Tremendous ongoing theory efforts are dedicated to developing new methods for QCD calculations. Qualitative rather than incremental advances needed fully exploit data still be collected at the LHC. The maximally supersymmetric Yang-Mills (${\mathcal N}=4$ sYM) shares with gluon sector, which contains most complicated Feynman graphs, but same time has many special properties, and is believed sol...

A bstract We study quantum chromodynamics including the two-index symmetric or anti-symmetric quark (QCD(Sym/ASym)) on small ℝ 2 × T with a suitable magnetic flux. first discuss ’t Hooft anomaly of these theories and claim that discrete chiral symmetry should be spontaneously broken completely to satisfy matching condition. The compactification flux preserves anomaly, 2d effective theory is con...

A group G Sym(N) is cofinitary if g has finitely many fixed points for every g ∈G except the identity element. In this paper, we discuss the definability of maximal cofinitary groups and some related structures. More precisely, we show the following two results: (1) Assuming V = L, there is a Π1 1 set of permutations on N which generates a maximal cofinitary group. (2) Assuming V = L, there is ...

Recent progress in the nonperturbative solution of (3+1)-dimensional Yukawa theory and quantum electrodynamics (QED) and (1+1)-dimensional super Yang–Mills (SYM) theory will be summarized. The work on Yukawa theory has been extended to include two-boson contributions to the dressed fermion state and has inspired similar work on QED, where Feynman gauge has been found surprisingly convenient. In...

We study N = 4 supersymmetric Yang-Mills (SYM) theory with gauge group SU(2) com-pactified to three dimensions on a circle of circumference β. The eight fermion terms in the effective action on the Coulomb branch are determined exactly, for all β, assuming the existence of an interacting Spin(8) invariant fixed point at the origin. The resulting formulae are manifestly invariant under the SL(2,...

We consider the solution of complex symmetric shifted linear systems. Such systems arise in large-scale electronic structure simulations and there is a strong need for the fast solution of the systems. With the aim of solving the systems efficiently, we consider a special case of the QMR method for non-Hermitian shifted linear systems and propose its weighted quasi-minimal residual approach. A ...

We give a description of asymptotic quadratic growth rates for geodesic segments on covers of Veech surfaces in terms of the modular fiber parameterizing coverings of a fixed Veech surface. To make the paper self contained we derive the necessary asymptotic formulas from the Gutkin-Judge formula. As an application of the method we define and analyze d-symmetric elliptic differentials and their ...

The classical n-variable Kloosterman sums over the finite field Fp give rise to a lisse Ql-sheaf Kln+1 on Gm,Fp = P 1 Fp − {0,∞}, which we call the Kloosterman sheaf. Let Lp(Gm,Fp ,Sym Kln+1, s) be the L-function of the k-fold symmetric product of Kln+1. We construct an explicit virtual scheme X of finite type over Spec Z such that the p-Euler factor of the zeta function of X coincides with Lp(...

The Monte Carlo simulation of Majorana fermions is discussed on the example of supersymmetric Yang-Mills (SYM) theory.

I summarize recent results in lattice supersymmetry with special attention to N = 1 Super Yang-Mills (SYM) theory.