Related papers: Topology and index theorem with a generalized Vill…
In this contribution we revisit the lattice discretization of the topological charge for abelian lattice field theories. The construction departs from an initially non-compact discretization of the gauge fields and after absorbing $2\pi$…
We simulate the 2d U(1) gauge Higgs model on the lattice with a topological angle $\theta$. The corresponding complex action problem is overcome by using a dual representation based on the Villain action appropriately endowed with a…
We discuss a gauged XY model a $\theta$-term on an arbitrary lattice in 1+1 dimensions, and show that the theory reduces exactly to the 2d Ising model on the dual lattice in the limit of the strong gauge coupling, provided that the…
The index, which is given in terms of the number of zero modes of the Dirac operator with definite chirality, plays a central role in various topological aspects of gauge theories. We investigate its properties in non-commutative geometry.…
We discuss general aspects of charge conjugation symmetry in Euclidean lattice field theories, including its dynamical gauging. Our main focus is $O(2) = U(1)\rtimes \mathbb{Z}_2 $ gauge theory, which we construct using a non-abelian…
We investigate topological charge and the index theorem on finite lattices numerically. Using mean field improved gauge field configurations we calculate the topological charge Q using the gluon field definition with ${\cal…
We analyze topological charge contributions from classical SU(2) center vortices with shapes of planes and spheres using different topological charge definitions, namely the center vortex picture of topological charge, a discrete version of…
A way to identify the would-be zero-modes of staggered lattice fermions away from the continuum limit is presented. Our approach also identifies the chiralities of these modes, and their index is seen to be determined by gauge field…
We present a comparison of different definitions of the topological charge on the lattice, using a small-volume ensemble with 2 flavours of dynamical twisted mass fermions. The investigated definitions are: index of the overlap Dirac…
The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a…
We study topological properties of classical spherical center vortices with the low-lying eigenmodes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations. In…
We formulate $U(1)_k$ Chern-Simons theory on a Euclidean spacetime lattice using the modified Villain approach. Various familiar aspects of continuum Chern-Simons theory such as level quantization, framing, the discrete 1-form symmetry and…
The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of Neuberger's lattice Dirac operator, is shown to have analogous properties…
We discuss a particular lattice discretization of abelian gauge theories in arbitrary dimensions. The construction is based on gauging the center symmetry of a non-compact abelian gauge theory, which results in a Villain type action. We…
Recent studies of the topological properties of a general class of lattice Dirac operators are reported. This is based on a specific algebraic realization of the Ginsparg-Wilson relation in the form…
We consider a gauge-Higgs system on a fuzzy 2-sphere and study the topological structure of gauge configurations, when the U(2) gauge symmetry is spontaneously broken to U(1) times U(1) by the vev of the Higgs field. The topology is…
An explicit, detailed evaluation of the classical continuum limit of the axial anomaly/index density of the overlap Dirac operator is carried out in the infinite volume setting, and in a certain finite volume setting where the continuum…
We construct Villain Hamiltonians for compact scalars and abelian gauge theories. The Villain integers are promoted to integral spectrum operators, whose canonical conjugates are naturally compact scalars. Further, depending on the theory,…
It is showed that the very recently introduced Lagrangian $loop$ formulation of the lattice Maxwell theory is equivalent to the Villain form in 2+1 dimensions. A transparent description of the classical $loop$ action is given in pure…
In two dimensions, $U(N_c)$ gauge theories exhibit a non-trivial topological structure, while $SU(N_c)$ theories are topologically trivial. Hence, for $G = U(N_c)$ the phase space is divided into topological sectors, characterized by a…