Non-Gaussian fixed points in fermionic field theories without auxiliary Bose fields

The functional equation governing the renormalization flow of fermionic field theories is investigated in $$d$$d dimensions without introducing auxiliary Bose fields on the example of the Gross–Neveu and the Nambu–Jona-Lasinio model. The UV-safe fixed points and the eigenvectors of the renormalization group equations linearized around them are found in the local potential approximation. The results are compared carefully with those obtained with partial bosonization. The results do not receive any correction in the next-to-leading order approximation of the gradient expansion of the effective action.

[1]  de Calan C,et al.  Constructing the three-dimensional Gross-Neveu model with a large number of flavor components. , 1991, Physical review letters.

[2]  Joseph Polchinski,et al.  Renormalization and effective lagrangians , 1984 .

[3]  Equation of state and coarse grained free energy for matrix models , 1996, hep-th/9609019.

[4]  Flow equations without mean field ambiguity , 2002, hep-ph/0207094.

[5]  H. Gies,et al.  Higgs Mass Bounds from Renormalization Flow for a simple Yukawa model , 2013, 1308.5075.

[6]  V. A. Miransky.  Dynamic mass generation and renormalizations in quantum field theories , 1980 .

[7]  C. Wetterich,et al.  Phase transition and critical behavior of the d=3 Gross-Neveu model , 2002 .

[8]  Kupiainen,et al.  Renormalizing the nonrenormalizable. , 1985, Physical review letters.

[9]  D. Litim.  Optimized renormalization group flows , 2001, hep-th/0103195.

[10]  Renormalization Flow of Bound States , 2001, hep-th/0107221.

[11]  David J. Gross,et al.  Dynamical symmetry breaking in asymptotically free field theories , 1974 .

[12]  Park,et al.  Four-fermion theory is renormalizable in 2+1 dimensions. , 1989, Physical review letters.

[13]  H. Gies,et al.  Higgs mass bounds from renormalization flow for a Higgs–top–bottom model , 2014, 1407.8124.

[14]  J. Braun.  Fermion interactions and universal behavior in strongly interacting theories , 2011, 1108.4449.

[15]  John B. Kogut,et al.  Four-Fermi Theories in Fewer Than Four Dimensions , 1993 .

[16]  P. Lacock,et al.  Critical behaviour of the three-dimensional Gross-Neveu and Higgs-Yukawa models , 1994 .

[17]  A. Wipf,et al.  Critical behavior of supersymmetric O(N) models in the large-N limit , 2011, 1107.3011.

[18]  G. Jona-Lasinio,et al.  DYNAMICAL MODEL OF ELEMENTARY PARTICLES BASED ON AN ANALOGY WITH SUPERCONDUCTIVITY. PART II , 1961 .

[19]  T. Morris,et al.  Large N and the renormalization group , 1997, hep-th/9704094.

[20]  C. Wetterich,et al.  Exact evolution equation for the effective potential , 1993, 1710.05815.

[21]  F. Saueressig,et al.  Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation , 2002 .

[22]  A. Houghton,et al.  Renormalization group equation for critical phenomena , 1973 .

[23]  Kogut,et al.  New phase of quantum electrodynamics: A nonperturbative fixed point in four dimensions. , 1988, Physical review letters.

[24]  M. Salmhofer,et al.  Functional renormalization group approach to correlated fermion systems , 2011, 1105.5289.

[25]  C. Wetterich,et al.  Average action and the renormalization group equations , 1991 .

[26]  Tim R. Morris.  The Exact renormalization group and approximate solutions , 1994 .

[27]  Love,et al.  Dilaton and chiral-symmetry breaking. , 1986, Physical review letters.

[28]  K. Aoki,et al.  Weak solution of the non-perturbative renormalization group equation to describe dynamical chiral symmetry breaking , 2014, 1403.0174.

[29]  G. Jona-Lasinio,et al.  Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II , 1961 .

[30]  C. Wetterich,et al.  Critical exponents of the Gross-Neveu model from the effective average action. , 2001, Physical review letters.

[31]  Jens Braun,et al.  Asymptotic safety: a simple example , 2010, 1011.1456.

[32]  H. Gies,et al.  An asymptotic safety scenario for gauged chiral Higgs–Yukawa models , 2013, 1306.6508.

[33]  Holger Gies,et al.  UV fixed-point structure of the three-dimensional Thirring model , 2010, 1006.3747.