From 4d ambitwistor strings to on shell diagrams and back

Self Cite

118

119

We consider the momentum-space 3-point correlators of currents, stress tensors and marginal scalar operators in general odd-dimensional conformal field theories. We show that the flat space limit of these correlators is spanned by gauge and gravitational scattering amplitudes in one higher dimension which are related by a double copy. Moreover, we recast three-dimensional CFT correlators in terms of tree-level Feynman diagrams without energy conservation, suggesting double copy structure beyond the flat space limit.

Section: Resultsmentioning

confidence: 57%

Double copy structure of CFT correlators

Farrow

Lipstein

McFadden

2019

Self Cite

118

119

“…One is the application of our results to infrared physics in gauge theory and gravity, where the scattering equations and ambitwistor strings have already proven to be fruitful [96] for describing the new soft theorems discovered in [97]. Another line of work is the study of the four-dimensional ambitwistor strings [51], whose loop-level development has been initiated in [98] but is still largely an open problem. It would be interesting to find explicit integrand formulae that can in principle be integrated, along the lines of our work.…”

Section: Discussionmentioning

confidence: 87%

Gluons and gravitons at one loop from ambitwistor strings

Geyer

Monteiro

2018

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 doublecopy 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 looplevel scattering equations. The starting point in our work are the expressions based on the scattering equations that were recently derived from ambitwistor string theory. We turn these expressions into explicit formulae depending only on the loop momentum, the external momenta and the external polarisations. These formulae are valid in any number of spacetime dimensions for pure Yang-Mills theory (gluon) and its natural double copy, NS-NS gravity (graviton, dilaton, B-field), and we also present formulae in four spacetime dimensions for pure gravity (graviton). We perform several tests of our results, such as checking gauge invariance and directly matching our four-particle formulae to previously known expressions. While these tests would be elaborate in a Feynman-type representation of the loop integrand, they become straightforward in the representation we use.

“…Let us first check explicitly that all terms of order q −1 1 , q −1 2 and q −1 1 q −1 2 cancel. 42 As a first check, this is easily verified for four external particles from the degeneration of the relations in appendix A. To generalise this cancellation to n points, we will rely on the relative signs in the partition functions and the Szegő kernels for the different spin structures.…”

Section: The Chiral Integrand On the Bi-nodal Riemann Spherementioning

confidence: 94%

Two-loop scattering amplitudes from ambitwistor strings: from genus two to the nodal Riemann sphere

Geyer

Monteiro

2018

111

We derive from ambitwistor strings new formulae for two-loop scattering amplitudes in supergravity and super-Yang-Mills theory, with any number of particles. We start by constructing a formula for the type II ambitwistor string amplitudes on a genus-two Riemann surface, and then study the localisation of the moduli space integration on a degenerate limit, where the genus-two surface turns into a Riemann sphere with two nodes. This leads to scattering amplitudes in supergravity, expressed in the formalism of the two-loop scattering equations. For super-Yang-Mills theory, we import 'half' of the supergravity result, and determine the colour dependence by considering a current algebra on the nodal Riemann sphere, thereby completely specifying the two-loop analogue of the Parke-Taylor factor, including non-planar contributions. We also present in appendices explicit expressions for the Szegő kernels and the partition functions for even spin structures, up to the relevant orders in the degeneration parameters, which may be useful for related investigations in conventional superstring theory. arXiv:1805.05344v3 [hep-th] 17 Dec 2018 6 The amplitude on the bi-nodal Riemann sphere 51 6.1 The measure on the bi-nodal Riemann sphere 52 6.2 The scattering equations on the bi-nodal Riemann sphere 53 6.3 The chiral integrand on the bi-nodal Riemann sphere 55 6.4 Absence of unphysical poles 58 7 Super-Yang-Mills amplitudes 62 7.1 Parke-Taylor factor on the bi-nodal Riemann sphere 62 7.2 Colour trace decomposition 64 8 Discussion 65 -i -A Useful identities 67 A.1 Identities involving the chiral partition function 67 A.2 Useful identities for the PCO gauge slice 68 B Modular transformations and M g,n 68C The separating degeneration q 12 = 0 and uniqueness of f (q 12 )