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Techni-dilaton at Conformal Edge
Techni-dilaton (TD) was proposed long ago in the technicolor (TC) near
criticality/conformality. To reveal the critical behavior of TD, we explicitly
compute the nonperturbative contributions to the scale anomaly
, which
are generated by the dynamical mass m of the techni-fermions. Our computation
is based on the (improved) ladder Schwinger-Dyson equation, with the gauge
coupling replaced by the two-loop running one having the
Caswell-Banks-Zaks IR fixed point : for the IR region , where is
the intrinsic scale (analogue of of QCD) relevant to the
perturbative scale anomaly. We find that
and in the
criticality limit () ("conformal edge"). Our result precisely
reproduces the formal identity , where is the nonperturbative beta function
corresponding to the above essential singularity scaling of .
Accordingly, the PCDC implies at criticality limit, where is the mass of TD and
the decay constant of TD. We thus conclude that at criticality limit
the TD could become a "true (massless) Nambu-Goldstone boson" ,
only when , namely getting decoupled, as was the case of
"holographic TD" of Haba-Matsuzaki-Yamawaki. The decoupled TD can be a
candidate of dark matter.Comment: 17 pages, 14 figures; discussions clarified, references added, to
appear in Phys.Rev.
Point symmetries in the Hartree-Fock approach: Symmetry-breaking schemes
We analyze breaking of symmetries that belong to the double point group
D2h(TD) (three mutually perpendicular symmetry axes of the second order,
inversion, and time reversal). Subgroup structure of the D2h(TD) group
indicates that there can be as much as 28 physically different, broken-symmetry
mean-field schemes --- starting with solutions obeying all the symmetries of
the D2h(TD) group, through 26 generic schemes in which only a non-trivial
subgroup of D2h(TD) is conserved, down to solutions that break all of the
D2h(TD) symmetries. Choices of single-particle bases and the corresponding
structures of single-particle hermitian operators are discussed for several
subgroups of D2h(TD).Comment: 10 RevTeX pages, companion paper in nucl-th/991207
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