arXiv subjects
Publications and source records attributed to A. Solovyov.
We consider the Bethe Ansatz Equations for orbifolds of N =4 SYM w.r.t. an arbitrary discrete group. Techniques used for the Abelian orbifolds can be extended to the generic non-Abelian case with minor modifications. We show how to make a transition between the different notations in the quiver gauge theory.
We calculate the ring of differential operators on some singular affine varieties (intersecting stacks, a point on a singular curve or an orbifold). Our results support the proposed connection of the ring of differential operators with geometry of D-branes in (bosonic) string theory. In particular, the answer does know about the resolution of singularities in accordance with the string theory predictions.
We consider the complex scalar field coupled to background NC U(1) YM and calculate the correlator of two gauge invariant composite operators. We show how the noncommutative gauge invariance is restored for higher correlators (though the Green's function itself is not invariant). It is interesting that the recently discovered noncommutative solitons appear in the calculation.
We consider 2+1-dimensional classical noncommutative scalar field theory. The general ansatz for a radially symmetric solution is obtained. Some exact solutions are presented. Their possible physical meaning is discussed. The case of the finite $θ$ is discussed qualitatively and illustrated by some numerical results.