  The goal of this paper is to arrive at a low energy effective theory of QCD
with two massless flavors of quarks at very high isospin density and zero
baryon density. In a seminal paper by Son and Stephanov in the year 2001, it
was conjectured that the low energy dynamics of QCD with two light flavors at
asymptotically high isospin density was described by that of a pure Yang-Mills
effective Lagrangian. Since the existence of a first order deconfinement phase
transition with increasing temperature is a feature of every pure SU(N)
Yang-Mills theory with N greater than or equal to 3, the regime considered in
this paper is also expected to exhibit a first order deconfinement phase
transition with increasing temperature. However, the low energy constants(LEC)
of this pure Yang-Mills theory have not been calculated till date. We calculate
the LEC s for this effective theory which in turn enables us to calculate the
critical temperature of the deconfinement transition as a function of the
isospin chemical potential $\mu_I$.The scaling of the critical temperature as a
function of the isospin chemical potential that we find in this paper can be
compared with future lattice calculations at finite isospin density.
