Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-06-14
Phys.Rev.D62:125021,2000
Physics
High Energy Physics
High Energy Physics - Theory
66 pages, latex, 8 figures, corrected some typos, added some comments, regrouped Appendix A
Scientific paper
10.1103/PhysRevD.62.125021
Motivated by an analogy with the conformal factor problem in gravitational theories of the $R+R^2$-type we investigate a $d$-dimensional Euclidean field theory containing a complex scalar field with a quartic self interaction and with a nonstandard inverse propagator of the form $-p^2+p^4$. Nonconstant spin-wave configurations minimize the classical action and spontaneously break the rotation symmetry to a lower-dimensional one. In classical statistical physics this corresponds to a spontaneous formation of layers. Within the effective average action approach we determine the renormalization group flow of the dressed inverse propagator and of a family of generalized effective potentials for nonzero-momentum modes. Already in the leading order of the semiclassical expansion we find strong ``instability induced'' renormalization effects which are due to the fact that the naive vacuum (vanishing field) is unstable towards the condensation of modes with a nonzero momentum. We argue that the (quantum) ground state of our scalar model indeed leads to spontaneous breaking of rotation symmetry.
Lauscher Oliver
Reuter Martin
Wetterich Christof
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