arXiv subjects

Omer Gurdogan

Publications and source records attributed to Omer Gurdogan.

9 recordsLinked to original sources

arXiv2023

Bootstrapping a Stress-Tensor Form Factor through Eight Loops

We bootstrap the three-point form factor of the chiral stress-tensor multiplet in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory at six, seven, and eight loops, using boundary data from the form factor operator product expansion. This may represent the highest perturbative order to which multi-variate quantities in a unitary four-dimensional quantum field theory have been computed. In computing this form factor, we observe and employ new restrictions on pairs and triples of adjacent letters in the symbol. We provide details about the function space required to describe the form factor through eight loops. Plotting the results on various lines provides striking numerical evidence for a finite radius of convergence of perturbation theory. By the principle of maximal transcendentality, our results are expected to give the highest weight part of the $g g \rightarrow H g$ and $H \rightarrow ggg$ amplitudes in the heavy-top limit of QCD through eight loops. These results were also recently used to discover a new antipodal duality between this form factor and a six-point amplitude in the same theory.

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arXiv2022

Folding Amplitudes into Form Factors: An Antipodal Duality

We observe that the three-gluon form factor of the chiral part of the stress-tensor multiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory is dual to the six-gluon MHV amplitude on its parity-preserving surface. Up to a simple variable substitution, the map between these two quantities is given by the antipode operation defined on polylogarithms (as part of their Hopf algebra structure), which acts at symbol level by reversing the order of letters in each term. We provide evidence for this duality through seven loops.

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arXiv2018

Cluster adjacency beyond MHV

We explore further the notion of cluster adjacency, focussing on non-MHV amplitudes. We extend the notion of adjacency to the BCFW decomposition of tree-level amplitudes. Adjacency controls the appearance of poles, both physical and spurious, in individual BCFW terms. We then discuss how this notion of adjacency is connected to the adjacency already observed at the level of symbols of scattering amplitudes which controls the appearance of branch cut singularities. Poles and symbols become intertwined by cluster adjacency and we discuss the relation of this property to the $\bar{Q}$-equation which imposes constraints on the derivatives of the transcendental functions appearing in loop amplitudes.

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arXiv2018

Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs

We consider a special double scaling limit, recently introduced by two of the authors, combining weak coupling and large imaginary twist, for the $γ$-twisted $\mathcal{N}=4$ SYM theory. We also establish the analogous limit for ABJM theory. The resulting non-gauge chiral 4D and 3D theories of interacting scalars and fermions are integrable in the planar limit. In spite of the breakdown of conformality by double-trace interactions, most of the correlators for local operators of these theories are conformal, with non-trivial anomalous dimensions defined by specific, integrable Feynman diagrams. We discuss the details of this diagrammatics. We construct the doubly-scaled asymptotic Bethe ansatz (ABA) equations for multi-magnon states in these theories. Each entry of the mixing matrix of local conformal operators in the simplest of these theories - the bi-scalar model in 4D and tri-scalar model in 3D - is given by a single Feynman diagram at any given loop order. The related diagrams are in principle computable, up to a few scheme dependent constants, by integrability methods (quantum spectral curve or ABA). These constants should be fixed from direct computations of a few simplest graphs. This integrability-based method is advocated to be able to provide information about some high loop order graphs which are hardly computable by other known methods. We exemplify our approach with specific five-loop graphs.

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arXiv2017

Cluster adjacency properties of scattering amplitudes

We conjecture a new set of analytic relations for scattering amplitudes in planar N=4 super Yang-Mills theory. They generalise the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr(4,n). In terms of the symbol, they dictate which letters can appear consecutively. We study heptagon amplitudes and integrals in detail and present symbols for previously unknown integrals at two and three loops which support our conjecture.

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arXiv2016

Modular Graph Functions

In earlier work we studied features of non-holomorphic modular functions associated with Feynman graphs for a conformal scalar field theory on a two-dimensional torus with zero external momenta at all vertices. Such functions, which we will refer to as modular graph functions, arise, for example, in the low energy expansion of genus-one Type II superstring amplitudes. We here introduce a class of single-valued elliptic multiple polylogarithms, which are defined as elliptic functions associated with Feynman graphs with vanishing external momenta at all but two vertices. These functions depend on a coordinate, $ζ$, on the elliptic curve and reduce to modular graph functions when $ζ$ is set equal to $1$. We demonstrate that these single-valued elliptic multiple polylogarithms are linear combinations of multiple polylogarithms, and that modular graph functions are sums of single-valued elliptic multiple polylogarithms evaluated at the identity of the elliptic curve, in both cases with rational coefficients. This insight suggests the many interrelations between modular graph functions (a few of which were established in earlier papers) may be obtained as a consequence of identities involving multiple polylogarithms, and explains an earlier observation that the coefficients of the Laurent polynomial at the cusp are given by rational numbers times single-valued multiple zeta values.

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arXiv2016

New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM

We consider the $γ$-deformed $\mathcal{N}=4$ SYM in the double scaling limit of large imaginary twists and small coupling, which discards the gauge fields and retains only certain Yukawa and scalar interactions with three arbitrary effective couplings. In the 't~Hooft limit, these 4D theories are integrable, with most of the correlators being conformal such that the whole arsenal of AdS/CFT integrability remains applicable. In particular, for one non-zero effective coupling, we obtain a QFT of two complex scalars with a chiral, quartic interaction. The BMN vacuum anomalous dimension is dominated in each non-zero loop order by a single "wheel" graph, in principle computable by integrability. Thus we also provide an explicit conjecture for the periods of double-wheel graphs with an arbitrary number of spokes.

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arXiv2013

Two-loop Sudakov Form Factor in ABJM

We compute the two-loop Sudakov form factor in three-dimensional N=6 superconformal Chern-Simons theory, using generalised unitarity. As an intermediate step, we derive the non-planar part of the one-loop four-point amplitude in terms of box integrals. Our result for the Sudakov form factor is given by a single non-planar tensor integral with uniform degree of transcendentality, and is in agreement with the known infrared divergences of two-loop amplitudes in ABJM theory. We also discuss a number of interesting properties satisfied by related three-dimensional integral functions.

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arXiv2011

Harmony of Super Form Factors

In this paper we continue our systematic study of form factors of half-BPS operators in N=4 super Yang-Mills. In particular, we extend various techniques known for amplitudes to the case of form factors, including MHV rules, recursion relations, unitarity and dual MHV rules. As an application, we present the solution of the recursion relation for split-helicity form factors. We then consider form factors of the stress-tensor multiplet operator and of its chiral truncation, and write down supersymmetric Ward identities using chiral as well as non-chiral superspace formalisms. This allows us to obtain compact formulae for families of form factors, such as the maximally non-MHV case. Finally we generalise dual MHV rules in dual momentum space to form factors.

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