On the null origin of the ambitwistor string

In this paper we present the null string origin of the ambitwistor string. Classically, the null string is the tensionless limit of string theory, and so too is the Ambitwistor string. Both have as constraint algebra the Galilean Conformal Algebra in two dimensions. But something interesting happens in the quantum theory since there is an ambiguity in quantizing the null string. We show that, given a particular choice of quantization scheme and a particular gauge, the null string coincides with the ambitwistor string both classically and quantum mechanically. We also show that the same holds for the spinning versions of the null string and Ambitwistor string. With these results we clarify the relationship between the Ambitwistor string, the null string, the usual string and the Hohm-Siegel-Zwiebach theory.Comment: 22 pages, 1 figur

Windings of twisted strings

Twistor string models have been known for more than a decade now but have come back under the spotlight recently with the advent of the scattering equation formalism which has greatly generalized the scope of these models. A striking ubiquitous feature of these models has always been that, contrary to usual string theory, they do not admit vibrational modes and thus describe only conventional field theory. In this paper we report on the surprising discovery of a whole new sector of one of these theories which we call "twisted strings," when spacetime has compact directions. We find that the spectrum is enhanced from a finite number of states to an infinite number of interacting higher spin massive states. We describe both bosonic and world sheet supersymmetric models, their spectra and scattering amplitudes. These models have distinctive features of both string and field theory, for example they are invariant under stringy T-duality but have the high energy behavior typical of field theory. Therefore they describe a new kind of field theories in target space, sitting on their own halfway between string and field theory.Comment: 6 pages. v2 : a few clarifications and references added. v3 : published PRD versio

Infrared behaviour of the one-loop scattering equations and supergravity integrands

The recently introduced ambitwistor string led to a striking proposal for one-loop maximal supergravity amplitudes, localised on the solutions of the ambitwistor one-loop scattering equations. However, these amplitudes have not yet been explicitly analysed due to the apparent complexity of the equations that determine the localisation. In this paper we propose an analytic solution to the four-point one-loop scattering equations in the infrared (IR) regime of the amplitude. Using this solution, we compute the ambitwistor integrand and demonstrate that it correctly reproduces the four-graviton integrand, in the IR regime. This solution qualitatively extends to n points. To conclude, we explain that the ambitwistor one-loop scattering equations actually correspond to the standard Gross & Mende saddle point.Comment: 23 pages, 5 figure

Scattering Equations and String Theory Amplitudes

Scattering equations for tree-level amplitudes are viewed in the context of string theory. As a result of the comparison we are led to define a new dual model which coincides with string theory in both the small and large $\alpha'$ limit, and whose solution is found algebraically on the surface of solutions to the scattering equations. Because it has support only on the scattering equations, it can be solved exactly, yielding a simple resummed model for $\alpha'$-corrections to all orders. We use the same idea to generalize scattering equations to amplitudes with fermions and any mixture of scalars, gluons and fermions. In all cases checked we find exact agreement with known results.Comment: v2: 18 pp, 1 figure, added clarifications and comments. Version to be published in PR

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 algebra; we study its local and global action and gauge-fixing. We finish by presenting an operator formalism, that we use to compute tree-level scattering amplitudes based on the scattering equations and a one-loop partition function. These results hopefully will open the way to understand conceptual questions related to the loop expansion in these twistor-like string models

One-loop monodromy relations on single cuts

The discovery of colour-kinematic duality has led to significant progress in the computation of scattering amplitudes in quantum field theories. At tree level, the origin of the duality can be traced back to the monodromies of open-string amplitudes. This construction has recently been extended to all loop orders. In the present paper, we dissect some consequences of these new monodromy relations at one loop. We use single cuts in order to relate them to the tree-level relations. We show that there are new classes of kinematically independent single-cut amplitudes. Then we turn to the Feynman diagrammatics of the string-theory monodromy relations. We revisit the string-theoretic derivation and argue that some terms, that vanish upon integration in string and field theory, provide a characterisation of momentum-shifting ambiguities in these representations. We observe that colour-dual representations are compatible with this analysis

Loop Integrands for Scattering Amplitudes from the Riemann Sphere

The scattering equations on the Riemann sphere give rise to remarkable formulae for tree-level gauge theory and gravity amplitudes. Adamo, Casali and Skinner conjectured a one-loop formula for supergravity amplitudes based on scattering equations on a torus. We use a residue theorem to transform this into a formula on the Riemann sphere. What emerges is a framework for loop integrands on the Riemann sphere that promises to have wide application, based on off-shell scattering equations that depend on the loop momentum. We present new formulae, checked explicitly at low points, for supergravity and super-Yang-Mills amplitudes and for n-gon integrands at one loop. Finally, we show that the off-shell scattering equations naturally extend to arbitrary loop order, and we give a proposal for the all-loop integrands for supergravity and planar super-Yang-Mills theory.Comment: 5 pages, 1 figure. v3: published versio

Tropical Amplitudes

In this work, we argue that the α′→0 limit of closed string theory scattering amplitudes is a tropical limit. The motivation is to develop a technology to systematize the extraction of Feynman graphs from string theory amplitudes at higher genus. An important technical input from tropical geometry is the use of tropical theta functions with characteristics to rigorously derive the worldline limit of the worldsheet propagator. This enables us to perform a non-trivial computation at two loops: we derive the tropical form of the integrand of the genus-two four-graviton type II string amplitude, which matches the direct field theory computations. At the mathematical level, this limit is an implementation of the correspondence between the moduli space of Riemann surfaces and the tropical moduli space.This research is supported by the Agence Nationale de la Recherche Grant 12-BS05-003-01, from the European Research Council Advanced Grant No. 247252 and from the Centre National de la Recherche Scientifique Grant Projet International de Collaboration Scientifique 6076

An R^4 non-renormalisation theorem in N=4 supergravity

We consider the four-graviton amplitudes in CHL constructions providing four-dimensional N=4 models with various numbers of vector multiplets. We show that in these models the two-loop amplitude has a prefactor of d^2R^4. This implies a non-renormalisation theorem for the R^4 term, which forbids the appearance of a three-loop ultraviolet divergence in four dimensions in the four-graviton amplitude. We connect the special nature of the R^4 term to the U(1) anomaly of pure N=4 supergravity.Comment: v2: added comments about one-loop UV divergences. Assorted stylistic corrections. Added references. v3: Eq. III.21 corrected and assorted minor corrections and clarifications. Version to be published. v4: minor corrections. 18 pages. one figur

Two-loop scattering amplitudes from the Riemann sphere

Financial support from EPSRC Grant No. EP/K032208/1 during the program GTA 2016. Y. G. is supported by the EPSRC Doctoral Prize Scheme EP/M508111/1, LJM by the EPSRC Grant No. EP/M018911/1, and the work of P. T. is supported by STFC Grant No. ST/L000385/1