Ambitwistor superstring in the Green–Schwarz formulation

The European Physical Journal C, Jul 2017

In this paper we construct the ambitwistor superstring in the Green–Schwarz formulation. The model is obtained from the related pure spinor version. We show that the spectrum contains only ten-dimensional supergravity and that kappa symmetry in a curved background implies some of the standard constraints.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-017-5048-6.pdf

Ambitwistor superstring in the Green–Schwarz formulation

Eur. Phys. J. C Ambitwistor superstring in the Green-Schwarz formulation Osvaldo Chandía 1 Brenno Carlini Vallilo 0 0 Departamento de Ciencias Físicas, Universidad Andres Bello , Sazié 2212, Santiago , Chile 1 Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez , Diagonal Las Torres 2640, Peñalolén, Santiago , Chile In this paper we construct the ambitwistor superstring in the Green-Schwarz formulation. The model is obtained from the related pure spinor version. We show that the spectrum contains only ten-dimensional supergravity and that kappa symmetry in a curved background implies some of the standard constraints. Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . 2 Flat superspace formulation . . . . . . . . . . . . . 3 Relation to the pure spinor formalism . . . . . . . . 4 Light-cone gauge quantization and spectrum . . . . 5 Curved background . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction Perturbative superstring theory determines not only physical states but also their interactions. These include supergravity interactions, gauge interactions and a tower of very massive states in ten dimensions. The presence of this infinite set of states complicates calculations of scattering amplitudes but it also provides a control of the quantum aspects of the theory. One could eliminate the massive states in the limit α → 0. In this way, the spectrum obtained in perturbation quantization is the massless states only. The world-sheet description of these class of strings has been recently introduced in [ 1 ]. This new string can be seen as the α → 0 limit of the usual string. Note that they provide the scattering amplitudes proposed by Cachazo, He and Ye (CHY) [ 2–4 ] in gauge and gravity theories. A manifest space-time supersymmetric extension was constructed in [ 5 ] using the pure spinor formalism where the CHY scattering amplitudes were generalized to ten-dimensional superspace. Since supergravity theories are not exact quantum theories, it is expected that world-sheet loops contributions to scattering amplitudes should modify them. In our case, the modification should be done on type II supergravity. A one-loop analysis was done in [ 6 ] for the NS–NS part of the spectrum. It would be interesting to determine the RR contributions by using our pure spinor formulation. A natural next step is to consider the string moving in a curved space. In the RNS case it was done in [ 7 ] where the superdiffemorphism algebra is satisfied if the background NS–NS fields satisfy the supergravity equations of motion in ten dimensions. Their result is exact for all orders in world-sheet perturbation theory. The RR contributions can be naturally obtained using the pure spinor formalism. The coupling to a curved background was studied in [ 8 ], where the BRST invariance of the particle-like hamiltonian of the system helps to put the background superfields on-shell. It was noted that the system has an additional symmetry whose BRST invariance implies the so-called nilpotency constraints in [ 9 ] involving H = d B, where B is the super two-form of type II supergravity in ten dimensions. It is natural to consider the generator of this symmetry as part of the BRST charge. This was done in [ 10 ] where the nilpotency of the new BRST charge and the BRST invariance of the particle-like hamiltonian determine the type II supergravity constraints in ten dimensions of [ 9 ]. In the present paper, we obtain the Green– Schwarz superstring for the pure spinor string of [ 10 ]. This paper is organized as follows. In Sect. 2 we define the GS ambitwistor superstring in flat superspace. We show that the action is invariant under space-time supersymmetry transformations as well as under kappa symmetry. In this case, the necessary Virasoro-like constraints are determined. In Sect. 3, we relate the GS superstring to the pure spinor ambitwistor string in flat space. The relation allows one to obtain the particle-like hamiltonian of the pure spinor ambitwistor superstring from the Virasoro-like constraints of the GS ambitwistor superstring. In Sect. 4 the spectrum of the GS ambitwistor superstring is computed using the lightcone gauge quantization. The spectrum is described by the linearization of the type II supergravity fields, as expected. It would be interesting to apply the well known light-cone methods to compute scattering amplitudes in this string and see if they match with the ones obtained from the Mason– Skinner string and the pure spinor version. We conclude in Sect. 5 by studying the GS action in a curved superspace. The action turns out to be invariant under kappa symmetries if the constraints of type II supergravity are imposed. 2 Flat superspace formulation We construct an action for the ambitwistor in Green–Schwarz formalism. We find the κ symmetry of the theory and the Virasoro-like constraints. (...truncated)


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-017-5048-6.pdf

Osvaldo Chandía, Brenno Carlini Vallilo. Ambitwistor superstring in the Green–Schwarz formulation, The European Physical Journal C, 2017, pp. 473, Volume 77, Issue 7, DOI: 10.1140/epjc/s10052-017-5048-6