arXiv subjects

Aidan Herderschee

Publications and source records attributed to Aidan Herderschee.

28 records · Page 2Linked to original sources

arXiv2022

Emergence of String Monodromy in Effective Field Theory

String monodromy is a set of linear relations among open string tree amplitudes with different orderings of the vertex operators. In this Letter, we show how these intrinsically stringy relations emerge in low-energy effective field theory from the assumptions of locality and the field theory Kleiss-Kuijf (KK) and Bern-Carrasco-Johansson (BCJ) relations. Specifically, we study the bi-adjoint scalar model effective field theory (BAS EFT). We impose the field theory KK and BCJ relations on one of the two color-orderings of the BAS EFT amplitudes and show that the second color-ordering has an emergent set of linear relations that, as checked at 4-point to 36-derivative order, are exactly the monodromy relations. The 4-point results depend on a delicate interplay between consistent factorization of 6-point BAS EFT amplitudes and the 6-point KK BCJ conditions. As a consequence of the analysis, the 4-point Z-theory tree amplitudes are bootstrapped up to a symmetric function in $s,t,u$ whose simple exponentiated form has free parameters that capture all the odd zeta values when matched to Z-theory.

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arXiv2022

On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators

The AdS boundary correlators and their dual correlation functions of boundary operators have been the main dynamic observables of the holographic duality relating a bulk AdS theory and a boundary conformal field theory. We show that tree-level AdS boundary correlators for generic states can be expressed as nonlocal differential operators of a certain structure acting on contact Witten diagrams. We further write the boundary correlators in a form that is very similar to flat space amplitudes, with Mandelstam variables replaced by certain combinations of single-state conformal generators, prove that all tree-level AdS boundary correlators have a differential representation, and detail the conversion of such differential expressions to position space. We illustrate the construction through the computation of the boundary correlators of scalars coupled to gluons and gravitons; when converted to position space, they reproduce known results. Color-kinematics duality and BCJ relations can be defined in analogy with their flat space counterparts, and are respected by the scalar correlators with a gluon exchange. We also discuss potential approaches to the double copy and find that its direct generalization may require nontrivial extensions.

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arXiv2021

A New Framework for Higher Loop Witten Diagrams

The differential representation is a novel formalism for studying boundary correlators in $(d+1)$-dimensional anti-de Sitter space. In this letter, we generalize the differential representation beyond tree level using the notion of operator-valued integrals. We use the differential representation to compute three-point bubble and triangle Witten diagrams with external states of conformal dimension $Δ=d$. We compare the former to a position space computation.

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arXiv2021

BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space

We generalize the color/kinematics duality of flat-space scattering amplitudes to the embedding space formulation of AdS boundary correlators. Kinematic numerators and propagators are replaced with differential operators acting on a scalar contact diagram that is the AdS generalization of the momentum conserving delta function of flat space scattering amplitudes. We show that color/kinematics duality implies differential relations among AdS boundary correlators that naturally generalize the flat space BCJ amplitude relations and verify them for the correlators of Yang-Mills theory and of the Nonlinear Sigma Model through four- and six-points, respectively. For the latter we also find representations of the four- and six-point correlator that manifest the duality. Possible double-copy procedures in AdS space are also discussed.

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arXiv2021

Algebraic branch points at all loop orders from positive kinematics and wall crossing

There is a remarkable connection between the boundary structure of the positive kinematic region and branch points of integrated amplitudes in planar $\mathcal{N}=4$ SYM. A long standing question has been precisely how algebraic branch points emerge from this picture. We use wall crossing and scattering diagrams to systematically study the boundary structure of the positive kinematic regions associated with MHV amplitudes. The notion of asymptotic chambers in the scattering diagram naturally explains the appearance of algebraic branch points. Furthermore, the scattering diagram construction also motivates a new coordinate system for kinematic space that rationalizes the relations between algebraic letters in the symbol alphabet. As a direct application, we conjecture a complete list of all algebraic letters that could appear in the symbol alphabet of the 8-point MHV amplitude.

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arXiv2021

Generalizations of the Double-Copy: the KLT Bootstrap

We formulate a new program to generalize the double-copy of tree amplitudes. The approach exploits the link between the identity element of the KLT algebra and the KLT kernel, and we demonstrate how this leads to a set of KLT bootstrap equations that the double-copy kernel has to satisfy (in addition to locality constraints). We solve the KLT bootstrap equations perturbatively to find the most general higher-derivative corrections to the 4- and 5-point field theory KLT kernel. The new kernel generalizes the string KLT kernel and its associated monodromy relations. It admits new color-structures in the effective theories it double-copies. It provides distinct generalized KK and BCJ relations for the left and right single-color theories and is in that sense a heterotic-type double-copy. We illustrate the generalized double-copy in detail for 4d Yang-Mills theory with higher-derivative corrections that produce dilaton-axion-gravity with local operators up order $\nabla^{10} R^4$. Finally, we initiate a search for new double-copy kernels.

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arXiv2020

Open associahedra and scattering forms

We continue the study of open associahedra associated with bi-color scattering amplitudes initiated in arXiv:1912.08307. We focus on the facet geometries of the open associahedra, uncovering many new phenomena such as fiber-product geometries. We then provide novel recursion procedures for calculating the canonical form of open associahedra, generalizing recursion relations for bounded polytopes to unbounded polytopes.

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arXiv2020

On Positive Geometry and Scattering Forms for Matter Particles

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 supplements the bi-adjoint theory with scalars in the (anti-)fundamental representations of both groups. Using a recursive construction we obtain a class of unbounded polytopes called open associahedra (or associahedra with certain facets at infinity) whose canonical form computes amplitudes in bi-color theory, for arbitrary number of legs and flavor assignments. In addition, we discuss the duality between color factors and wedge products, or "color is kinematics", for amplitudes with matter particles as well.

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arXiv2019

Massive On-Shell Supersymmetric Scattering Amplitudes

We introduce a manifestly little group covariant on-shell superspace for massive particles in four dimensions using the massive spinor helicity formalism. This enables us to construct massive on-shell superfields and fully utilize on-shell symmetry considerations to derive all possible $\mathcal{N}=1$ three-particle amplitudes for particles of spin as high as one, as well as some simple amplitudes for particles of any spin. Throughout, the conceptual and computational simplicity of this approach is exhibited.

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arXiv2019

Constructing $\mathcal{N}=4$ Coulomb Branch Superamplitudes

We study scattering amplitudes of massive BPS states on the Coulomb branch of $4d$ $\mathcal{N}=4$ super-Yang-Mills, utilising a little group covariant on-shell superspace for massive particles. Super-BCFW recursion for massive amplitudes is constructed and its validity is proven for all Coulomb branch superamplitudes. We then determine the exact three-particle superamplitudes for massive states. These ingredients allow us to explicitly compute the four- and five-particle superamplitudes, which is the first non-trivial usage of BCFW recursion for amplitudes with entirely massive external states. The manifest little group covariance helps clarify both the role of special kinematic properties of BPS states and the organizational structures of the superamplitudes.

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