  We consider QCD with two degenerate flavors of light quarks(up and down) at
asymptotically high isospin chemical potential with zero baryon chemical
potential and calculate for the first time a quantitative expression for the
critical temperature of the deconfinement transition in this regime. At high
isospin chemical potential and sufficiently low temperatures this theory
becomes equivalent to a pure Yang-Mills theory and accordingly has a first
order deconfinement phase transition. Although this was conjectured in a
seminal paper by Son and Stephanov in the year 2001, the critical temperature
of this deconfinement phase transition was not computed. This paper computes
the energy scale associated with this transition as a function of the isospin
chemical potential by relating the parameters of the equivalent Yang-Mills
theory to those of the underlying theory. We also relate the equation of state
in one strongly interacting regime of QCD namely at finite isospin density to
that in pure Yang-Mills, with the latter being amenable to straightforward
numerical calculation. Our results for the critical temperature of
deconfinement transition can be compared with future lattice calculations.
