Ward–Schwinger–Dyson equations in $$\phi ^3_6$$ quantum field theory

Bellon, Marc P.; Russo, Enrico I.

doi:10.1007/s11005-021-01377-2

Cited by 8 publications

(12 citation statements)

References 34 publications

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“…and we will write s = 2υ + γ and q = 2γ + υ. This formalism was tested in [10] by showing that the renormalisation functions to order a 2 computed with it matched with known results.…”

Section: Wsd Equations For ϕmentioning

confidence: 99%

“…We introduced the Ward-Schwinger-Dyson scheme (often abbreviated to WSD in the following) in the case of the model ϕ 3 6 in [10]. We here recall only the equations which will be studied.…”

Section: Wsd Equations For ϕmentioning

confidence: 99%

“…where γ(a) and υ(a) are the anomalous dimensions of the 2-point and 3-point function and β(a) is the beta-function of the model. In [10], we established that β = 2υ + 3γ, but we must point out that our convention for the function β differs from the usual ones. Since γ 0 and υ 0 are left undetermined by the equations, we fix them to 1 as a normalisation condition.…”

Section: Wsd Equations For ϕmentioning

confidence: 99%

“…It is therefore very interesting that our recent work [10] gives a system of equations for the determination of the renormalisation group functions of the ϕ 3 6 model, that we called Ward-Schwinger-Dyson equations, most suitable for a resurgent analysis. Indeed, this scheme has the properties which made the analysis in [8] possible, the absence of any explicit regularisation parameter and the invariance of the solution under the renormalisation group.…”

Section: Introductionmentioning

confidence: 99%

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Resurgent Analysis of Ward-Schwinger-Dyson Equations

Bellon

Russo

2021

SIGMA

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Building on our recent derivation of the Ward-Schwinger-Dyson equations for the cubic interaction model, we present here the first steps of their resurgent analysis. In our derivation of the WSD equations, we made sure that they had the properties of compatibility with the renormalisation group equations and independence from a regularisation procedure which was known to allow for the comparable studies in the Wess-Zumino model. The interactions between the transseries terms for the anomalous dimensions of the field and the vertex is at the origin of unexpected features, for which the effect of higher order corrections is not precisely known at this stage: we are only at the beginning of the journey to use resurgent methods to decipher non-perturbative effects in quantum field theory.

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“…and we will write s = 2υ + γ and q = 2γ + υ. This formalism was tested in [10] by showing that the renormalisation functions to order a 2 computed with it matched with known results.…”

Section: Wsd Equations For ϕmentioning

confidence: 99%

“…We introduced the Ward-Schwinger-Dyson scheme (often abbreviated to WSD in the following) in the case of the model ϕ 3 6 in [10]. We here recall only the equations which will be studied.…”

Section: Wsd Equations For ϕmentioning

confidence: 99%

Section: Wsd Equations For ϕmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Resurgent Analysis of Ward-Schwinger-Dyson Equations

Bellon

Russo

2021

SIGMA

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“…One important motivation, which was also the main one of Amit and Roginsky, comes from the Potts model, which in its field theory formulation has a cubic interaction [33,38] (see also [39] and references therein), but much work has gone into models with cubic interactions for many other reasons, e.g. [40][41][42][43][44][45][46][47][48][49][50]. It is therefore interesting that a melonic limit can be realized in a theory with cubic interaction.…”

Section: Jhep04(2021)197mentioning

confidence: 99%

Remarks on a melonic field theory with cubic interaction

Benedetti

Delporte

2021

J. High Energ. Phys.

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We revisit the Amit-Roginsky (AR) model in the light of recent studies on Sachdev-Ye-Kitaev (SYK) and tensor models, with which it shares some important features. It is a model of N scalar fields transforming in an N-dimensional irreducible representation of SO(3). The most relevant (in renormalization group sense) invariant interaction is cubic in the fields and mediated by a Wigner 3jm symbol. The latter can be viewed as a particular rank-3 tensor coupling, thus highlighting the similarity to the SYK model, in which the tensor coupling is however random and of even rank. As in the SYK and tensor models, in the large-N limit the perturbative expansion is dominated by melonic diagrams. The lack of randomness, and the rapidly growing number of invariants that can be built with n fields, makes the AR model somewhat closer to tensor models. We review the results from the old work of Amit and Roginsky with the hindsight of recent developments, correcting and completing some of their statements, in particular concerning the spectrum of the operator product expansion of two fundamental fields. For 5.74 < d < 6 the fixed-point theory defines a real CFT, while for smaller d complex dimensions appear, after a merging of the lowest dimension with its shadow. We also introduce and study a long-range version of the model, for which the cubic interaction is exactly marginal at large N , and we find a real and unitary CFT for any d < 6, both for real and imaginary coupling constant, up to some critical coupling.

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Introduction to Perturbative Quantum Field Theory

Balduf

2024

Springer Theses

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Ward–Schwinger–Dyson equations in $$\phi ^3_6$$ quantum field theory

Cited by 8 publications

References 34 publications

Resurgent Analysis of Ward-Schwinger-Dyson Equations

Resurgent Analysis of Ward-Schwinger-Dyson Equations

Remarks on a melonic field theory with cubic interaction

Introduction to Perturbative Quantum Field Theory

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