Nuclear Physics B362 (1991) 21-32 North-Holland COMMENTS ON THE SPACE-SYMMETRY INTERPRETATION OF THE GAUGE ORIENTATIONS OF THE INSTANTON IN THE HIGGS PHASE M.A. SHIFMAN and A.I. VAINSHTEIN* Theoretical Physics Institute, University of Minnesota, 116 Church St. SE, Minneapolis, MN 55455, USA Received 5 March 1991 (Revised 16 May 1991) We comment on introduction of the instanton collective coordinates in the theories with the spontaneously broken gauge symmetry. In distinction with the pure gauge theories some gauge-invariant quantities acquire explicit dependence on the collective coordinates associated with the gauge field orientation in the gauge group, which looks rather paradoxically. This dependence, however, is absolutely necessary for preserving the Lorentz invariance of the instanton-induced amplitudes. I. Introduction Recent works [1,2] devoted to the baryon number violating processes at high energies have revived interest to instantons in non-abelian gauge theories with the spontaneously broken gauge symmetry. Instanton calculus [3-6] in such theories has certain peculiarities: although the number of the collective coordinates is the same as in the unbroken case their explicit realization in the Higgs sector is somewhat unusual. We are unaware of any discussion of the issue in the previous literature in spite of the fact that the correct introduction of the collective coordinates is absolutely crucial for preservation of the explicit Lorentz invariance of the instanton-induced interactions. The main assertion to be presented below is as follows. Introduction of the Higgs field reveals the fact that actually there are no collective coordinates associated with the global orientations in the instantonic SU(2) gauge group. The corresponding three collective coordinates should be introduced through the Lorentz rotations in the SU(2) R subgroup of the 0(4) euclidean space-time symmetry*. In the sector of the vector fields they cannot be distinguished from the * Also at Institute for Nuclear Physics, 630090 Novosibirsk, USSR. * The instanton configuration considered refers to SU(2) L Lorentz sub-group. As a matter of fact, according to the established nomenclature we consider anti-instanton. 0550-3213/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)