Related papers: Wess-Zumino-Witten term on the lattice
As first realized by Witten an SU(2) gauge theory coupled to a single Weyl fermion suffers from a global anomaly. This problem is addressed here in the context of the recent developments on chiral gauge theories on the lattice. We find…
In continuum field theory, it has been discussed that chiral gauge theories with Weyl fermions in anomalous gauge representations (anomalous gauge theories) can consistently be quantized, provided that some of gauge bosons are permitted to…
We study the gauge anomaly ${\cal A}$ defined on a 4-dimensional infinite lattice while keeping the lattice spacing finite. We assume that (I) ${\cal A}$ depends smoothly and locally on the gauge potential, (II) ${\cal A}$ reproduces the…
It is shown that the lattice Wess-Zumino model written in terms of Ginsparg-Wilson fermions is invariant under a generalized supersymmetry transformation which is determined by an iterative procedure in the coupling constant. This…
We derive higher Wess--Zumino--Witten (WZW) and gauged WZW (gWZW) terms within strict higher Chern--Simons (CS) gauge theory. Starting from the Cartan homotopy formula, we obtain the $(2n+2)$-dimensional higher CS forms and transgression…
We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the lattice Dirac operator. These conditions are locality, gauge covariance and the absense of…
We demonstrate that in the topologically trivial gauge sector the Ginsparg-Wilson relation for lattice Dirac operators admits an exactly gauge invariant path integral formulation of the Weyl fermions on a lattice.
We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the lattice Dirac operator. These conditions are locality, gauge covariance and the absense of…
The axial anomaly in abelian lattice gauge theories is shown to be equal to a simple quadratic expression in the gauge field tensor plus a removable divergence term if the lattice Dirac operator satisfies the Ginsparg-Wilson relation. The…
Based upon the mathematical formulas of Lattice gauge theory and non-commutative geometry differential calculus, we developed an approach of generalized gauge theory on a product of the spacetime lattice and the two discrete points(or a…
Witten's anomaly for SU(2) with a single I=1/2 Weyl fermion in four dimension is shown to be reproduced by the lattice overlap. The mechanism is based on Berry's phase, and on the analyticity of the matrix $H$ by which the overlap is…
The low-energy physics of systems with spontaneously broken continuous symmetry is dominated by the ensuing Nambu-Goldstone bosons. It has been known for half a century how to construct invariant Lagrangian densities for the low-energy…
We prove that lattice QCD generates the axial anomaly in the continuum limit under very general conditions on the lattice action, which includes the case of Ginsparg-Wilson fermions. The ingredients going into the proof are gauge…
We consider a 4d non-linear sigma model on the coset $(\mathrm{SU}(N)_L \times \mathrm{SU}(N)_R \times \mathrm{SU}(2))/(\mathrm{SU}(N)_{L+R}\times \mathrm{U}(1))\cong \mathrm{SU}(N) \times S^2$, that features a topological…
The major obstacle to a supersymmetric theory on the lattice is the failure of the Leibniz rule. We analyze this issue by using the Wess-Zumino model and a general Ginsparg-Wilson operator, which is local and free of species doublers. We…
A Fermi surface threaded by a Berry phase can be described by the Wess-Zumino-Witten (WZW) term. After gauging, it produces a five-dimensional Chern-Simons term in the action. We show how this Chern-Simons term captures the essence of the…
A lattice formulation of the four dimensional Wess-Zumino model that uses Ginsparg-Wilson fermions and keeps exact supersymmetry is presented. The supersymmetry transformation that leaves invariant the action at finite lattice spacing is…
By carrying out a systematic expansion of Feynman integrals in the lattice spacing, we show that the axial anomaly in the U(1) lattice gauge theory with Wilson fermions, as determined in one-loop order from an irrelevant lattice operator in…
The observation that SU(3)/SU(2) ~ S^5 implies the existence of a particularly simple quantized topological action, or Wess-Zumino-Witten (WZW) term. This action plays an important role in anomaly cancellation in extensions of the Standard…
The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for L\"uscher's gauge-invariant lattice formulation of chiral gauge theories. We can explicitly construct the fermion…