相关论文: Index theorem for topological excitations on R^3 *…

An expression is found for the $L^2$-index of a Dirac operator coupled to a connection on a $U_n$ vector bundle over $S^1\times{\mathbb R}^3$. Boundary conditions for the connection are given which ensure the coupled Dirac operator is…

Topological fermions as excitations from multi-degenerate Fermi points have been attracting increasing interests in condensed matter physics. They are characterized by topological charges, and magnetic fields are usually applied in…

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 consider a Wilson-Dirac operator with improved chiral properties. We show that, for arbitrarily rough gauge fields, it satisfies the index theorem if we identify the zero modes with the small real eigenvalues of the fermion operator and…

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 provide a general formula for the partition function of three-dimensional $\mathcal{N}=2$ gauge theories placed on $S^2 \times S^1$ with a topological twist along $S^2$, which can be interpreted as an index for chiral states of the…

We investigate numerically the spectral flow introduced by Adams for the staggered Dirac operator on realistic (quenched) gauge configurations. We obtain clear numerical evidence that the definition works as expected: there is a clear…

Index theorems for the Dirac operator allow one to study spinors on manifolds with boundary and torsion. We analyse the modifications of the boundary Chern-Simons correction and APS eta invariant in the presence of torsion. The bulk…

The fixed point Dirac operator on the lattice has exact chiral zero modes on topologically non-trivial gauge field configurations independently whether these configurations are smooth, or coarse. The relation $n_L-n_R = Q^{FP}$, where $n_L$…

We consider the $S^3\times S^1$ superconformal index $\mathcal{I}(\tau)$ of 4d $\mathcal{N}=1$ gauge theories. The Hamiltonian index is defined in a standard manner as the Witten index with a chemical potential $\tau$ coupled to 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 investigate index theory in the context of Dirac operators coupled to superconnections. In particular, we prove a local index theorem for such operators, and for families of such operators. We investigate eta-invariants and prove an…

The index theorems relate the gauge field and metric on a manifold to the solution of the Dirac equation on it. In the standard approach, the Dirac operator must be massless in order to make the chirality operator well-defined. In physics,…

We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We find a clear separation of the spectrum into would-be zero modes and others. The…

Making use of index theorem and spin Chern Simons theory, we construct an effective topological field theory of strongly correlated topological insulators coupling to a nonabelian gauge field $ SU(N) $ with an interaction constant $ g $ in…

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 various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We find a clear separation of the spectrum of eigenvalues into would-be zero modes and…

We present a rigorous but elementary index theory for a class of one-dimensional systems of interacting (and possibly disordered) fermions with $\Uone\rtimes\bbZ_2$ symmetry defined on the infinite chain. The class includes the…

This article is a tribute to the memory of Professor Enzo Martinelli, with deep respect and reconesance. Nicolae Teleman. The index formula is a local statement made on global and local data; for this reason we introduce local Alexander -…

We investigate the index of the Neuberger's Dirac operator in abelian gauge theories on finite lattices by numerically analyzing the spectrum of the hermitian Wilson-Dirac operator for a continuous family of gauge fields connecting…