Related papers: Weighted Laplacians, cocycles and recursion relati…
We prove universal (case-free) formulas for the weighted enumeration of factorizations of Coxeter elements into products of reflections valid in any well-generated reflection group $W$, in terms of the spectrum of an associated operator,…
In this paper we study tree-level amplitudes from higher-dimensional operators, including $F^3$ operator of gauge theory, and $R^2$, $R^3$ operators of gravity, in the Cachazo-He-Yuan formulation. As a generalization of the reduced Pfaffian…
A mixed graph $M_{G}$ is the graph obtained from an unoriented simple graph $G$ by giving directions to some edges of $G$, where $G$ is often called the underlying graph of $M_{G}$. In this paper, we introduce two classes of incidence…
Motivated by recent progress in calculating field theory amplitudes, we study applications of the basic ideas in these developments to the calculation of amplitudes in string theory. We consider in particular both non-Abelian and Abelian…
We establish explicit operator norm bounds and essential self-adjointness criteria for discrete Hodge Laplacians on weighted graphs and simplicial complexes. For unweighted $d$-regular graphs we prove the universal estimate…
We demonstrate that all tree-level string theory amplitudes can be computed using the BCFW recursion relations. Our proof utilizes the pomeron vertex operator introduced by Brower, Polchinski, Strassler, and Tan. Surprisingly, we find that…
We present a new formulation of the loop-tree duality theorem for higher loop diagrams valid both for massless and massive cases. $l$-loop integrals are expressed as weighted sum of trees obtained from cutting $l$ internal propagators of…
We study the soft limit of a recently proposed generalization of the biadjoint scalar amplitudes $m^{(k)}_{n}$, which have been conjectured to have a relation to the tropical Grassmannian $\text{Tr G}(k,n)$. Using the CHY formulation along…
We derive compact analytical formulae for all tree-level color-ordered gauge theory amplitudes involving any number of external gluons and up to three massless quark-anti-quark pairs. A general formula is presented based on the…
We extract cubic interactions from the covariant equations of motion of Chiral Higher Spin Gravity and compute the corresponding amplitudes. These amplitudes are found to agree with earlier results obtained in the light-cone gauge. We also…
We present new recursion relations for tree amplitudes in gauge theory that give very compact formulas. Our relations give any tree amplitude as a sum over terms constructed from products of two amplitudes of fewer particles multiplied by a…
We define a graph Laplacian with vertex weights in addition to the more classical edge weights, which unifies the combinatorial Laplacian and the normalised Laplacian. Moreover, we give a combinatorial interpretation for the coefficients of…
We examine the variational and conformal structures of higher order theories of gravity which are derived from a metric-connection Lagrangian that is an arbitrary function of the curvature invariants. We show that the constrained first…
We present new short proofs of known spanning tree enumeration formulae for threshold and Ferrers graphs by showing that the Laplacian matrices of such graphs admit triangular rank-one perturbations. We then characterize the set of graphs…
The Cachazo-Svrcek-Witten approach to perturbative gauge theory is extended to gauge theories with quarks and gluinos. All googly amplitudes with quark-antiquark pairs and gluinos are computed and shown to agree with the previously known…
The story of positive geometry of massless scalar theories was pioneered in [1] in the context of bi-adjoint $\phi^3$ theories. Further study proposed that the positive geometry for a generic massless scalar theory with polynomial…
We study n-point tree amplitudes of N=4 super Yang-Mills theory and N=8 supergravity for general configurations of external particles of the two theories. We construct generating functions for n-point MHV and NMHV amplitudes with general…
In this note we make a field-theoretical derivation of a series of new recursion relations by a one-parameter deformation of kinematic variables for tree and one-loop amplitudes of bi-adjoint $\phi^3$ theory. Tree amplitudes are given by…
The BCFW recursion relation allows to find out the tree-level scattering amplitudes for gluons and tensor gauge bosons in generalized Yang-Mills theory. We demonstrate that the corresponding MHV amplitudes for the tensor gauge bosons of…
In this talk, we review our recent work on direct evaluation of tree-level MHV amplitudes by Cachazo-He-Yuan (CHY) formula. We also investigate the correspondence between solutions to scattering equations and amplitudes in four dimensions…