Abstract:
We discuss the harmonic spheres conjecture, relatingthe space of harmonic maps of the Riemann sphere into the loop space of a compact Lie group G with the moduli space of Yang–Mills G-fields on four-dimensional Euclidean space.
While preparingthis paper the author was partly supported by the RFBR grants 10-01-00178, 11-01-12033-ofi-m-2011, the program of supporting the Leading Scientific Schools (grant NSh-7675.2010.1), and the Scientific Program of the Russian Academy of Sciences “Nonlinear dynamics”.