one analyzed in the past in a perturbative continuum framework.

35 pages, one figure, plain TeX; minor typos corrected; to appear in PRD

References in corpus (2)

• Bounds on the Wilson Dirac Operator
• Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories

Cited by in corpus (22)

• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• A lattice non-perturbative definition of an SO(10) chiral gauge theory and its induced standard model
• Non-Perturbative Regularization of 1+1D Anomaly-Free Chiral Fermions and Bosons: On the equivalence of anomaly matching conditions and boundary gapping rules
• A Solution to the 1+1D Gauged Chiral Fermion Problem
• Exact Chiral Symmetry on the Lattice
• Chiral Lattice Gauge Theories and The Strong Coupling Dynamics of a Yukawa-Higgs Model with Ginsparg-Wilson Fermions
• Domain wall fermion and chiral gauge theories on the lattice with exact gauge invariance
• Locality Properties of a New Class of Lattice Dirac Operators
• Lattice chirality and the decoupling of mirror fermions
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Gauge fixing, families index theory, and topological features of the space of lattice gauge fields
• Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice
• Warped Domain Wall Fermions
• A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance
• New overlap construction of Weyl fermions
• A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance
• A numerical solution to the local cohomology problem in U(1) chiral gauge theories
• Anomalous gauge theories revisited
• Remarks on left-handed lattice fermions
• Four-dimensional lattice chiral gauge theories with anomalous fermion content
• CP symmetry and lattice chiral gauge theories