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We propose a new formulation which realizes exact twisted supersymmetry for all the supercharges on a lattice by twisted superspace formalism. We show explicit examples of N=2 twisted supersymmetry invariant BF and Wess-Zumino models in two dimensions. We introduce mild lattice noncommutativity to preserve Leibniz rule on the lattice. The formulation is based on the twisted superspace formalism for N=D=2 supersymmetry which was proposed recently. From the consistency condition of the noncommutativity of superspace, we find an unexpected three-dimensional lattice structure which may reduce into two dimensional lattice where the superspace describes semilocally scattered fermions and bosons within a double size square lattice.
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We report the results of the lattice simulation of the ${mathbb C} P^{N-1}$ sigma model on $S_{s}^{1}$(large) $times$ $S_{tau}^{1}$(small). We take a sufficiently large ratio of the circumferences to approximate the model on ${mathbb R} times S^1$. For periodic boundary condition imposed in the $S_{tau}^{1}$ direction, we show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as the compactified circumference is decreased, where the peak of the associated susceptibility gets sharper for larger $N$. For ${mathbb Z}_{N}$ twisted boundary condition, we find that, even at relatively high $beta$ (small circumference), the regular $N$-sided polygon-shaped distributions of Polyakov loop leads to small expectation values of Polyakov loop, which implies unbroken ${mathbb Z}_{N}$ symmetry if sufficient statistics and large volumes are adopted. We also argue the existence of fractional instantons and bions by investigating the dependence of the Polyakov loop on $S_{s}^{1}$ direction, which causes transition between ${mathbb Z}_{N}$ vacua.
In this work a lattice formulation of a supersymmetric theory is proposed and tested that preserves the complete supersymmetry on the lattice. The results of a one-dimensional nonperturbative simulation show the realization of the full supersymmetry and the correct continuum limit of the theory. It is proven that the violation of supersymmetry due to the absence of the Leibniz rule on the lattice can be amended only with a nonlocal derivative and nonlocal interaction term. The fermion doubling problem is also discussed, which leads to another important source of supersymmetry breaking on the lattice. This problem is also solved with a nonlocal realization.
We perform a numerical study of ghost condensation -- in the so-called Overhauser channel -- for SU(2) lattice gauge theory in minimal Landau gauge. The off-diagonal components of the momentum-space ghost propagator G^{cd}(p) are evaluated for lattice volumes V = 8^4, 12^4, 16^4, 20^4, 24^4 and for three values of the lattice coupling: beta = 2.2, 2.3, 2.4. Our data show that the quantity phi^b(p) = epsilon^{bcd} G^{cd}(p) / 2 is zero within error bars, being characterized by very large statistical fluctuations. On the contrary, |phi^b(p)| has relatively small error bars and behaves at small momenta as L^{-2} p^{-z}, where L is the lattice side in physical units and z approx 4. We argue that the large fluctuations for phi^b(p) come from spontaneous breaking of a global symmetry and are associated with ghost condensation. It may thus be necessary (in numerical simulations at finite volume) to consider |phi^b(p)| instead of phi^b(p), to avoid a null average due to tunneling between different broken vacua. Also, we show that phi^b(p) is proportional to the Fourier-transformed gluon field components {widetilde A}_{mu}^b(q). This explains the L^{-2} dependence of |phi^b(p)|, as induced by the behavior of | {widetilde A}_{mu}^b(q) |. We fit our data for |phi^b(p)| to the theoretical prediction (r / L^2 + v) / (p^4 + v^2), obtaining for the ghost condensate v an upper bound of about 0.058 GeV^2. In order to check if v is nonzero in the continuum limit, one probably needs numerical simulations at much larger physical volumes than the ones we consider. As a by-product of our analysis, we perform a careful study of the color structure of the inverse Faddeev-Popov matrix in momentum space.
A common problem in lattice QCD simulations on the torus is the extremely long autocorrelation time of the topological charge, when one approaches the continuum limit. The reason is the suppressed tunneling between topological sectors. The problem can be circumvented by replacing the torus with a different manifold, so that the connectivity of the configuration space is changed. This can be achieved by using open boundary conditions on the fields, as proposed earlier. It has the side effect of breaking translational invariance strongly. Here we propose to use a non-orientable manifold, and show how to define and simulate lattice QCD on it. We demonstrate in quenched simulations that this leads to a drastic reduction of the autocorrelation time. A feature of the new proposal is, that translational invariance is preserved up to exponentially small corrections. A Dirac-fermion on a non-orientable manifold poses a challenge to numerical simulations: the fermion determinant becomes complex. We propose two approaches to circumvent this problem.
We present results on the nucleon electromagnetic form factors within lattice QCD using two flavors of degenerate twisted mass fermions. Volume effects are examined using simulations at two volumes of spatial length L=2.1 fm and L=2.8 fm. Cut-off effects are investigated using three different values of the lattice spacings, namely a=0.089 fm, a=0.070 and a=0.056 fm. The nucleon magnetic moment, Dirac and Pauli radii are obtained in the continuum limit and chirally extrapolated to the physical pion mass allowing for a comparison with experiment.
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