Ambitwistor strings and the scattering equations at one loop

Abstract

Ambitwistor strings are chiral, infinite tension analogues of conventional string theory whose target space is the space of complex null geodesics and whose spectrum consists exclusively of massless states. At genus zero, these strings underpin the CachazoHe-Yuan formulae for tree level scattering of gravitons, gluons and scalars. In this paper we extend these formulae in a number of directions. Firstly, we consider Ramond sector vertex operators and construct simple amplitudes involving space-time fermions. These agree with tree amplitudes in ten dimensional supergravity and super Yang-Mills. We then show that, after the usual GSO projections, the ambitwistor string partition function is modular invariant. We consider the scattering equations at genus one, and calculate one loop scattering amplitudes for NS-NS external states in the Type II ambitwistor string. We conjecture that these give new representations of (the integrand of) one loop supergravity amplitudes and we show that they have the expected behaviour under factorization of the worldsheet in both non-separating and separating degenerations.

New ambitwistor string theories

“…Another issue is as to whether there are any further vertex operators in the theories and if so, we can hope to extend the theory to include additional fields and calculate the corresponding amplitudes. This in particular happens in theories containing worldsheet supersymmetry S Ψ and leads to supersymmetric extensions of the theories and amplitudes as described also in [12]. We will find a number of new critical theories and give a brief discussion of these issues in the conclusions section.…”

“…For example, if they are critical and anomaly free, then one can attempt to calculate loop amplitudes by taking the correlation functions on higher genus Riemann surfaces as described in [12]. For this to work at 1-loop, we must check modularity.…”

“…They give the physical theory underlying these formulae and lead to new extensions. For example, in the case of the critical type II gravity model in 10 dimensions, the ambitwistor model leads to proposals for how the formulae might be extended to loop amplitudes [12][13][14]. They also give new insights into the relationship [15,16] between asymptotic symmetries and soft theorems [17][18][19][20].…”

On soft theorems and form factors in N = 4 $$ \mathcal{N}=4 $$ SYM theory

“…and is also interesting in connection with different twistor string theories formulations proposed recently [43][44][45][46][47]. Besides, it allows study of scattering amplitudes with the use of powerful tools from combinatorics and algebraic geometry [40].…”

Sudakov representation of the Cachazo-He-Yuan scattering equations formalism

“…The CHY proposal for the calculation of tree-level scattering amplitudes has an interpretation in terms of ambitwistor strings [9][10][11][12][13] defined on a Riemann surface at genus zero. At loop level, supergravity integrands of four-point amplitudes at one and two loops have been obtained when introducing higher genus [11,[14][15][16]. Other connections to string theory amplitudes can be found in, for example, [17][18][19].…”