Abstract
We study nonperturbative renormalizability of ad=4 hierarchical SU(2) gauge model that realizes Migdal's recursion relation as an exact renormalization group transformation. A continuum limit of effective actions is shown to exist as the scaling limit, both for initial Wilson and heat kernel actions. These limit effective actions exhibit ultraviolet asymptotic freedom and provide a strictly positive string tension.
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References
Wilson, K.G.: Confinement of quarks. Phys. Rev. D10, 2445–2459 (1974)
Wilson, K.G.: Renormalization group and strong interactions. Phys. Rev. D3, 1818–1846 (1971);
Kogut, J., Wilson, K.G.: The renormalization group and the ε expansion. Phys. Rep.12 C, 75–199 (1974)
Bałaban, T.: The variational problem and background fields in renormalization group method for lattice gauge theories. Commun. Math. Phys.102, 277–309 (1985), and further references quoted there
Federbush, P.: A phase cell approach to Yang-Mills theory I. Modes, lattice-continuum duality. Commun. Math. Phys.107, 319–329 (1986) and University of Michigan preprints
Migdal, A.A.: Recursion equations in gauge field theories. JETP69, 810–822 (1975)
Berker, A.N., Ostlund, S.: Renormalization-group calculations of finite systems: Order parameter and specific heat for epitaxial ordering. J. Phys. C12, 4961–4975 (1979)
Bleher, P.M., Zalys, E.: Existence of long-range order in the Migdal recursion equations. Commun. Math. Phys.67, 17–42 (1979)
Griffiths, R.B., Kaufman, M.: Spin systems on hierarchical lattices. Introduction and thermodynamic limit. Phys. Rev. B26, 5022–5032 (1982)
Ito, K.R.: Analytic study of the Migdal-Kadanoff recursion formula. Commun. Math. Phys.95, 247–255 (1984)
Müller, V.F., Schiemann, J.: Convergence of Migdal-Kadanoff iterations in non-abelian lattice gauge models. Commun. Math. Phys.97, 605–614 (1985), referred to as (I)
Gawedzki, K., Kupiainen, A.: Triviality of φ 44 and all that in a hierarchical model approximation. J. Stat. Phys.29, 683–698 (1982)
Gawedzki, K., Kupiainen, A.: Non-trivial continuum limit of a φ 44 model with negative coupling constant. Nucl. Phys. B257 [FS 14] 474–504 (1985)
Ito, K.R.: Permanent quark confinement in four-dimensional hierarchical lattice gauge theories of Migdal-Kadanoff type. Phys. Rev. Lett.55, 558–561 (1985)
Gradshteyn, J.S., Ryshik, J.M.: Table of integrals, series and products. New York: Academic Press, Eq. (1.331.2)
Hille, E.: Analytic function theory, Vol. II. New York: Chelsea, Theorem 15.2.3
Hille, E.: Loc. cit., Chap. 13.5
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Communicated by K. Osterwalder
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Müller, V.F., Schiemann, J. Continuum limit of a hierarchical SU(2) lattice gauge theory in 4 dimensions. Commun.Math. Phys. 110, 261–286 (1987). https://doi.org/10.1007/BF01207367
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DOI: https://doi.org/10.1007/BF01207367