Related papers: An All-Loop Amplituhedron in Two Dimensions

A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of…

In this work, we compute the one-loop four-graviton amplitudes with a massive abelian vector field (Proca) circulating in the loop. Instead of the conventional Einstein-Hilbert formulation, we employ the Landau-Lifshitz metric density…

Starting with the light-cone Hamiltonian for gravity, we perform a field redefinition that reveals a hidden symmetry in four dimensions, namely the Ehlers $SL(2,R)$ symmetry. The field redefinition, which is non-local in space but local in…

We present an ansatz for all one-loop amplitudes in pure Einstein gravity for which the n external gravitons have the same outgoing helicity. These loop amplitudes, which are rational functions of the momenta, also arise in the quantization…

All positive helicity four-point gluon-graviton amplitudes in Einstein-Yang-Mills theory coupled to a dilaton and axion field are computed at the leading one-loop order using colour-kinematics duality. In particular, all relevant…

We calculate the all-loop anomalous dimensions of current operators in $\lambda$-deformed $\sigma$-models. For the isotropic integrable deformation and for a semi-simple group $G$ we compute the anomalous dimensions using two different…

We construct a 4-dimensional quantum field theory on a Hilbert space, dependent on a simple Lie Algebra of a compact Lie group, that satisfies Wightman's axioms. This Hilbert space can be written as a countable sum of non-separable Hilbert…

We study the global topology of the space $\mathcal L$ of loops of contactomorphisms of a non-orderable closed contact manifold $(M^{2n+1}, \alpha)$. We filter $\mathcal L$ by a quantitative measure of the ``positivity'' of the loops and…

We present the full color two-loop six-point all-plus Yang-Mills amplitude in compact analytic form. The computation uses four dimensional unitarity and augmented recursion.

We present new triangulations of the $m=4$ amplituhedron relevant for scattering amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills, obtained directly from the combinatorial definition of the geometry. Using the "sign flip"…

We construct all supergravity theories that can be obtained through factorized orbifold projections of N=8 supergravity, exposing their double-copy structure, and calculate their one-loop four-point scattering amplitudes. We observe a…

We prove that the space of contractible simple loops of a given fixed area in any compact oriented surface has infinite diameter as a homogeneous space of the group of area-preserving diffeomorphisms endowed with the $L^p$-metric. As a…

The infrared exponentiation properties of dimensionally-regularized multi-loop scattering amplitudes are typically hidden at the level of the integrand, materializing only after integral evaluation. We address this long-standing problem by…

Dual conformal symmetry has had a huge impact on our understanding of planar scattering amplitudes in N=4 super Yang-Mills. At tree level, it combines with the original conformal symmetry generators to a Yangian algebra, a hallmark of…

We review the state-of-the-art knowledge of IR singularities in multileg QCD amplitudes, identifying the key reasons for the remarkable simplicity of the soft anomalous dimension. We then present a novel strategy to compute this quantity…

Let $X$ be a finite simply connected CW complex of dimension $n$. The loop space homology $H\_*(\Omega X;\mathbb Q)$ is the universal enveloping algebra of a graded Lie algebra $L\_X$ isomorphic with $ pi\_{*-1} (X)\otimes \mathbb Q$. Let…

The expansion method of Lie algebras by a semigroup or S-expansion is generalized to act directly on the group manifold, and not only at the level of its Lie algebra. The consistency of this generalization with the dual formulation of the…

We use geometric Landau analysis to determine the singularity structure of four-point, one-cycle negative geometries in $\mathcal{N}=4$ super-Yang-Mills theory, which represent certain contributions to the logarithm of the four-point…

Positive geometries were introduced by Arkani-Hamed--Bai--Lam as a method of computing scattering amplitudes in theoretical physics. We show that a positive geometry from a polytope admits a log resolution of singularities to another…

We present results for Wilson loops in strongly coupled gauge theories. The loops may be taken around an arbitrarily shaped contour and in any field theory with a dual IIB geometry of the form M x S^5. No assumptions about supersymmetry are…