arXiv:hep-ph/9909419v2 3 Nov 1999 The Color-Flavor Locking Phase at T = 0. R. Casalbuoni a,b and R. Gatto c a Dipartimento di Fisica, Universit` a di Firenze, I-50125 Firenze, Italia b I.N.F.N., Sezione di Firenze, I-50125 Firenze, Italia c D´ epart. de Physique Th´ eorique, Universit´ e de Gen` eve, CH-1211 Gen` eve 4, Suisse Abstract We study the color-flavor locked phase of QCD with three massless quarks at high chemical potential and small non zero temperatures. We make use of the recently introduced effective action to describe such a phase. We obtain the exact order T 2 behaviour of the conden- sates and of the pressure by formally comparing the derivative from the QCD functional with symmetry breaking to that from the effective lagrangian with external sources, respecting the residual Z 2 invariance of the color-flavor locked phase. From these exact results, but now at a very tentative level of conjecture, we are lead to think that the phase structure of QCD at very high density consists of two superconducting phases and a symmetric one. 1 Introduction QCD at high density has attracted a great interest lately. A recent review by Frank Wilczek [1] is entitled ”The recent excitement in high-density QCD”. We refer to this article and also to a latest review by Krishna Rajagopal [2] for clear and authoritative descriptions of the subject. Numerous authors have recently contributed to this rapidly advancing field [3]. A particularly interesting situation occurs in QCD with three massless flavors at high values of the baryonic chemical potential, where the suggested condensation pattern would imply the phenomenon of color-flavor locking (CFL), as discussed in the papers by Alford, Rajagopal and F.Wilczek [4], by T. Sch¨afer and F. Wilczek [5], and by M. Alford, J. Berges, and K. Rajagopal [6]. 1