Supermagnets and Sigma models

We discuss new methods for non-compact sigma models with and without RR fluxes. The methods include reduction to one dimensional supermagnets, supercoset constructions and supertwistors. This work is a first step towards the solution of these models, which are important in several areas of physics. I dedicate it to the memory of Volodya Gribov.Comment: 22 page

The wall of the cave

In this article old and new relations between gauge fields and strings are discussed. We add new arguments that the Yang Mills theories must be described by the non-critical strings in the five dimensional curved space. The physical meaning of the fifth dimension is that of the renormalization scale represented by the Liouville field. We analyze the meaning of the zigzag symmetry and show that it is likely to be present if there is a minimal supersymmetry on the world sheet. We also present the new string backgrounds which may be relevant for the description of the ordinary bosonic Yang-Mills theories. The article is written on the occasion of the 40-th anniversary of the IHES.Comment: 18 pages, Late

Gravitating Monopole-Antimonopole Systems at Large Scalar Coupling

We discuss static axially symmetric solutions of SU(2) Einstein-Yang-Mills-Higgs theory for large scalar coupling. These regular asymptotically flat solutions represent monopole-antimonopole chain and vortex ring solutions, as well as new configurations, present only for larger values of the scalar coupling. When gravity is coupled to the Yang-Mills-Higgs system, branches of gravitating solutions emerge from the flat-space solutions, and extend up to critical values of the gravitational coupling constant. For small scalar coupling only two branches of gravitating solutions exist, where the second branch connects to a generalized Bartnik-McKinnon solution. For large scalar coupling, however, a plethora of gravitating branches can be present and indicate the emergence of new flat-space branches.Comment: 29 pages, 13 figure

Gauge Fields and Space-Time

In this article I attempt to collect some ideas,opinions and formulae which may be useful in solving the problem of gauge/ string / space-time correspondence This includes the validity of D-brane representation, counting of gauge-invariant words, relations between the null states and the Yang-Mills equations and the discussion of the strong coupling limit of the string sigma model. The article is based on the talk given at the "Odyssey 2001" conference.Comment: 20 page

Electric charge in the field of a magnetic event in three-dimensional spacetime

We analyze the motion of an electric charge in the field of a magnetically charged event in three-dimensional spacetime. We start by exhibiting a first integral of the equations of motion in terms of the three conserved components of the spacetime angular momentum, and then proceed numerically. After crossing the light cone of the event, an electric charge initially at rest starts rotating and slowing down. There are two lengths appearing in the problem: (i) the characteristic length $\frac{q g}{2 \pi m}$, where $q$ and $m$ are the electric charge and mass of the particle, and $g$ is the magnetic charge of the event; and (ii) the spacetime impact parameter $r_0$. For $r_0 \gg \frac{q g}{2 \pi m}$, after a time of order $r_0$, the particle makes sharply a quarter of a turn and comes to rest at the same spatial position at which the event happened in the past. This jump is the main signature of the presence of the magnetic event as felt by an electric charge. A derivation of the expression for the angular momentum that uses Noether's theorem in the magnetic representation is given in the Appendix.Comment: Version to appear in Phys. Rev.