Loopedia, a Database for Loop Integrals

Bogner, Christian; Borowka, S.; Hahn, Thomas; Heinrich, G.; Jones, Stephen; Kerner, M.; Manteuffel, Andreas von; Michel, Martin C.; Panzer, Erik; Papara, V.

doi:10.1088/1742-6596/1085/5/052003

Cited by 5 publications

(5 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is a common approach in general, and the existence of wide plateaus in this case was for example pointed out in [121]. 17 The power of studying the sensitivity with respect to the resummation parameters was also demonstrated in [59], and indeed we will also apply this criterion with respect to variations of λ.…”

Section: B Dependence On Resummation Parametersmentioning

confidence: 86%

“…Asymptotically, the number of graphs grows factorially with the number of loops and precise higher order expansions were recently presented in [22]. 5 Some of the results in [25] in terms of zeta values were based on numeric techniques, and one value in particular was only later identified in [29] as the double zeta value (17). Analytic proofs of these 6-loop periods were later given in [128,137,139].…”

Section: Calculational Techniquesmentioning

confidence: 99%

“…Therefore we provide an extensive set of data with this article as described in Appendix A and available under DOI 10.5287/bodleian:pvx4nMyQr. We added the computed Feynman integrals to the Loopedia [17].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Minimally subtracted six-loop renormalization of O(n) -symmetric ϕ4 theory and critical exponents

Kompaniets¹,

Panzer²

2017

Phys. Rev. D

214

285

View full text Add to dashboard Cite

We present the perturbative renormalization group functions of O(n)-symmetric φ 4 theory in 4 − 2ε dimensions to the sixth loop order in the minimal subtraction scheme. In addition, we estimate diagrams without subdivergences up to 11 loops and compare these results with the asymptotic behaviour of the beta function. Furthermore we perform a resummation to obtain estimates for critical exponents in three and two dimensions.

show abstract

Section: B Dependence On Resummation Parametersmentioning

confidence: 86%

Section: Calculational Techniquesmentioning

confidence: 99%

See 1 more Smart Citation

Minimally subtracted six-loop renormalization of O(n) -symmetric ϕ4 theory and critical exponents

Kompaniets¹,

Panzer²

2017

Phys. Rev. D

214

285

View full text Add to dashboard Cite

show abstract

“…One of the aims of the present paper is to fill this gap. We do so by mapping the AdS calculations to flat space calculations where an impressive machinery for an analytic evaluation of Feynman integrals has been developed in recent years [46][47][48][49][50][51][52]. Here, we bring the four-point function of a conformally coupled scalar φ 4 -theory in euclidean AdS 4 into a JHEP08(2022)052 form we can interpret as a flat space Feynman diagram and evaluate it analytically.…”

Section: Introductionmentioning

confidence: 99%

Analytical evaluation of AdS4 Witten diagrams as flat space multi-loop Feynman integrals

Heckelbacher

Sachs

Skvortsov

et al. 2022

J. High Energ. Phys.

View full text Add to dashboard Cite

We describe a systematic approach for the evaluation of Witten diagrams for multi-loop scattering amplitudes of a conformally coupled scalar ϕ4-theory in Euclidean AdS4, by recasting the Witten diagrams as flat space Feynman integrals. We derive closed form expressions for the anomalous dimensions for all double-trace operators up to the second order in the coupling constant. We explain the relation between the flat space unitarity methods and the discontinuities of the short distance expansion on the boundary of Witten diagrams.

show abstract

“…One of the aims of the present paper is to fill this gap. We do so by mapping the AdS calculations to flat space calculations where an impressive machinery for an analytic evaluation of Feynman integrals has been developed in recent years [45][46][47][48][49][50][51]. Here, we bring the four-point function of a conformally coupled scalar φ 4 -theory in euclidean AdS 4 into a form we can interpret as a flat space Feynman diagram and evaluate it analytically.…”

Section: Introductionmentioning

confidence: 99%

Analytical evaluation of AdS${}_4$ Witten diagrams as flat space multi-loop Feynman integrals

Heckelbacher¹,

Sachs²,

Skvortsov³

et al. 2022

Preprint

View full text Add to dashboard Cite

We describe a systematic approach for the evaluation of Witten diagrams for multi-loop scattering amplitudes of a conformally coupled scalar φ 4 -theory in Euclidean AdS 4 , by recasting the Witten diagrams as flat space Feynman integrals. We derive closed form expressions for the anomalous dimensions for all double-trace operators up to the second order in the coupling constant. We explain the relation between the flat space unitarity methods and the discontinuities of the short distance expansion on the boundary of Witten diagrams. B Evaluation of the Witten cross diagram B.1 The analytic evaluation of cross diagram for all ∆ B.2 Cross in dimensional regularisation B.3 The expansion of the cross diagram C Evaluation of the one-loop Witten bubble diagram C.1 The one-loop diagram C.1.1 ∆ = 1 C.1.2 ∆ = 2 C.1.3 L ∆ 0 integrals C.1.4 L ′ 0 integrals C.2 Expressions from unitarity cuts D Conformal blocks and OPE coefficients

show abstract

Loopedia, a Database for Loop Integrals

Cited by 5 publications

References 5 publications

Minimally subtracted six-loop renormalization of O(n) -symmetric ϕ4 theory and critical exponents

Minimally subtracted six-loop renormalization of O(n) -symmetric ϕ4 theory and critical exponents

Analytical evaluation of AdS4 Witten diagrams as flat space multi-loop Feynman integrals

Analytical evaluation of AdS${}_4$ Witten diagrams as flat space multi-loop Feynman integrals

Contact Info

Product

Resources

About