arXiv subjects

Lecheng Ren

Publications and source records attributed to Lecheng Ren.

23 records · Page 2Linked to original sources

arXiv2022

On Effective Field Theories with Celestial Duals

We show that associativity of the tree-level OPE in a celestial CFT imposes constraints on the coupling constants of the corresponding bulk theory. These constraints are the same as those derived in arXiv:2111.11356 from the Jacobi identity of the algebra of soft modes. The constrained theories are interesting as apparently well-defined celestial CFTs with a deformed $w_{1+\infty}$ symmetry algebra. We explicitly work out the ramifications of these constraints on scattering amplitudes involving gluons, gravitons and scalars in these theories. We find that all four-point amplitudes constructible solely from holomorphic or anti-holomorphic three-point amplitudes vanish on the support of these constraints, which implies that all purely holomorphic or purely anti-holomorphic higher-point amplitudes vanish.

hep-th↗

arXiv2022

Loop-level gluon OPEs in celestial holography

We compute one-loop corrections to the OPE of gluons in the celestial conformal field theory corresponding to Yang-Mills coupled to arbitrary matter. We exploit universal hard/soft factorization to derive an IR finite OPE for the hard gluon operators. This OPE involves logarithms and operators that resemble logarithmic partners of primary operators. We derive an exact all-loop OPE in a limit of the Higgs-regulated planar $\mathcal{N}=4$ super Yang-Mills theory.

hep-th↗

arXiv2021

Symbol Alphabets from Tensor Diagrams

We propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of $n$-particle amplitudes in planar $\mathcal{N}=4$ Yang-Mills theory and certain polytopes associated to the Grassmannian G(4, $n$). We show how to assign a web (a planar tensor diagram) to each facet of these polytopes. Webs with no inner loops are associated to cluster variables (rational symbol letters). For webs with a single inner loop we propose and explicitly evaluate an associated web series that contains information about algebraic symbol letters. In this manner we reproduce the results of previous analyses of $n \le 8$, and find that the polytope $\mathcal{C}^\dagger(4,9)$ encodes all rational letters, and all square roots of the algebraic letters, of known nine-particle amplitudes.

hep-th↗

arXiv2021

Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals

We continue the study of positive geometries underlying the {\it Grassmannian string integrals}, which are a class of "stringy canonical forms", or stringy integrals, over the positive Grassmannian mod torus action, $G_+(k,n)/T$. The leading order of any such stringy integral is given by the canonical function of a polytope, which can be obtained using the Minkowski sum of the Newton polytopes for the regulators of the integral, or equivalently given by the so-called scattering-equation map. The canonical function of the polytopes for Grassmannian string integrals, or the volume of their dual polytopes, is also known as the generalized bi-adjoint $ϕ^3$ amplitudes. We compute all the linear functions for the facets which cut out the polytope for all cases up to $n=9$, with up to k=4 and their parity conjugate cases. The main novelty of our computation is that we present these facets in a manifestly gauge-invariant and cyclic way, and identify the boundary configurations of $G_+(k,n)/T$ corresponding to these facets, which have nice geometric interpretations in terms of $n$ points in $(k{-}1)$-dimensional space. All the facets and configurations we discovered up to $n=9$ directly generalize to all $n$, although new types are still needed for higher $n$.

hep-th↗

arXiv2021

Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations

Celestial and momentum space amplitudes for massless particles are related to each other by a change of basis provided by the Mellin transform. Therefore properties of celestial amplitudes have counterparts in momentum space amplitudes and vice versa. In this paper, we study the celestial avatar of dual superconformal symmetry of $\mathcal{N}=4$ Yang-Mills theory. We also analyze various differential equations known to be satisfied by celestial $n$-point tree-level MHV amplitudes and identify their momentum space origins.

hep-th↗