Nikhil Kalyanapuram
It is established that in the tensionless limit the chiral superstring integrand is reduced to the chiral integrand of the ambitwistor string.
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Scattering amplitudes computed by superstring perturbation theory are known to holomorphically split into chiral half integrands at fixed internal loop momentum. It is established by direct computation that upon reduction to the ordinary moduli space, the chiral half integrands of the superstring match those computed by the ambitwistor string in the limit of zero tension ($α'\rightarrow\infty$). Subtleties that arise at higher genus due to the nonprojectedness of the supermoduli space are considered and arguments as to their resolution are furnished.
Infrared behaviour of the one-loop scattering equations and supergravity integrands
最近推出的ambitwistor字符串导致了一个惊人的建议单圈最大超重力振幅，本地化的解决方案的ambitwistor单圈散射方程。然而，由于确定局部化的方程的明显复杂性，这些振幅尚未被明确分析。本文给出了振幅在红外波段的四点单圈散射方程的解析解。使用这个解决方案，我们计算的ambitwistor积分，并证明它正确地再现四引力子积分，在IR制度。该解定性地扩展到n个点。最后，我们解释了ambitwistor单圈散射方程实际上对应于标准的格罗斯和门德鞍点。
A Gluing Operator for the Ambitwistor String
我们提出了一个新的算子的ambitwistor字符串，粘在一起的更少的点或较低的亏格的分配器。它是Dolan \& Goddard递归构造树级CHY散射振幅以及Geyer等人计算黎曼球面上的圈被积的基础。由于谱的有限性，胶合算子是一个易于处理的对象。特别是，我们演示了它如何产生完整的一个循环被积函数SYM和SUGRA。该算子被证明是ambitwistor弦传播子的路径积分的化身，并与标准弦论传播子的场论极限相一致。
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…
We present new and explicit formulae for the one-loop integrands of scattering amplitudes in non-supersymmetric gauge theory and gravity, valid for any number of particles. The results exhibit the colour-kinematics duality in gauge theory and the double-copy relation to gravity, in a form that was recently observed in supersymmetric theories. The new formulae are expressed in a particular representation of the loop integrand, with only one quadratic propagator, which arises naturally from the framework of the loop-level scattering equations. The starting point in our work are the expressions b…
Twistor/ambitwistor strings and null-superstrings in spacetime of D=4,10 and 11 dimensions
我们表明，在经典的水平上，最近提出的“ambitwistor字符串”模型是等价的旋量移动框架制定的零supersting，这反过来又相当于西格尔的制定封闭扭弦或其高维推广。虽然空弦通常被认为是描述了超弦的无张力极限，但我们证明了在无限张力极限下，它的作用量也可以由超弦的旋量移动标架公式导出.这一观察结果使我们能够对临界尺寸的缺乏进行争论，并表明计算场论振幅的基于（双）扭率弦的技术不仅可以在D=10或26中发展，而且可以在D=11和其他维度中发展。详细描述了D=11和D=10扭振串。
In the low-energy effective action of string theories, non-abelian gauge interactions and supergravity are augmented by infinite towers of higher-mass-dimension operators. We propose a new method to construct one-loop matrix elements with insertions of operators $D^{2k} F^n$ and $D^{2k} R^n$ in the tree-level effective action of type-I and type-II superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of moduli-space integrals using string tree-level amplitudes with two extra points, expanded in powers of the inverse string tension $α'$. Similar to one-loo…
We propose a procedure to determine the moduli-space integrands of loop-level superstring amplitudes for massless external states in terms of the field theory limit. We focus on the type II superstring. The procedure is to: (i) take a supergravity loop integrand written in a BCJ double-copy representation, (ii) use the loop-level scattering equations to translate that integrand into the ambitwistor string moduli-space integrand, localised on the nodal Riemann sphere, and (iii) uplift that formula to one on the higher-genus surface valid for the superstring, guided by modular invariance. We sho…
We propose new formulae for the two-loop n-point D-dimensional integrands of scattering amplitudes in Yang-Mills theory and gravity. The loop integrands are written as a double-forward limit of tree-level trivalent diagrams, and are inferred from the formalism of the two-loop scattering equations. We discuss the relationship between the formulae for non-supersymmetric theories and the Neveu-Schwarz sector of the formulae for maximally supersymmetric theories, which can be derived from ambitwistor strings. An important property of the loop integrands is that they are expressed in a representati…
In this paper, we develop a rather general way to reduce integrands with polarization involved in the Cachazo-He-Yuan formulae, such as the reduced Pfaffian, its compactiffcation and its squeezing, as well as the new object for F^3 amplitude. We prove that the reduced Pfaffian vanishes unless evaluated on a certain set of solutions. It leads us to build up the 4d CHY formulae using spinors, which strains off many useless solutions. The supersymmetrization is straightforward and may provide a hint to understand ambitwistor string in 4d.
We investigate massless n-point one-loop amplitudes of the open RNS superstring with two external fermions and determine their worldsheet integrands. The contributing correlation functions involving spin-1/2 and spin-3/2 operators from the fermion vertices are evaluated to any multiplicity. Moreover, we introduce techniques to sum these correlators over the spin structures of the worldsheet fermions such as to manifest all cancellations due to spacetime supersymmetry. These spin sums require generalizations of the Riemann identities among Jacobi theta functions, and the results can be expresse…
A chiral string can be seen as an ordinary string in a singular gauge for the worldsheet metric and has the ambitwistor string as its tensionless limit. As proposed by Siegel, there is a one-parameter ($β$) gauge family interpolating between the chiral limit and the usual conformal gauge in string theory. This idea was used to compute scattering amplitudes of tensile chiral strings, which are given by standard string amplitudes with modified ($β$-dependent) antiholomorphic propagators. Due to the absence of a sensible definition of the integrated vertex operator, there is still no ordinary pre…
Worldsheet Formalism for Decoupling Limits in String Theory
研究IIA超弦理论脱耦极限中的玻色子部分，揭示D0膜的动力学与BFSS矩阵理论的关系，并发展了基本弦的膜形式主义，探讨了T对称性变换与脱耦极限的统一。
On Type 0 Open String Amplitudes and the Tensionless Limit
平坦时空中0型开弦NS+扇区的平面多圈图求和是Thorn提出的解决规范理论在大$N$极限下的非微扰问题的一个候选方法。利用$SU (N)$ Chan-Paton因子，平面开弦多圈图上的和描述了$Ng_s^2$保持不变的t Hooft极限$N\to \infty$。通过在求和中只包括平面图，通常用于消除圈发散的机制（例如，通过选择特定的规范群，在平面图和莫比乌斯带图之间发生）是不可用的，并且需要重整化过程。在这篇文章中，重整化是通过在模上积分的被积函数的水平上将总动量守恒暂停一个量$p\equiv \sum_i^n k_i\neq 0$，并在最后将它们解析地延续到$p=0$来实现的。这个过程已成功地测试了2和3胶子平面环振幅的Thorn。考虑了规范不变性，得到了耦合在极限规范场理论中的正确运行。在这篇文章中，我们在两个方向上扩展这些结果。首先，我们将重整化方法推广到任意的$n$ -胶子平面环振幅，给出了4点情形的全部细节。我们的主要结果之一是提供一个完全重整化的振幅，这是免费的UV和通常的虚假的分歧，只留下物理奇点在它。第二，使用完整的重整化振幅，我们提取的高能散射制度在固定的角度（无张力限制）。除了在高能量下获得通常的指数衰减，我们计算的散射角的充分依赖性，这表明存在一个光滑的连接之间的Regge和硬散射制度。
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