Related papers: Biadjoint scalar tree amplitudes and intersecting …
Scattering and production amplitudes involving scalar resonances are known, according to Watson's theorem, to share the same phase $\delta(s)$. We show that, at low energies, the production amplitude is fully determined by the combination…
We calculate on-shell scattering amplitudes involving fermions at the tree level in open superstring field theory. We confirm that four-point and five-point amplitudes in the world-sheet path integral with the standard prescription using…
We study open and closed string amplitudes at tree-level in string perturbation theory using the methods of single-valued integration which were developed in the prequel to this paper. Using dihedral coordinates on the moduli spaces of…
In this note we revisit the problem of explicitly computing tree-level scattering amplitudes in various theories in any dimension from worldsheet formulas. The latter are known to produce cubic-tree expansion of tree amplitudes with…
We show how one-loop corrections to scattering amplitudes of scalars and gauge bosons can be obtained from tree amplitudes in one higher dimension. Starting with a complete tree-level scattering amplitude of n+2 particles in five…
Biadjoint scalar field theories are increasingly important in the study of scattering amplitudes in various string and field theories. Recently, some first exact nonperturbative solutions of biadjoint scalar theory were presented, with a…
In light of the grammar given by Ji for the $(\alpha,\beta)$-Eulerian polynomials introduced by Carlitz and Scoville, we provide a labeling scheme for increasing binary trees. In this setting, we obtain a combinatorial interpretation of the…
We introduce a new set of symmetries obeyed by tree-level gauge-theory amplitudes involving at least one gluon. The symmetry acts as a momentum-dependent shift on the color factors of the amplitude. Using the radiation vertex expansion, we…
In this text we review various relations between building blocks of closed and open string amplitudes at tree-level and genus one. We explain that KLT relations between tree-level closed and open string amplitudes follow from the…
We emphasize that scattering amplitudes of a wide class of models to any order in the coupling are constructible by on-shell tree subamplitudes. This follows from the Feynman-tree theorem combined with BCFW on-shell recursion relations. In…
In this thesis, we take a journey through two different but not dissimilar stories with an underlying theme of combinatorics emerging from scattering amplitudes in quantum field theories. The first part tells the tale of the…
We present a new formulation for Yang-Mills scattering amplitudes in any number of dimensions and at any loop order, based on the same combinatorial and binary-geometric ideas in kinematic space recently used to give an all-order…
Bi-adjoint scalars are helpful in studying properties of color/kinematics duality and the double copy, which relates scattering amplitudes of gauge and gravity theories. Here we study bi-adjoint scalars from a worldline perspective. We show…
We investigate the use of the embedding formalism and the Mellin transform in the calculation of tree-level conformal correlation functions in $AdS$/CFT. We evaluate 5- and 6-point Mellin amplitudes in $\phi^3$ theory and even a 12-pt…
The computation of CFT correlation functions via Witten diagrams in AdS space can be simplified via the Mellin transform. Recently a set of Feynman rules for tree-level Mellin space amplitudes has been proposed for scalar theories. In this…
Scattering amplitudes in quantum field theory are independent of the field parameterization, which has a natural geometric interpretation as a form of `coordinate invariance.' Amplitudes can be expressed in terms of Riemannian curvature…
In recent work of Cachazo, Guevara, Mizera and the author, a generalization of the biadjoint scattering amplitude $m^{(k)}(\mathbb{I}_n,\mathbb{I}_n)$ was introduced as an integral over the moduli space of $n$ points in $\mathbb{CP}^{k-1}$,…
A remarkable connection between perturbative scattering amplitudes of four-dimensional planar SYM, and the stratification of the positive grassmannian, was revealed in the seminal work of Arkani-Hamed et. al. Similar extension for…
Let $q$ be an odd prime power and let $X(m,q)$ be the set of symmetric bilinear forms on an $m$-dimensional vector space over $\mathbb{F}_q$. The partition of $X(m,q)$ induced by the action of the general linear group gives rise to a…
Open string amplitudes at tree level have been studied for over fifty years, but there is no known analytic form for general $n$-point amplitudes, and their conventional representation in terms of worldsheet integrals does not make many of…