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Coupling running through the Looking-Glass of dimensional Reduction · Around

2010

Coupling running through the Looking-Glass of dimensional Reduction

Shirkov, D. V.

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The dimensional reduction, in a form of transition from four to two dimensions, was used in the 90s in a context of HE Regge scattering.

Recently, it got a new impetus in quantum gravity where it opens the way to renormalizability and finite short-distance behavior.
We consider a QFT model $g\,\varphi^4\,$ with running coupling defined in both the two domains of different dimensionality; the $\gbar(Q^2)\,$ evolutions being duly conjugated at the reduction scale $\,Q\sim M.$ Beyond this scale, in the deep UV 2-dim region, the running coupling does not increase any more.
Instead, it {\it slightly decreases} and tends to a finite value $\gbar_2(\infty) \,< \, \gbar_2(M^2)\,$ from above.

Built on

P.A.M. Dirac in
1934
Earlier work this paper cites.
N.N.Bogoliubov and D.V.Shirkov,
1956
Earlier work this paper cites.
V.Z. Blank, D.V. Shirkov,
1956
Earlier work this paper cites.
N.N. Bogoliubov and D.V.Shirkov,
1959
Earlier work this paper cites.
N.N. Bogoliubov and D.V. Shirkov,
1980
Earlier work this paper cites.

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Then

A.V.Gladyshev and D.I.Kazakov, “Supersymmetry and LHC”,
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2007
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2009
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Petr Horava,
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