(2+1)-dimensional QED with dynamically massive fermions in vacuum polarization

Gusynin, V. P.; Hams, Anthony; Reenders, Manuel

doi:10.1103/physrevd.53.2227

Cited by 54 publications

(61 citation statements)

References 26 publications

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“…For example, in a paper [20] these ansatze were used to solve a coupled system of DSE for the photon and fermion propagators and to get an estimate for a critical number N c for chiral symmetry breaking in QED3. Although such an approach reproduces the value N c ≈ 4 close to the value N c found in leading order of the 1/N expansion [16][17][18], it cannot be considered as a reliable one since the approach does not permit to identify the ansatz with a class of Feynman diagrams. Also one cannot estimate corrections terms to results obtained in this approach.…”

Section: )mentioning

confidence: 82%

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Critical number of fermions in three-dimensional QED

Gusynin

Pyatkovskiy

2016

Phys. Rev. D

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Previous analytical studies of quantum electrodynamics in 2 + 1 dimensions (QED3) have shown the existence of a critical number of fermions for onset of chiral symmetry breaking, the most known being the value Nc ≈ 3.28 obtained by Nash to 1/N 2 order in the 1/N expansion [D. Nash, Phys. Rev. Lett. 62, 3024 (1989)]. This analysis is reconsidered by solving the Dyson-Schwinger equations for the fermion propagator and the vertex to show that the more accurate gauge-independent value is Nc ≈ 2.85, which means that the chiral symmetry is dynamically broken for integer values N ≤ 2, while for N ≥ 3 the system is in a chirally symmetric phase. An estimate for the value of chiral condensate ψ ψ is given for N = 2. Knowing precise Nc would be important for comparison between continuum studies and lattice simulations of QED3.

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Section: )mentioning

confidence: 82%

“…Numerous papers using this approach gave the results for the value of N c in the range 2 < N c < 5 [7,[16][17][18][19][20]. Renormalization group studies give the critical value N c approximately in the same range [21,22] with possible existence of a third intermediate phase for…”

Section: Introductionmentioning

confidence: 99%

Critical number of fermions in three-dimensional QED

Gusynin

Pyatkovskiy

2016

Phys. Rev. D

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“…It has been suggested that, in noncompact QED with fermions, the phase diagram is dependent on the number of flavors and that, at weak coupling, chiral symmetry is broken only for a small number (less than about 3.5) of fermions [17,18,19,20]. (A recent description of the status of three-dimensional QED can be found in [21,22].) It is quite probable that, at weak coupling, both the compact and non-compact formulations have quite similar properties.…”

Section: The Modelmentioning

confidence: 99%

Strongly coupled lattice gauge theory with dynamical fermion mass generation in three dimensions

et al. 1998

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We investigate the critical behaviour of a three-dimensional lattice χU φ 3 model in the chiral limit. The model consists of a staggered fermion field, a U (1) gauge field (with coupling parameter β) and a complex scalar field (with hopping parameter κ). Two different methods are used: 1) fits of the chiral condensate and the mass of the neutral unconfined composite fermion to an equation of state and 2) finite size scaling investigations of the Lee-Yang zeros of the partition function in the complex fermion mass plane. For strong gauge coupling (β < 1) the critical exponents for the chiral phase transition are determined. We find strong indications that the chiral phase transition is in one universality class in this β interval: that of the three-dimensional Gross-Neveu model with two fermions. Thus the continuum limit of the χU φ 3 model defines here a nonperturbatively renormalizable gauge theory with dynamical mass generation. At weak gauge coupling and small κ, we explore a region in which the mass in the neutral fermion channel is large but the chiral condensate on finite lattices very small. If it does not vanish in the infinite volume limit, then a continuum limit with massive unconfined fermion might be possible in this region, too.

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“…(26)) or N c as a function of the ratio πe 2 /µ (α = N e 2 /8) with the numerical solution of the integral equation (1) which was obtained by using numerical methods described in Ref. [24]. Basically, starting with some initial guess for Σ(p), the integral equation is iterated using splines on a logarithmic momentum scale, until sufficient precision is reached.…”

Section: The Gap Equation Of Massless Qedmentioning

confidence: 99%

Infrared cutoff dependence of the critical flavor number in three-dimensional QED

Gusynin¹,

Reenders²,

Reenders³

2003

Phys. Rev. D

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We solve, analytically and numerically, a gap equation in parity invariant QED3 in the presence of an infrared cutoff µ and derive an expression for the critical fermion number Nc as a function of µ. We argue that this dependence of Nc on the infrared scale might solve the discrepancy between continuum Schwinger-Dyson equations studies and lattice simulations of QED3.PACS numbers: 11.10. Kk, 11.30.Qc, 12.20.Ds Parity invariant quantum electrodynamics in 2+1 dimensions with N flavors of four-component massless fermions (QED 3 ) [1] has been attracting a lot of interest for almost two decades. While it was often regarded as a nice polygon for studying nonperturbative phenomena in gauge field theories, such as dynamical mass generation, recently the model has found applications in condensed matter physics, in particular in high-T c superconductivity [2].QED 3 is ultraviolet finite and has a built-in intrinsic mass scale given by the dimensionful gauge coupling e, or α = e 2 N/8, which plays a role similar to the Λ scale parameter in QCD. In the leading order in 1/N expansion, it was found that at large momenta (p ≫ α) the effective coupling between fermions and gauge bosons vanishes (asymptotic freedom) whereas it has a finite value or infrared stable fixed point at p ≪ α [3]. This behavior was shown to be robust against the introduction of higher order 1/N corrections [4,5]. Studies of the gap equation for a fermion dynamical mass in the leading order in the 1/N expansion have shown that massless QED 3 exhibits chiral symmetry breaking whenever the number of fermion species N is less than some critical value N c , which is estimated to be in the region 3 < N c < 5 (N c = 32/π 2 ≃ 3.2 in the simplest ladder approximation [6]). A renormalization group analysis gives 3 < N c < 4 [7]. Below such a critical N c , the U (2N ) flavor symmetry is broken down to U (N ) × U (N ), the fermions acquire a dynamical mass, and 2N 2 Goldstone bosons appear; for N > N c the particle spectrum of the model consists of interacting massless fermions and a photon. In addition, it was argued that the dynamical symmetry breaking phase transition at N = N c is a conformal phase transition [8,9]. The last one is characterized by a scaling function for the dynamical fermion mass with an essential singularity [6,8].On the other hand, there is an argument due to Appelquist et al. [10] that N c ≤ 3/2. The argument is based on the inequality f IR ≤ f UV where f is the thermodynamic free energy which is estimated in both infrared and ultraviolet regimes by counting massless degrees of freedom.The above-described version of QED 3 , the so-called parity invariant noncompact version, was studied on a lattice [11]. Recent lattice simulations of QED 3 with N ≥ 2 have found no decisive signal for chiral symmetry breaking [12]. In particular, for N = 2, Ref. [12] reports an upper bound for the chiral condensate ψ ψ to be of order 5 × 10 −5 in units of e 4 . We recall that for quenched, N = 0, QED 3 both numerical [13] and analytical [14] studies hav...

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(2+1)-dimensional QED with dynamically massive fermions in vacuum polarization

Cited by 54 publications

References 26 publications

Critical number of fermions in three-dimensional QED

Critical number of fermions in three-dimensional QED

Strongly coupled lattice gauge theory with dynamical fermion mass generation in three dimensions

Infrared cutoff dependence of the critical flavor number in three-dimensional QED

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