Related papers: The $SU(2)$ Global Anomaly Through Level Circling
We present a simple exactly solvable quantum mechanical example of the global anomaly in an $O(3)$ model with an odd number of fermionic triplets coupled to a gauge field on a circle. Because the fundamental group is non-trivial, $\pi_1…
A familiar anomaly affects SU(2) gauge theory in four dimensions: a theory with an odd number of fermion multiplets in the spin 1/2 representation of the gauge group, and more generally in representations of spin 2r+1/2, is inconsistent. We…
The response of isodoublet fermions to classical backgrounds of essentially 2-dimensional boson fields in SU(2) Yang-Mills-Higgs theory is investigated. In particular, the spectral flow of Dirac eigenvalues is calculated for a…
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 this work we present the results of our investigation of \su{2} gauge theory with two Dirac fermions in the adjoint representation (aQCD2), which belongs to the class of strongly interacting gauge theories that are of basic interest for…
We propose a six-dimensional regularization of four dimensional chiral gauge theories. We consider a massive Dirac fermion in six dimensions with two different operators having domain-wall profiles in the fifth and the sixth directions,…
We demonstrate that the number of fermionic zero modes of the static $2$-dimensional Dirac operator in the background of $SU(2)$ static gauge-Higgs field configurations is a topological invariant modulo four. Static configurations which are…
In the minimal model of electroweak interactions we carefully investigate the spectrum of the massive euclidean \dop \ in three, four and five dimensions ($D$) in the presence of \tly \ nontrivial \exl \ fields. More specifically we study…
We study two well-known $SU(N)$ chiral gauge theories with fermions in the symmetric, anti-symmetric and fundamental representations. We give a detailed description of the global symmetry, including various discrete quotients. Recent work…
We present the supersymmetric $SU(5)$ models which provide a simple ``all order'' solution to the doublet-triplet splitting problem through the missing doublet mechanism. The crucial role is played by the anomalous $U(1)_A$ gauge symmetry…
On the basis of an observation due to Kiskis, Narayanan and Neuberger, we show that there is a remnant of chiral anomalies in the reduced model when a Dirac operator which obeys the Ginsparg-Wilson relation is employed for the fermion…
We study quantum multicritical behavior in a (2+1)-dimensional Gross-Neveu-Yukawa field theory with eight-component Dirac fermions coupled to two triplets of order parameters that act as Dirac masses, and transform as $(1,0) + (0,1)$…
We discuss anomaly cancellation in $U(2)$ gauge theories in four dimensions. For a $U(2)$ gauge theory defined with a spin structure, the vanishing of the bordism group $\Omega_5^{\text{Spin}}(BU(2))$ implies that there can be no global…
We propose a regularization of four dimensional chiral gauge theories using six-dimensional Dirac fermions. In our formulation, we consider two different mass terms having domain-wall profiles in the fifth and the sixth directions,…
We consider 1+1 dimensional SU(N) gauge theory coupled to a multiplet of massive Dirac fermions transforming in the adjoint representation of the gauge group. The only global symmetry of this theory is a U(1) associated with the conserved…
Motivated by recent scenarios of exotic infrared behaviour and by earlier lattice findings, we present results for the SU(2) gauge theory with one Dirac flavor in the adjoint representation. This provides a major update on our previous…
We point out that fermionic unitary operators which anticommute among themselves appear in various situations in quantum field theories with anomalies in the Hamiltonian formalism. To illustrate, we give multiple derivations of the fact…
We compute the spectrum of SU(2) gauge theory with two, four or six Dirac fermions in the fundamental representation of the gauge group. We investigate the scaling of the meson masses as a function of the quark mass when approaching the…
We consider N Dirac fermions on a 4-dimensional Euclidean space with a quadratic interaction given by arbitrary external Clifford-valued fields. The divergence of the axial current satisfies on the classical level a relation that is…
We propose an extension of the Yang-Mills paradigm from Lie algebras to internal chiral superalgebras. We replace the Lie algebra-valued connection one-form $A$, by a superalgebra-valued polyform $\widetilde{A}$ mixing exterior-forms of all…