Related papers: Positive Geometry for Stringy Scalar Amplitudes
We build upon the prior works of [1-3] to study tree-level planar amplitudes for a massless scalar field theory with polynomial interactions. Focusing on a specific example, where the interaction is given by $\lambda_3\phi^{3}\ +\lambda_4…
The geometric structure of S-matrix encapsulated by the "Amplituhedron program" has begun to reveal itself even in non-supersymmetric quantum field theories. Starting with the seminal work of Arkani-Hamed, Bai, He and Yan it is now…
We show that accordiohedra furnish polytopes which encode amplitudes for all massive scalar field theories with generic interactions. This is done by deriving integral formulae for the Feynman diagrams at tree level and integrands at one…
A new perspective on the inverse string theory Kawai-Lewellen-Tye (KLT) kernel is provided which establishes the universality of scattering amplitudes in the bi-adjoint scalar (BAS) theory, pions in the Non-linear sigma model (NLSM), and…
We introduce the notion of "binary" positive and complex geometries, giving a completely rigid geometric realization of the combinatorics of generalized associahedra attached to any Dynkin diagram. We also define open and closed "cluster…
A new way of computing scattering amplitudes in a certain very important QFT (N=4 SYM) has recently been developed, in which an algebraic structure called the positive Grassmannian plays a very important role. The mathematics of the…
This thesis investigates geometric descriptions of scattering amplitudes, with a specific focus on scattering amplitudes in N=4 SYM and ABJM theory. The recent development of the field of positive geometries provides us with a suitable…
The field theory Kawai-Lewellen-Tye (KLT) kernel, which relates scattering amplitudes of gravitons and gluons, turns out to be the inverse of a matrix whose components are bi-adjoint scalar partial amplitudes. In this note we propose an…
Scattering amplitudes are both a wonderful playground to discover novel ideas in Quantum Field Theory and simultaneously of immense phenomenological importance to make precision predictions for e.g.~particle collider observables and more…
Arkani-Hamed, Bai, He, and Yan (ABHY) discovered a convex realisation of the associahedron whose combinatorial and geometric structure generates tree-level amplitudes in bi-adjoint scalar theory. In this paper, we identify S-matrix of…
Starting with the seminal work of Arkani-Hamed et al arXiv:1711.09102, in arXiv:1811.05904, the "Amplituhedron program" was extended to analyzing (planar) amplitudes in massless $\phi^{4}$ theory. In this paper we show that the program can…
We initiate the study of positive geometry and scattering forms for tree-level amplitudes with matter particles in the (anti-)fundamental representation of the color/flavor group. As a toy example, we study the bi-color scalar theory, which…
Scattering amplitudes for the simplest theory of colored scalar particles - the Tr($\Phi^3$) theory - have recently been the subject of active investigations. In this letter we describe an unanticipated wider implication of this work: the…
The orbifold CFT dual to string theory on $ADS_3 \times S^3$ allows a construction of gravitational actions based on collective field techniques. We describe a fundamental role played by a Lie algebra constructed from chiral primaries and…
We elaborate on a recently proposed geometric framework for scalar effective field theories. Starting from the action, a metric can be identified that enables the construction of geometric quantities on the associated functional manifold.…
Positive geometries provide a purely geometric point of departure for studying scattering amplitudes in quantum field theory. A positive geometry is a specific semi-algebraic set equipped with a unique rational top form - the canonical…
Positive geometry provides a geometric framework where physical observables are encoded as canonical forms associated to regions of kinematic space. In this paper we consider a generalisation to an infinite union of line segments, which…
We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem…
Recent years have seen the emergence of a new understanding of scattering amplitudes in the simplest theory of colored scalar particles - the Tr$(\phi^3)$ theory - based on combinatorial and geometric ideas in the kinematic space of…
The amplituhedron determines scattering amplitudes in planar ${\cal N}=4$ super Yang-Mills by a single "positive geometry" in the space of kinematic and loop variables. We study a closely related definition of the amplituhedron for the…