Dr. Burkhard Eden
Profil
Forschungsthemen6
DFG-Eigene Stelle/2: Eich-/Stringtheorie Dualität und integrable Systeme
Quelle ↗Förderer: DFG Eigene Stelle (Sachbeihilfe) Zeitraum: 11/2013 - 11/2015 Projektleitung: Dr. Burkhard Eden
DFG-Eigene Stelle/3: Eichtheorie/Stringtheorie Dualität und integrable Systeme III
Quelle ↗Förderer: DFG Eigene Stelle (Sachbeihilfe) Zeitraum: 10/2016 - 09/2018 Projektleitung: Dr. Burkhard Eden
Gauge/string theory duality and integrable systems
Quelle ↗Förderer: DFG Eigene Stelle (Sachbeihilfe) Zeitraum: 11/2011 - 06/2014 Projektleitung: Dr. Burkhard Eden
N-Punkt Funktionen und integrable Systeme
Quelle ↗Förderer: DFG Heisenberg Programm Zeitraum: 04/2024 - 03/2026 Projektleitung: Dr. Burkhard Eden
N-Punkt Funktionen und integrable Systeme
Quelle ↗Förderer: DFG Heisenberg Programm Zeitraum: 04/2021 - 03/2026 Projektleitung: Dr. Burkhard Eden
N-Punkt Funktionen und integrable Systeme
Quelle ↗Förderer: DFG Heisenberg Programm Zeitraum: 04/2021 - 03/2026 Projektleitung: Dr. Burkhard Eden
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Publikationen25
Top 25 nach Zitationen — Quelle: OpenAlex (BAAI/bge-m3 embedded für Matching).
Journal of Statistical Mechanics Theory and Experiment · 784 Zitationen · DOI
We discuss possible phase factors for the S-matrix of planar N=4 gauge theory, leading to modifications at four-loop order as compared to an earlier proposal. While these result in a four-loop breakdown of perturbative BMN-scaling, Kotikov-Lipatov transcendentality in the universal scaling function for large-spin twist operators may be preserved. One particularly natural choice, unique up to one constant, modifies the overall contribution of all terms containing odd zeta functions in the earlier proposed scaling function based on a trivial phase. Excitingly, we present evidence that this choice is non-perturbatively related to a recently conjectured crossing-symmetric phase factor for perturbative string theory on AdS_5xS^5 once the constant is fixed to a particular value. Our proposal, if true, might therefore resolve the long-standing AdS/CFT discrepancies between gauge and string theory.
Physics Letters B · 156 Zitationen · DOI
Nuclear Physics B · 147 Zitationen · DOI
Journal of High Energy Physics · 144 Zitationen · DOI
We study the correlation functions of half-BPS protected operators in N = 4 super-Yang-Mills theory, in the limit where the positions of adjacent operators become light-like separated. We compute the loop corrections by means of Lagrangian insertions. The divergences resulting from the light-cone limit are regularized by changing the dimension of the integration measure over the insertion points. Switching from coordinates to dual momenta, we show that the logarithm of the correlation function is identical with twice the logarithm of the matching MHV gluon scattering amplitude. We present a number of examples of this new relation, at one and two loops.
Journal of High Energy Physics · 138 Zitationen · DOI
A bstract The three-loop four-point function of stress-tensor multiplets in $ \mathcal{N}=4 $ super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In this paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol — with an appropriate ansatz for its structure — as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certain limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. The techniques we develop can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same four-point function at four loops. This example shows a connection between the leading singularities and the entries of the symbol.
Nuclear Physics B · 130 Zitationen · DOI
Nuclear Physics B · 129 Zitationen · DOI
Nuclear Physics B · 122 Zitationen · DOI
Physics Letters B · 121 Zitationen · DOI
Journal of High Energy Physics · 101 Zitationen · DOI
Nuclear Physics B · 98 Zitationen · DOI
We compute the three-loop anomalous dimension of the BMN operators with charges J=0 (the Konishi multiplet) and J=1 in the N=4 super-Yang–Mills theory. We employ a method which effectively reduces the calculation to two loops. Instead of using the superconformal primary states, we consider the ratio of the two-point functions of suitable descendants of the corresponding multiplets. Our results unambiguously select the form of the N=4 SYM dilatation operator which is compatible with BMN scaling. Thus, we provide evidence for BMN scaling at three loops.
Physics Letters B · 88 Zitationen · DOI
Physics Letters B · 80 Zitationen · DOI
Nuclear Physics B · 78 Zitationen · DOI
Nuclear Physics B · 71 Zitationen · DOI
Nuclear Physics B · 71 Zitationen · DOI
Journal of High Energy Physics · 66 Zitationen · DOI
We continue the study of four-point correlation functions by the hexagon tessellation approach initiated in [38] and [39]. We consider planar tree-level correlation functions in $$ \mathcal{N}=4 $$ supersymmetric Yang-Mills theory involving two non-protected operators. We find that, in order to reproduce the field theory result, it is necessary to include SU(N) colour factors in the hexagon formalism; moreover, we find that the hexagon approach as it stands is naturally tailored to the single-trace part of correlation functions, and does not account for multi-trace admixtures. We discuss how to compute correlators involving double-trace operators, as well as more general 1/N effects; in particular we compute the whole next-to-leading order in the large-N expansion of tree-level BMN two-point functions by tessellating a torus with punctures. Finally, we turn to the issue of “wrapping”, Lüscher-like corrections. We show that SU(N) colour-dressing reproduces an earlier empirical rule for incorporating single-magnon wrapping, and we provide a direct interpretation of such wrapping processes in terms of $$ \mathcal{N}=2 $$ supersymmetric Feynman diagrams.
Nuclear Physics B · 60 Zitationen · DOI
Repository for Publications and Research Data (ETH Zurich) · 58 Zitationen · DOI
We consider a class of planar tree-level four-point functions in N = 4 SYM in a special kinematic regime: one BMN operator with two scalar excitations and three half-BPS operators are put onto a line in configuration space; additionally, for the half-BPS operators a co-moving frame is chosen in flavour space. In configuration space, the four-punctured sphere is naturally triangulated by tree-level planar diagrams. We demonstrate on a number of examples that each tile can be associated with a modified hexagon form-factor in such a way as to efficiently reproduce the tree-level four-point function. Our tessellation is not of the OPE type, fostering the hope of finding an independent, integrability-based approach to the computation of planar four-point functions.
Journal of High Energy Physics · 45 Zitationen · DOI
We give a new method for computing the correlation functions of the chiral part of the stress-tensor supermultiplet that relies on the reformulation of $$ \mathcal{N}=4 $$ SYM in twistor space. It yields the correlation functions in the Born approximation as a sum of Feynman diagrams on twistor space that involve only propagators and no integration vertices. We use this unusual feature of the twistor Feynman rules to compute the correlation functions in terms of simple building blocks which we identify as a new class of $$ \mathcal{N}=4 $$ off-shell superconformal invariants. Making use of the duality between correlation functions and planar scattering amplitudes, we demonstrate that these invariants represent an off-shell generalisation of the on-shell invariants defining tree-level scattering amplitudes in $$ \mathcal{N}=4 $$ SYM.
Journal of High Energy Physics · 44 Zitationen · DOI
We introduce a new geometric object, the correlahedron, which we conjecture to be equivalent to stress-energy correlators in planar $$ \mathcal{N}=4 $$ super Yang-Mills. Re-expressing the Grassmann dependence of correlation functions of n chiral stress-energy multiplets with Grassmann degree 4k in terms of 4(n + k)-linear bosonic variables, the resulting expressions have an interpretation as volume forms on a Gr(n+k, 4+n+k) Grassmannian, analogous to the expressions for planar amplitudes via the amplituhedron. The resulting volume forms are to be naturally associated with the correlahedron geometry. We construct such expressions in this bosonised space both directly, in general, from Feynman diagrams in twistor space, and then more invariantly from specific known correlator expressions in analytic superspace. We give a geometric interpretation of the action of the consecutive lightlike limit and show that under this the correlahedron reduces to the squared amplituhedron both as a geometric object as well as directly on the corresponding volume forms. We give an explicit easily implementable algorithm via cylindrical decompositions for extracting the squared amplituhedron volume form from the squared amplituhedron geometry with explicit examples and discuss the analogous procedure for the correlators.
Repository for Publications and Research Data (ETH Zurich) · 39 Zitationen · DOI
Basso, Komatsu and Vieira recently proposed an all-loop framework for the computation of three-point functions of single-trace operators of N=4 super-Yang-Mills, the “hexagon program”. This proposal results in several remarkable predictions, including the three-point function of two protected operators with an unprotected one in the SU(2) and SL(2) sectors. Such predictions consist of an “asymptotic” part — similar in spirit to the asymptotic Bethe Ansatz of Beisert and Staudacher for two-point functions — as well as additional finite-size “wrapping” Lüscher-like corrections. The focus of this paper is on such wrapping corrections, which we compute at three-loops in the SL(2) sector. The resulting structure constants perfectly match the ones obtained in the literature from four-point correlators of protected operators.
arXiv (Cornell University) · 39 Zitationen · DOI
We present a conjecture for the normalisation of the twist two conformal partial waves in a double OPE limit of the four-point function of stress tensor multiplets in N = 4 super Yang-Mills theory up to three loops. This contains information about the structure constants in the OPE. Like the twist two anomalous dimensions our result is expressed as a linear combination of harmonic sums whose argument is the spin of the exchanged operators. To arrive at the result we derive asymptotic expansions for the twist two part of two unknown three-loop integrals using the method of expansion by regions, complemented by some intuition gained on the example of the ladder integrals up to three loops.
39 Zitationen
Four-point correlation functions of hypermultiplet bilinear composites are analysed in N = 2 superconformal field theory using the superconformal Ward identities and the analyticity properties of the composite operator superfields. It is shown that the complete amplitude is determined by a single arbitrary function of the two conformal cross-ratios of the space-time variables. 1 In this paper we examine in detail the constraints imposed by superconformal invariance and analyticity on four-point correlation functions of analytic operators in four-dimensional superconformal field theories with N = 2 supersymmetry. The analytic operators under consideration are gauge-invariant products of hypermultiplets which are represented by analytic superfields in
Journal of High Energy Physics · 30 Zitationen · DOI
Integrands for colour ordered scattering amplitudes in planar N=4 SYM are dual to those of correlation functions of the energy-momentum multiplet of the theory. The construction can relate amplitudes with different numbers of legs. By graph theory methods the integrand of the four-point function of energy-momentum multiplets has been constructed up to six loops in previous work. In this article we extend this analysis to seven loops and use it to construct the full integrand of the five-point amplitude up to five loops, and in the parity even sector to six loops. All results, both parity even and parity odd, are obtained in a concise local form in dual momentum space and can be displayed efficiently through graphs. We have verified agreement with other local formulae both in terms of supertwistors and scalar momentum integrals as well as BCJ forms where those exist in the literature, i.e. up to three loops. Finally we note that the four-point correlation function can be extracted directly from the four-point amplitude and so this uncovers a direct link from four- to five-point amplitudes.
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Stammdaten
Identität, Organisation und Kontakt aus HU-FIS.
- Name
- Dr. Burkhard Eden
- Titel
- Dr.
- Fakultät
- Mathematisch-Naturwissenschaftliche Fakultät
- Institut
- Institut für Physik
- Arbeitsgruppe
- Theoretische Physik (Mathematische Physik von Raum, Zeit und Materie)
- Telefon
- +49 30 2093-66397
- HU-FIS-Profil
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- 26.4.2026, 01:04:09