String correlators: recursive expansion, integration-by-parts and scattering equations

Abstract

We further elaborate on the general construction proposed in [1], which connects, via tree-level double copy, massless string amplitudes with color-ordered QFT amplitudes that are given by Cachazo-He-Yuan formulas. The current paper serves as a detailed study of the integration-by-parts procedure for any tree-level massless string correlator outlined in the previous letter. We present two new results in the context of heterotic and (compactified) bosonic string theories. First, we find a new recursive expansion of any multitrace mixed correlator in these theories into a logarithmic part corresponding to the CHY integrand for Yang-Mills-scalar amplitudes, plus correlators with the total number of traces and gluons decreased. By iterating the expansion, we systematically reduce string correlators with any number of subcycles to linear combinations of Parke-Taylor factors and similarly for the case with gluons. Based on this, we then derive a CHY formula for the corresponding (DF ) 2 + YM + φ 3 amplitudes. It is the first closed-form result for such multitrace amplitudes and thus greatly extends our result for the single-trace case. As a byproduct, it gives a new CHY formula for all Yang-Mills-scalar amplitudes. We also study consistency checks of the formula such as factorizations on massless poles.

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

“…Relatedly, it may be worth to find the analog of polytope in [6] and those in [42]. Besides, one can also study α ′ expansion of Grassmannian string integrals or even the structure at finite α ′ , such as the recurrence relation [1] and integration-by-parts reduction as in [43,44] for k = 2.…”

Bosonic sectorized strings and the (DF)2 theory

“…Theories whose Lagrangians include a (DF ) 2 -type kinetic term were first introduced as a way of obtaining conformal (super)gravity amplitudes from color-kinematics duality [18], and were shown to admit CHY/ambitwistor representations in [19]. More recently, amplitudes of (DF ) 2 theories have been found to play a crucial role in the double-copy construction of (ordinary) bosonic and heterotic string tree-level amplitudes [20] -see also [21,22]. This paper is organized as follows.…”

Efficient calculation of crossing symmetric BCJ tree numerators

“…The formalism explicitly constructs tree amplitudes from the product of two half-integrands. There is now a well-developed program for exploring the types of objects needed in each half-integrand to generate theories of interest [27][28][29][30][31][32][33][34], which can be derived from world-sheet models based on ambitwistor strings [35][36][37][38][39] and their deformation [40,41]. The half-integrands are known to be expressible completely in Del Duca-Dixon-Maltoni half-ladder basis [42] on the support of scattering equations [26], 1…”