External leg amputation in conformal-invariant three-point function

Mitra, Indrajit

doi:10.1140/epjc/s10052-011-1621-6

Cited by 7 publications

(10 citation statements)

References 23 publications

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“…Nevertheless, the three-point function of dressed mean gluons of Refs. [13,14,15] can be fixed by conformal symmetry in analogy to [27,28,29,30,31], however, we cannot find higher-point correlators of the dressed mean fields from this Green's function by using ST identity.…”

Section: Introductionmentioning

confidence: 90%

Solution to Bethe–Salpeter equation via Mellin–Barnes transform

et al. 2013

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We consider Mellin-Barnes transform of triangle ladder-like scalar diagram in d = 4 dimensions. It is shown how the multi-fold MB transform of the momentum integral corresponding to an arbitrary number of rungs is reduced to the two-fold MB transform. For this purpose we use Belokurov-Usyukina reduction method for four-dimensional scalar integrals in the position space. The result is represented in terms of Euler ψ-function and its derivatives. We derive new formulas for the MB two-fold integration in complex planes of two complex variables. We demonstrate that these formulas solve Bethe-Salpeter equation. We comment on further applications of the solution to the Bethe-Salpeter equation for the vertices in N = 4 supersymmetric Yang-Mills theory. We show that the recursive property of the MB transforms observed in the present work for that kind of diagrams has nothing to do with quantum field theory, theory of integral transforms, or with theory of polylogarithms in general, but has an origin in a simple recursive property for smooth functions which can be shown by using basic methods of mathematical analysis.

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Section: Introductionmentioning

confidence: 90%

Solution to Bethe–Salpeter equation via Mellin–Barnes transform

et al. 2013

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“…Later, this property was generalized via the MB transform to any threepoint Green's function in the massless theory for arbitrary space-time dimension [9,13]. Due to this invariance with respect to Fourier transformation, UD functions appear in the results of calculations of the Green's functions in position space [14,15,16,17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Two-fold Mellin–Barnes transforms of Usyukina–Davydychev functions

et al. 2013

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In our previous paper [Nucl. Phys. B 870 (2013) 243], we showed that multi-fold Mellin-Barnes (MB) transforms of Usyukina-Davydychev (UD) functions may be reduced to twofold MB transforms. The MB transforms were written there as polynomials of logarithms of ratios of squares of the external momenta with certain coefficients. We also showed that these coefficients have a combinatoric origin. In this paper, we present an explicit formula for these coefficients. The procedure of recovering the coefficients is based on taking the double-uniform limit in certain series of smooth functions of two variables which is constructed according to a pre-determined iterative way. The result is obtained by using basic methods of mathematical analysis. We observe that the finiteness of the limit of this iterative chain of smooth functions should reflect itself in other mathematical constructions, too, since it is not related in any way to the explicit form of the MB transforms. This finite double-uniform limit is represented in terms of a differential operator with respect to an auxiliary parameter which acts on the integrand of a certain two-fold MB integral. To demonstrate that our result is compatible with original representations of UD functions, we reproduce the integrands of these original integral representations by applying this differential operator to the integrand of the simple integral representation of the scalar triangle four-dimensional integral J(1, 1, 1 − ε).

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“…11 have been given in Refs. [156,293,301,302] and [303]. Another direction is the construction of a uniqueness rule for vertices involving fermions which can be applied to Yukawa type theories.…”

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confidence: 99%

“…Therefore we have not provided a graphical representation of the rule for this particular gauge choice but it can be found in Ref. [303] as well as in Ref. [150,156].…”

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confidence: 99%

Large $N_f$ quantum field theory

Gracey

2018

Preprint

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We review the development of the large N method, where N indicates the number of flavours, used to study perturbative and nonperturbative properties of quantum field theories. The relevant historical background is summarized as a prelude to the introduction of the large N critical point formalism. This is used to compute large N corrections to d-dimensional critical exponents of the universal quantum field theory present at the Wilson-Fisher fixed point. While pedagogical in part the application to gauge theories is also covered and the use of the large N method to complement explicit high order perturbative computations in gauge theories is also highlighted. The usefulness of the technique in relation to other methods currently used to study quantum field theories in d-dimensions is also summarized.

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External leg amputation in conformal-invariant three-point function

Cited by 7 publications

References 23 publications

Solution to Bethe–Salpeter equation via Mellin–Barnes transform

Solution to Bethe–Salpeter equation via Mellin–Barnes transform

Two-fold Mellin–Barnes transforms of Usyukina–Davydychev functions

Large $N_f$ quantum field theory

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