Related papers: High precision study of the structure of D=4 super…
The spectrum of the $D=4$ supersymmetric Yang-Mills quantum mechanics with $SU(3)$ gauge group symmetry is computed in different channels with definite total angular momentum and the total number of fermions. In sectors with small number of…
The $D=4$ supersymmetric Yang-Mills quantum mechanics with $SU(2)$ and $SU(3)$ gauge symmetry groups is studied. A numerical method to find finite matrix representation of the Hamiltonian is presented in detail. It is used to find spectrum…
The new approach to quantum mechanical problems is proposed. Quantum states are represented in an algebraic program, by lists of variable length, while operators are well defined functions on these lists. Complete numerical solution of a…
New results obtained within the recently developed approach to supersymmetric quantum mechanical systems are presented. The method does not suffer from the sign problem in any dimensions and is capable to provide any quantum observable with…
We review the last year progress in understanding supersymmetric SU(2) Yang-Mills quantum mechanics in four and ten space-time dimensions. The four dimensional system is now well under control and the precise spectrum is obtained in all…
The new method of solving quantum mechanical problems is proposed. The finite, i.e. cut off, Hilbert space is algebraically implemented in the computer code with states represented by lists of variable length. Complete numerical solution of…
Recent analytical and numerical solutions of the above systems are reviewed. Discussed results include: a) exact construction of the supersymmetric vacua in two space-time dimensions, and b) precise numerical calculations of the coexisting…
Supersymmetric Yang-Mills quantum mechanics (SYMQM) results from the dimensional reduction of the Yang-Mills field theory in $D$ space-time dimensions to a single point in the $D-1$ dimensional space. It can be also viewed as the effective…
The spectrum of Supersymmetric Yang-Mills Quantum Mechanics (SYMQM) in D=4 dimensions for SU(2) gauge group is computed for a maximal number of bosonic quanta $B\le60$ in the two-fermion sector with the angular momentum $j=0$. We analyse…
A supersymmetric collective coordinate expansion of the monopole solution of $N=4$ Yang-Mills theory is performed resulting in an $N=4$ supersymmetric quantum mechanics on the moduli space of monopole solutions.
We investigate the structure of the spectrum of states in D=2 SU(N) supersymmetric Yang-Mills matrix quantum mechanics, which is a simplified model of Matrix theory. We compute the thermal partition function of this system and give evidence…
The scalar and vector topological Yang-Mills symmetries on Calabi-Yau manifolds geometrically define consistent sectors of Yang-Mills D=4,6 N=1 supersymmetry, which fully determine the supersymmetric actions up to twist. For a CY_2…
Supersymmetric Yang-Mills theory is formulated in six dimensions, without the use of anti-commuting variables. This is achieved using a new Nicolai map, to third order in the coupling constant. This is the second such map in six dimensions…
We will discuss an integrable structure for weakly coupled superconformal Yang-Mills theories, describe certain equivalences for the Yangian algebra, and fill a technical gap in our previous study of this subject.
We solve exactly the Dyson-Schwinger equations for Yang-Mills theory in 3 and 4 dimensions. This permits us to obtain the exact correlation functions till order 2. In this way, the spectrum of the theory is straightforwardly obtained and…
We apply numerical and analytic techniques to the study of Yang-Mills integrals with orthogonal, symplectic and exceptional gauge symmetries. The main focus is on the supersymmetric integrals, which correspond essentially to the bulk part…
Non-perturbative investigations of $\mathcal N = 4$ supersymmetric Yang--Mills theory formulated on a space-time lattice have advanced rapidly in recent years. Large-scale numerical calculations are currently being carried out based on a…
Numerical simulations of supersymmetric theories on the lattice are intricate and challenging with respect to their theoretical foundations and algorithmic realisation. Nevertheless, the simulations of a four-dimensional supersymmetric…
In this paper we review recent results on symmetries in N=4 super Yang-Mills theory. Symmetries are of invaluable help in studying and constraining the scattering amplitudes, and there has been a lot of progress in recent years concerning…
We describe an infinite-dimensional algebra of hidden symmetries of N=4 supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a generalization of the supertwistor correspondence. Using the latter, we construct an infinite…