CONFINEMENT, MONOPOLES AND STRINGS

I compute the ratio between the square root of the string tension for SU(2) and the renormalization group invariant scale as a function of the percolation temperature of a gas of magnetic monopoles. The key point in the computation is the derivation of an exact equivalence between the SU(N) lattice partition function in the gauge F01ch = 0 and a lattice gas of interacting charges and monopoles. The number and types of monopoles for SU(N) and more generally of magnetic defects for a gauge group G tum out to be determined by the root structure of the corresponding Lie algebra. At the same time the aforementioned equivalence determines precisely the string theory which effectively describes the fluctuations of large Wilson loops.