Ambitwistor strings and reggeon amplitudes in N=4 SYM

A Gluing Operator for the Ambitwistor String

We present a new operator in the ambitwistor string which glues together correlators with fewer points or of lower genus. It underpins the recursive construction of tree-level CHY scattering amplitudes by Dolan \& Goddard, as well as the computation of loop integrands on a Riemann sphere by Geyer et al. The gluing operator is a tractable object due to the finiteness of the spectrum. In particular, we demonstrate how it gives rise to the complete one-loop integrand in SYM and SUGRA. The operator is conjectured to be the path integral incarnation of the ambitwistor string propagator, and to coin…

Ambitwistor formulations of $R^2$ gravity and $(DF)^2$ gauge theories

We consider $D$-dimensional amplitudes in $R^2$ gravities (conformal gravity in $D=4$) and in the recently introduced $(DF)^2$ gauge theory, from the perspective of the CHY formulae and ambitwistor string theory. These theories are related through the BCJ double-copy construction, and the $(DF)^2$ gauge theory obeys color-kinematics duality. We work out the worldsheet details of these theories and show that they admit a formulation as integrals on the support of the scattering equations, or alternatively, as ambitwistor string theories. For gravity, this generalizes the work done by Berkovits …

Ambitwistor Strings: Worldsheet Approaches to perturbative Quantum Field Theories

Tree-level scattering amplitudes in massless theories not only exhibit a simplicity entirely unexpected from Feynman diagrams, but also an underlying structure remarkably reminiscent of worldsheet theory correlators. These features can be explained by ambitwistor strings - two-dimensional chiral conformal field theories in an auxiliary target space, the complexified phase space of null geodesics. The aim of this thesis is to explore the ambitwistor string approach to understand these structures in amplitudes, and thereby provide a new angle on quantum field theories. The first part of the thes…

A Note on Circle Compactification of Tensile Ambitwistor String

We discuss a number of problems associated with the circle compactification of the bosonic tensile ambitwistor string with the asymmetric vacuum choice. By considering the spectrum and physical state conditions, we show that the circle radius plays a role as a tuning parameter which determines the low energy effective field theory. At the self dual point, we construct the current operators and compute OPEs between them. While the final outcome remains as yet inconclusive, several new results are obtained. Through the current algebra analysis we show that there is a subsector of the massless st…

The complex null string, Galilean conformal algebra and scattering equations

The scattering equation formalism for scattering amplitudes, and its stringy incarnation, the ambitwistor string, remains a mysterious construction. In this paper, we pursue the study a gauged-unfixed version of the ambitwistor string known as the null string. We explore the following three aspects in detail; its complexification, gauge fixing, and amplitudes. We first study the complexification of the string; the associated symmetries and moduli, and connection to the ambitwistor string. We then look in more details at the leftover symmetry algebra of the string, called Galilean conformal alg…

最大超对称杨-米尔斯理论（$\boldsymbol{\textit{N}=4}$ SYM）中领头对数精度下的三雷吉子交换

Three-Reggeon exchange in $\mathcal{N}=4$ SYM to leading logarithmic accuracy

本文在$\boldsymbol{\textit{N}=4}$ SYM理论框架下，采用有效场论方法，结合双、三雷吉子交换贡献，得到了MRK中八边形振幅的微扰结果，可扩展至多粒子情形。

Massive ambitwistor-strings; twistorial models

Ambitwistor-strings are chiral strings whose targets are spaces of complex massless particles, and whose correlation functions directly lead to simple, compact formulae for scattering amplitudes and loop integrands for massless gauge and gravity theories. This article extends this framework to worldsheet models for massive particles in 4d, obtained via a symmetry reduction of a higher dimensional massless model. The target space of the resulting models turns out to be the phase space of 4d massive particles in a twistorial representation, and so the worldsheet theory agrees with the two-twisto…

Celestial amplitudes and conformal soft theorems

Scattering amplitudes in $d+2$ dimensions can be expressed in terms of a conformal basis, for which the S-matrix behaves as a CFT correlation function on the celestial $d$-sphere. We explain how compact expressions for the full tree-level S-matrix of gauge theory, gravity and other QFTs extend to this conformal basis, and are easily derived from ambitwistor strings. Using these formulae and their worldsheet origins, we prove various tree-level 'conformal soft theorems' in gauge theory and gravity in any dimension; these arise from limits where the scaling dimension of an external state in the …

Green-Schwarz and Pure Spinor Formulations of Chiral Strings

Bosonic and RNS chiral strings have been defined from a singular gauge fixing of the respective Polyakov and spinning string actions, enforcing, among other things, the finite nature of their physical spectra. Except for the heterotic case, the tensionless limits of such chiral models have been shown to describe the same field theories predicted by their ambitwistor analogues. In this paper, we study the Green-Schwarz formulation for Type II and heterotic superstrings in a singular gauge. After performing a light-cone gauge analysis, their physical spectra are shown to match those of RNS chira…

QCD中的双圈Lipatov顶点

The Two-Loop Lipatov Vertex in QCD

本文将QCD高能因子化框架从2到2扩展到2到3过程，通过计算多Reggeon交换并从非平面双圈QCD振幅中匹配，首次确定了维度正规化下双圈Lipatov顶点，并以单值广义多重对数函数基给出紧凑解析结果。

Analytic structure of the 8-point scattering amplitude in multi-Regge kinematics in N=4 SYM: conformal Regge pole and Regge cut contributions

Continuing our investigations of the analytic structure of the 2->n scattering amplitudes in the planar limit of N=4 SYM in multi-Regge kinematics we compute, in all kinematic regions, the Regge cut contributions of the 2->6 process in leading order. Compared to previous studies of the 2->4 and the 2->5 processes we encounter two new features: the 3-reggon cut and the product of two 2-reggeon cut contributions.

A Superstring Field Theory for Supergravity

A covariant closed superstring field theory, equivalent to classical ten-dimensional Type II supergravity, is presented. The defining conformal field theory is the ambitwistor string worldsheet theory of Mason and Skinner. This theory is known to reproduce the scattering amplitudes of Cachazo, He and Yuan in which the scattering equations play an important role and the string field theory naturally incorporates these results. We investigate the operator formalism description of the ambitwsitor string and propose an action for the string field theory of the bosonic and supersymmetric theories. …

Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space

We discuss multiloop MHV amplitudes in the N=4 SYM theory in terms of effective gravity in the momentum space with IR regulator branes as degrees of freedom. Kinematical invariants of external particles yield the moduli spaces of complex or Kahler structures which are the playgrounds for the Kodaira-Spencer(KS) or Kahler type gravity. We suggest fermionic representation of the loop MHV amplitudes in the N=4 SYM theory assuming the identification of the IR regulator branes with KS fermions in the B model and Lagrangian branes in A model. The two-easy mass box diagram is related to the correlato…