Chiral Symmetry Restoration in the Schwinger Model with Domain Wall Fermions

Domain-wall fermions preserve chiral symmetry up to terms that decrease exponentially when the lattice size in the fifth dimension is taken to infinity. The associated rates of convergence are given by the low-lying eigenvalues of a simple local operator in four dimensions. These can be computed using the Ritz functional technique and it turns out that the convergence tends to be extremely slow in the range of lattice spacings relevant to large-volume numerical simulations of...

We investigate a recent proposal to construct chiral gauge theories on the lattice using domain wall fermions. We restrict ourselves to the finite volume case, in which two domain walls are present, with modes of opposite chirality on each of them. We couple the chiral fermions on only one of the domain walls to a gauge field. In order to preserve gauge invariance, we have to add a scalar field, which gives rise to additional light mirror fermion and scalar modes. We argue th...

Some time ago Kaplan proposed a new model for the description of chiral fermions on the lattice by adding an extra dimension for the fermions. A variant of this proposal was introduced by Shamir and can be used to describe vector-like theories in even dimensions. We used this model for the simulation of the massive Schwinger model at different gauge couplings. The prediction that the fermion mass gets only multiplicative renormalization was tested and verified.

We present results from simulations of two flavor QCD thermodynamics at N_t=4 with domain wall fermions. In contrast to other lattice fermion formulations, domain wall fermions preserve the full chiral symmetry of the continuum at finite lattice spacing (up to terms exponentially small in an extra parameter). Just above the phase transition, we find that the axial U(1) symmetry is broken only by a small amount. We discuss an ongoing calculation to determine the order and prop...

We analyze the chiral Schwinger model on an infinite lattice using the continuum definition of the fermion determinant and a linear interpolation of the lattice gauge fields. For non-compact and Wilson formulation of the gauge field action it is proven that the effective lattice model is Osterwalder-Schrader positive, which is a sufficient condition for the reconstruction of a physical Hilbert space from the model defined on a Euclidean lattice. For the non-compact model we f...

We present results for the dependence of the residual mass of domain wall fermions (DWF) on the size of the fifth dimension and its relation to the density and localization properties of low-lying eigenvectors of the corresponding hermitian Wilson Dirac operator relevant to simulations of 2+1 flavor domain wall QCD. Using the DBW2 and Iwasaki gauge actions, we generate ensembles of configurations with a $16^3\times 32$ space-time volume and an extent of 8 in the fifth dimensi...

Quantum Chromodynamics (QCD) is the fundamental theory for the interaction between quarks and gluons. It manifests as the short-range strong interaction inside the nucleus, and plays an important role in the evolution of the early universe, from the quark-gluon phase to the hadron phase. To solve QCD is a grand challenge, since it requires very large-scale numerical simulations of the discretized action of QCD on the 4-dimensional space-time lattice. Moreover, since quarks ar...

The inverse of the fermion matrix squared is used to define a transfer matrix for domain-wall fermions. When the domain-wall height $M$ is bigger than one, the transfer matrix is complex. Slowly suppressed chiral symmetry violations may then arise from all eigenvalues of the transfer matrix which are located near the unit circle. Using a variable lattice spacing for the fifth coordinate we enforce the strict positivity of the transfer matrix for any $M$. We furthermore propos...

Domain wall fermions provide a complimentary alternative to traditional lattice fermion approaches. By introducing an extra dimension, the amount of chiral symmetry present in the lattice theory can be controlled in a linear way. This results in improved chiral properties as well as robust topological zero modes. A brief introduction on the subject and a discussion of chiral properties and applications, such as zero and finite temperature QCD, N = 1 super Yang-Mills, and four...

We study the restoration of the spontaneously broken chiral symmetry and the anomalously broken axial U(1) symmetry in finite temperature QCD at zero chemical potential. We use 2 flavors lattice QCD with optimal domain-wall fermion on the $ 16^3 \times 6 $ lattice, with the extent $ N_s = 16 $ in the fifth dimension, in the temperature range $ T = 130-230 $ MeV. To examine the restoration of the chiral symmetry and the axial $ U(1) $ symmetry, we use diluted $ Z_2 $ noises to...