Ambitwistor strings and the scattering equations at one loop (1312.3828v2)

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 Cachazo-He-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.

• The paper introduces Ramond sector vertex operators to compute fermionic amplitudes, bridging ambitwistor string theory with one-loop supergravity and super Yang-Mills methods.
• It verifies modular invariance at genus one through precise GSO projections, ensuring the chiral model retains essential symmetries of conventional string theories.
• The authors extend the scattering equations to genus one by imposing new residue constraints on the worldsheet, paving the way for streamlined one-loop amplitude calculations.

Ambitwistor Strings and One-Loop Scattering Equations

The paper "Ambitwistor Strings and the Scattering Equations at One Loop" by Adamo, Casali, and Skinner extends the theoretical framework of ambitwistor string theory, focusing on one-loop scattering amplitudes. Ambitwistor strings are chiral models of string theory with an infinite tension limit, prominently featuring the ambitwistor space—space composed of complex null geodesics.

The authors aim to bridge ambitwistor string theory with supergravity and super Yang-Mills amplitudes at one loop while preserving modular invariance. They introduce Ramond sector vertex operators, representing space-time fermions such as gravitinos and gauginos, thereby verifying the connection with supergravity and super Yang-Mills. Furthermore, they examine the ambitwistor string partition function under GSO projections, ascertain modular invariance, and extend scattering equations to genus one.

Key contributions are detailed as follows:

1. Ramond Sector Vertex Operators and Fermionic Amplitudes: By constructing vertex operators for fermionic states, the paper computes tree-level amplitudes, confirming consistency with known expressions in ten-dimensional supergravity and super Yang-Mills. This validation extends the ambitwistor string framework to accommodate fermionic states, traditionally encapsulated within supergravity theories.
2. Modular Invariance at Genus One: Through GSO projections, the paper confirms modular invariance of the ambitwistor string's one-loop partition function. This ensures that the ambitwistor string maintains vital symmetries inherent in string theories, despite its chiral nature.
3. Scattering Equations at Genus One: The transition of scattering equations to genus one involves imposing constraints both on the residues of field $P$ at vertex insertion points and on $P$ itself. These equations derive from integrating over the moduli space of elliptic curves, furthering the analogy to classic string theory while emphasizing differences in kinematic constraints.
4. Factorization and Consistency Checks: The paper examines factorization behavior under degenerations of the worldsheet, ensuring consistency with unitarity. It explicates the amplitude behavior in both separating and non-separating degeneration limits, pivotal in confirming the theory's coherence with field-theoretic expectations.
5. Pfa▯ans and Non-Elliptic Scattering Integrands: The Pfa▯ans that appear in scattering amplitude formulations align with the localization on solutions to genus one scattering equations. Intricate calculations ensure that these Pfa▯ans encapsulate the essence of gravitational amplitudes without resorting to higher string modes.

Theoretical implications are profound, as the ambitwistor string formalism bypasses standard massive string excitations, pointing to a pure supergravity spectrum in higher dimensions like in a ten-dimensional Type II supergravity context. Practically, this formulation redefines how one-loop supergravity amplitudes might be understood, potentially offering a computational framework devoid of the complexities intrinsic to conventional superstring theory.

Looking forward, elucidating the explicit solutions to these scattering equations—even at low multiplicity—could significantly simplify the connection between worldsheet formulations and loop integrals observed in classical field theory. Further refinement in this ambitwistor framework, particularly regarding fermionic amplitudes, may also exploit pure spinor methods, providing enhanced efficiency and clarity that align with manifest space-time supersymmetry.

In conclusion, the advancements in ambitwistor string theory fortify its position within the theoretical landscape, offering novel venues to explore the confluence of string theory and quantum field theory while yielding computational techniques applicable to advanced supergravity calculations.