Note on an application of the method of uniqueness to reduced quantum electrodynamics

Kotikov, A. V.; Teber, S.

doi:10.1103/physrevd.87.087701

Cited by 34 publications

(61 citation statements)

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“…Such a difference can be taken into account with the help of our present results for QED 3 together with the multi-loop results obtained in [30,31]. The case of reduced QED, and its relation with dynamical gap generation in graphene which is the subject of active ongoing research, see, e.g., the reviews [32,33], will be considered in a separate paper [34]. In the following, we shall focus exclusively on QED 3 .…”

Section: Introductionmentioning

confidence: 99%

Critical behavior of (2+1)-dimensional QED:1/Nfcorrections in an arbitrary nonlocal gauge

Kotikov

Teber

2016

Phys. Rev. D

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Dynamical chiral symmetry breaking (DχSB) is studied within (2 + 1)-dimensional QED with N four-component fermions. The leading and next-to-leading orders of the 1/N expansion are computed exactly. The analysis is carried out in an arbitrary non-local gauge. Resumming the wave-function renormalization constant at the level of the gap equation yields a strong suppression of the gauge dependence of the critical fermion flavour number, Nc(ξ) where ξ is the gauge fixing parameter, which is such that DχSB takes place for N < Nc(ξ). Neglecting the weak gaugedependent terms yields Nc = 2.8469 while, in the general case, it is found that: Nc(1) = 3.0084 in the Feynman gauge, Nc(0) = 3.0844 in the Landau gauge and Nc(2/3) = 3.0377 in the ξ = 2/3 gauge where the leading order fermion wave function is finite. These results suggest that DχSB should take place for integer values N ≤ 3.

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Section: Introductionmentioning

confidence: 99%

Critical behavior of (2+1)-dimensional QED:1/Nfcorrections in an arbitrary nonlocal gauge

Kotikov

Teber

2016

Phys. Rev. D

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“…In some intermediate cases, simpler forms can be obtained. 2,3,7,[10][11][12]14 In particular, in Ref.[2], an ingenious transformation was found from Gegenbauer two-fold series to one-fold 3 F 2 -hypergeometric series of unit argument for a complicated class of diagrams having two integer indices on adjacent lines and three other arbitrary indices. For this class of diagrams, similar results have been found in Ref.…”

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confidence: 99%

“…In Ref. [15], Eq. (2) appeared in the computation of the two-loop fermion self-energy in reduced quantum electrodynamics (RQED), [16], or RQED dγ ,de , see also Refs.…”

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confidence: 99%

“…[15], d γ = 4 − 2ε γ and d e = 4 − 2ε e − 2ε γ . In the case of usual QEDs, e.g., QED 4 and QED 3 , the parameter ε e = 0 and all indices are integers.…”

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confidence: 99%

“…This important diagram appears in various calculations, see, e.g., Refs. [3,7,10,13,14]; it was shown in Ref.[2] to reduce to a single 3 F 2 -hypergeometric series of unit argument. More recently, in Ref.…”

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Two-loop fermion self-energy and propagator in reducedQED3,2

Teber

2014

Phys. Rev. D

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We compute the two-loop fermion self-energy in massless reduced quantum electrodynamics (RQED) for an arbitrary gauge in the case where the photon field is three-dimensional and the fermion field two-dimensional: super-renormalizable RQED3,2 with NF fermions. We find that the theory is infrared finite at two-loop and that finite corrections to the fermion propagator have a remarkably simple form.One of the building blocks of multi-loop calculations is the two-loop massless propagator diagram, see Fig. 1:where G is the so-called coefficient function of the diagram, α i are arbitrary indices and p is an external momentum in a Minkowski space-time of dimensionality d e . This diagram is at the heart of numerous radiative correction calculations in quantum field theory and associated to the development of sophisticated methods such as, e.g., the Gegenbauer polynomial technique 1,2 , integration by parts 3,4 , and the method of uniqueness 3,5,6 , see Ref.[8] for a historical review on this diagram. In the case where all indices are integers, this diagram is well known and can be expressed in terms of recursively one-loop diagrams. When all indices are arbitrary, the result is highly non-trivial and can be represented 9 as a combination of two-fold series. In some intermediate cases, simpler forms can be obtained. 2,3,7,[10][11][12]14 In particular, in Ref.[2], an ingenious transformation was found from Gegenbauer two-fold series to one-fold 3 F 2 -hypergeometric series of unit argument for a complicated class of diagrams having two integer indices on adjacent lines and three other arbitrary indices. For this class of diagrams, similar results have been found in Ref. [11] using an ansatz to solve the recurrence relations arising from integration by parts. In Ref.[2], the results were applied to the computation of a diagram with a single non-integer index on the central line. This important diagram appears in various calculations, see, e.g., Refs. [3,7,10,13,14]; it was shown in Ref.[2] to reduce to a single 3 F 2 -hypergeometric series of unit argument. More recently, in Ref. [15], the results of [2] were applied to the case involving two arbitrary indices on non adjacent lines. In this case, the corresponding coefficient function: was shown to reduce to two 3 F 2 -hypergeometric series of argument 1. In Ref.[15], Eq. (2) appeared in the computation of the two-loop fermion self-energy in reduced quantum electrodynamics (RQED), [16], or RQED dγ ,de , see also Refs. [17] in relation with RQED 4,3 . In the general case, this relativistic model describes the interaction of an abelian U (1) gauge field living in d γ space-time dimensions with a fermion field localized in a reduced space-time of d e dimensions (d e d γ ). In RQED dγ ,de , while the bubble and rainbow diagrams, Figs. 2 a) and 2 b), respectively, naturally reduce to recursively one-loop diagrams, the crossed photon diagram, Fig. 2 c), involves a contribution of the type Eq. (2) with the indices given by:where, following the notation of Ref.[15], d γ = 4 − 2ε ...

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3d Abelian gauge theories at the boundary

Pietro

Gaiotto

Lauria

et al. 2019

J. High Energ. Phys.

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A four-dimensional Abelian gauge field can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFT) parametrized by the gauge coupling τ in the upper-half plane and by the choice of the CFT in the decoupling limit τ → ∞. Upon performing an SL(2, Z) transformation in the bulk and going to the decoupling limit in the new frame, one finds a different 3d CFT on the boundary, related to the original one by Witten's SL(2, Z) action [1]. In particular the cusps on the real τ axis correspond to the 3d gauging of the original CFT. We study general properties of this BCFT. We show how to express bulk one and two-point functions, and the hemisphere free-energy, in terms of the two-point functions of the boundary electric and magnetic currents. We then consider the case in which the 3d CFT is one Dirac fermion. Thanks to 3d dualities this BCFT is mapped to itself by a bulk S transformation, and it also admits a decoupling limit which gives the O(2) model on the boundary. We compute scaling dimensions of boundary operators and the hemisphere free-energy up to two loops. Using an S-duality improved ansatz, we extrapolate the perturbative results and find good approximations to the observables of the O(2) model. We also consider examples with other theories on the boundary, such as large-N f Dirac fermions -for which the extrapolation to strong coupling can be done exactly order-by-order in 1/N f -and a free complex scalar.

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Note on an application of the method of uniqueness to reduced quantum electrodynamics

Abstract: Using the method of uniqueness a two-loop massless propagator Feynman diagram with a noninteger index on the central line is evaluated in a very transparent way. The result is applied to the computation of the two-loop polarization operator in reduced quantum electrodynamics.

Cited by 34 publications

References 30 publications

Critical behavior of (2+1)-dimensional QED:1/Nfcorrections in an arbitrary nonlocal gauge

Critical behavior of (2+1)-dimensional QED:1/Nfcorrections in an arbitrary nonlocal gauge

Two-loop fermion self-energy and propagator in reducedQED3,2

3d Abelian gauge theories at the boundary

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