New variable stars in the field of open cluster NGC188

A photometric study of variable stars in the field of old open cluster NGC 188 is discussed. Observations were carried out in two bands R and I for 5513 stars up to R = 17 mag in the field of 1.5 x 1.5 grad. around the cluster. The photometric data were processed by the console application Astrokit, which corrects brightness variations associated with the variability of atmospheric transparency and carries out searching for variable stars. We found 18 new variable stars and determined the parameters of one previously known variable. Among discovered stars one is a low-amplitude pulsating variable, one is a EW eclipsing binary, six are eclipsing variables of EA type, five objects are long period variables, and for five stars variability type remains uncertain.

Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills Theory

It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R^{3,1}. We show that such solutions exist in SU(N) gauge theory on the spaces R^2times S^2 and R^1times S^1times S^2 with Minkowski signature (-+++). In the temporal gauge they are solutions of pure Yang-Mills theory on T^1times S^2, where T^1 is R^1 or S^1. Namely, imposing SO(3)-invariance and some reality conditions, we consistently reduce the Yang-Mills model on the above spaces to a non-Abelian analog of the phi^4 kink model whose static solutions give SU(N) monopole (-antimonopole) configurations on the space R^{1,1}times S^2 via the above-mentioned correspondence. These solutions can also be considered as instanton configurations of Yang-Mills theory in 2+1 dimensions. The kink model on R^1times S^1 admits also periodic sphaleron-type solutions describing chains of n kink-antikink pairs spaced around the circle S^1 with arbitrary n>0. They correspond to chains of n static monopole-antimonopole pairs on the space R^1times S^1times S^2 which can also be interpreted as instanton configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature (thermal time circle). We also describe similar solutions in Euclidean SU(N) gauge theory on S^1times S^3 interpreted as chains of n instanton-antiinstanton pairs.

Non-Abelian Vortices on Riemann Surfaces: an Integrable Case

We consider U(n+1) Yang-Mills instantons on the space Sigmatimes S^2, where Sigma is a compact Riemann surface of genus g. Using an SU(2)-equivariant dimensional reduction, we show that the U(n+1) instanton equations on Sigmatimes S^2 are equivalent to non-Abelian vortex equations on Sigma. Solutions to these equations are given by pairs (A,phi), where A is a gauge potential of the group U(n) and phi is a Higgs field in the fundamental representation of the group U(n). We briefly compare this model with other non-Abelian Higgs models considered recently. Afterwards we show that for g>1, when Sigmatimes S^2 becomes a gravitational instanton, the non-Abelian vortex equations are the compatibility conditions of two linear equations (Lax pair) and therefore the standard methods of integrable systems can be applied for constructing their solutions.