Related papers: Geometric Landau Analysis and Symbol Bootstrap
In this paper, we explore the chamber dissection of the loop-geometry of Correlahedron, which encodes the loop integrand of four-point stress-energy correlators in planar $\mathcal{N}=4$ super Yang-Mills. We demonstrate that at four loops,…
We define and study a positive geometry $\Delta^{(L)}$ which serves as a natural generalization of loop amplituhedra to two-dimensional Minkowski space $\mathbb{R}^{1,1}$. The geometry is formulated in the framework of lightcone geometries…
We develop a general power counting scheme for the infrared limit of Landau gauge SU(N) Yang-Mills theory in arbitrary dimensions. Employing a skeleton expansion, we find that the infrared behavior is qualitatively independent of the…
We shall interpret the null hexagonal Wilson loop (or, equivalently, six gluon scattering amplitude) in 4D ${\cal N}=4$ Super Yang-Mills, or, precisely, an integral representation of its matrix part, via an ADHM-like instanton construction.…
We present a symbol-level bootstrap construction of the planar, two-loop six-gluon scattering amplitude for the --++++ helicity configuration in QCD, focusing on the maximal weight pieces-the "most complicated terms" in the sense of Lipatov…
We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the Standard Model in dimensional regularization. After highlighting issues in the textbook treatment…
We compute dual-conformally invariant ladder integrals that are capped off by pentagons at each end of the ladder. Such integrals appear in six-point amplitudes in planar N=4 super-Yang-Mills theory. We provide exact, finite-coupling…
In massless quantum field theories the Landau equations are invariant under graph operations familiar from the theory of electrical circuits. Using a theorem on the $Y$-$\Delta$ reducibility of planar circuits we prove that the set of…
We propose a novel prescription for calculating the entanglement entropy of the $SU(N)$ Yang-Mills gauge theories on the lattice under the strong coupling expansion in powers of $\beta=2N/g^{2}$, where $g$ is the coupling constant. Using…
In this paper we focus on scattering amplitudes in maximally supersymmetric Yang-Mills theory and define a long sought-after geometry, the loop momentum amplituhedron, which we conjecture to encode tree and (the integrands of) loop…
The Amplituhedron provides, via geometric means, the all-loop integrand of scattering amplitudes in maximally supersymmetric Yang-Mills theory. Unfortunately, dimensional regularization, used conventionally for integration, breaks the…
Parametric representations of Feynman integrals have a key property: many, frequently all, of the Landau singularities appear as endpoint divergences. This leads to a geometric interpretation of the singularities as faces of Newton…
In this paper, we define the momentum amplituhedron in the four-dimensional split-signature space of dual momenta. It encodes scattering amplitudes at tree level and loop integrands for N=4 super Yang-Mills in the planar sector. In this…
We study, in the context of the three-dimensional ${\cal N}=6$ Chern-Simons-matter (ABJM) theory, the infrared-finite functions that result from performing $L-1$ loop integrations over the $L$-loop integrand of the logarithm of the…
Yang-Mills theories are an important building block of the standard model and in particular of quantum chromodynamics. Its correlation functions describe the behavior of its elementary particles, the gauge bosons. In quantum chromodynamics,…
We investigate elliptical Wilson loops in ${\cal N}=4$ Super Yang--Mills theory at weak and strong coupling for small values of the eccentricity. We obtain analytical results for the vacuum expectation value of the Wilson loop in the form…
Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant…
In the context of planar conformal gauge theory, we study five-point correlation functions between the interaction Lagrangian and four of the lightest single-trace, gauge-invariant scalar primaries. After performing two light-cone OPEs, we…
In this thesis, we investigate hidden symmetries for the Maldacena-Wilson loop in N=4 super Yang-Mills theory, mainly focusing on its strong-coupling description as a minimal surface in $AdS_5$. In the discussion of the symmetry structure…
The issue of the Gribov copies is discussed in Euclidean N=4 Super Yang-Mills theory quantized in the Landau gauge. As a consequence of the absence of a renormalization group invariant scale, it turns out that it is not possible to attach a…