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We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with…
We propose a lattice action for two dimensional super Yang-Mills theory with a twisted N=2 supersymmetry. The extended supersymmetry is fully and exactly realized on the lattice. The method employed is quite general and its extension to the…
We present a procedure to improve the lattice definition of $\mathcal N = 4$ supersymmetric Yang--Mills theory. The lattice construction necessarily involves U(1) flat directions, and we show how these can be lifted without violating the…
We give a gauge-covariant formulation of seven-dimensional super-Yang-Mills theory in terms of N=1 superfields. Furthermore, we show that five and seven dimensions are the only cases where such a formulation exists by analysing the…
We construct supersymmetric fermionic Wilson loops along general curves in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory and along general planar curves in $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver theory. These…
Recent progress in the nonperturbative solution of (3+1)-dimensional Yukawa theory and quantum electrodynamics and (1+1)-dimensional super Yang--Mills theory is summarized.
Vacuum structures of supersymmetric (SUSY) Yang-Mills theories in $1+1$ dimensions are studied with the spatial direction compactified. SUSY allows only periodic boundary conditions for both fermions and bosons. By using the…
The Yang-Mills theory is part of the Standard Model of particle physics. The lack of the mathematical understanding of the theory stands out in theoretical physics. In order to address this problem we observe that a recently proposed…
A new method to obtain the Picard-Fuchs equations of effective $N = 2$ supersymmetric gauge theories in 4 dimensions is developed. It includes both pure super Yang-Mills and supersymmetric gauge theories with massless matter…
Recently, new theoretical ideas have allowed the construction of lattice actions which are explicitly invariant under one or more supersymmetries. These theories are local and free of doublers and in the case of Yang-Mills theories also…
We classify the supersymmetric mass deformations of all the super Yang-Mills quantum mechanics, which are obtained by dimensional reductions of minimal super Yang-Mills in spacetime dimensions: ten, six, four, three and two. The resulting…
By numerically investigating the conservation law of the supercurrent, we confirm the restoration of supersymmetry in Sugino's lattice formulation of the two-dimensional $\mathcal{N}=(2,2)$ supersymmetric SU(2) Yang-Mills theory with a…
We show that the Hamiltonian of (N=1;d=10) super Yang-Mills can be expressed as a quadratic form in a very similar manner to that of the (N=4;d=4) theory. We find a similar quadratic form structure for pure Yang-Mills theory but this…
We construct three-dimensional, $\mathcal{N}=1$ off-shell supersymmetric massive Yang-Mills (YM) theory, whose YM equation is "third way" consistent. This means that the field equations of this model do not come from variation of a local…
It is shown that a $d$-dimensional classical SU(N) Yang-Mills theory can be formulated in a $d+2$-dimensional space, with the extra two dimensions forming a surface with non-commutative geometry.
The self-duality equations for gauge fields in pseudoeuclidean spaces of eight and seven dimensions are considered. Some new classes of solutions of the equations are found.
We consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint representation the gauge group is actually SU(2)/Z_2, which possesses nontrivial topology. In particular, there are…
Supersymmetric pure Yang-Mills theory is formulated with a local, i.e. space-time dependent, complex coupling in superspace. Super-Yang-Mills theories with local coupling have an anomaly, which has been first investigated in the Wess-Zumino…
We present new results from ongoing lattice investigations of supersymmetric Yang--Mills (SYM) theories in three and four space-time dimensions. First considering the maximally supersymmetric 3d theory with $Q = 16$ supercharges, we check…
The gradient flow equation is derived in four-dimensional N=1 supersymmetric Yang-Mills theory in terms of the component field of the Wess-Zumino gauge. We show that the flow-time derivative and supersymmetry transformation that is naively…