Abstract
A covariant closed superstring field theory, equivalent to classical tendimensional Type II supergravity, is presented. The defining conformal field theory is the ambitwistor string worldsheet theory of Mason and Skinner. This theory is known to reproduce the scattering amplitudes of Cachazo, He and Yuan in which the scattering equations play an important role and the string field theory naturally incorporates these results. We investigate the operator formalism description of the ambitwsitor string and propose an action for the string field theory of the bosonic and supersymmetric theories. The correct linearised gauge symmetries and spacetime actions are explicitly reproduced and evidence is given that the action is correct to all orders. The focus is on the NeveuSchwarz sector and the explicit description of tree level perturbation theory about flat spacetime. Application of the string field theory to general supergravity backgrounds and the inclusion of the Ramond sector are briefly discussed.
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References
C.M. Hull, Doubled Geometry and T-Folds, JHEP 07 (2007) 080 [hep-th/0605149] [INSPIRE].
C.M. Hull and R.A. Reid-Edwards, Flux compactifications of string theory on twisted tori, Fortsch. Phys. 57 (2009) 862 [hep-th/0503114] [INSPIRE].
C.M. Hull and R.A. Reid-Edwards, Flux compactifications of M-theory on twisted Tori, JHEP 10 (2006) 086 [hep-th/0603094] [INSPIRE].
C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].
W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].
C.M. Hull and P.K. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
J.P. Gauntlett, D. Martelli, S. Pakis and D. Waldram, G structures and wrapped NS5-branes, Commun. Math. Phys. 247 (2004) 421 [hep-th/0205050] [INSPIRE].
M. Graña, Flux compactifications in string theory: A Comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].
F. Bastianelli and P. van Nieuwenhuizen, Path Integrals and Anomalies in Curved Space, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2006).
L. Mason and D. Skinner, Ambitwistor strings and the scattering equations, JHEP 07 (2014) 048 [arXiv:1311.2564] [INSPIRE].
T. Adamo, E. Casali and D. Skinner, A Worldsheet Theory for Supergravity, JHEP 02 (2015) 116 [arXiv:1409.5656] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations, JHEP 01 (2015) 121 [arXiv:1409.8256] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons, JHEP 07 (2014) 033 [arXiv:1309.0885] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles in Arbitrary Dimensions, Phys. Rev. Lett. 113 (2014) 171601 [arXiv:1307.2199] [INSPIRE].
D.B. Fairlie and D.E. Roberts, Dual Models without Tachyons — A New Approach, unpublished Durham preprint PRINT-72-2440 (1972).
D.J. Gross and P.F. Mende, String Theory Beyond the Planck Scale, Nucl. Phys. B 303 (1988) 407 [INSPIRE].
K. Ohmori, Worldsheet Geometries of Ambitwistor String, JHEP 06 (2015) 075 [arXiv:1504.02675] [INSPIRE].
E. Casali, Y. Geyer, L. Mason, R. Monteiro and K.A. Roehrig, New Ambitwistor String Theories, JHEP 11 (2015) 038 [arXiv:1506.08771] [INSPIRE].
Y. Geyer, A.E. Lipstein and L.J. Mason, Ambitwistor Strings in Four Dimensions, Phys. Rev. Lett. 113 (2014) 081602 [arXiv:1404.6219] [INSPIRE].
T. Kugo, H. Kunitomo and K. Suehiro, Nonpolynomial Closed String Field Theory, Phys. Lett. B 226 (1989) 48 [INSPIRE].
T. Kugo and K. Suehiro, Nonpolynomial Closed String Field Theory: Action and Its Gauge Invariance, Nucl. Phys. B 337 (1990) 434 [INSPIRE].
B. Zwiebach, Closed string field theory: Quantum action and the B-V master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084] [INSPIRE].
A. Sen, BV Master Action for Heterotic and Type II String Field Theories, JHEP 02 (2016) 087 [arXiv:1508.05387] [INSPIRE].
T. Adamo, E. Casali and D. Skinner, Ambitwistor strings and the scattering equations at one loop, JHEP 04 (2014) 104 [arXiv:1312.3828] [INSPIRE].
Y. Geyer, L. Mason, R. Monteiro and P. Tourkine, One-loop amplitudes on the Riemann sphere, JHEP 03 (2016) 114 [arXiv:1511.06315] [INSPIRE].
C. LeBrun, Spaces of Complex Null Geodesics in Complex-Riemannian Geometry, Trans. Am. Math. Soc. 278 (1983) 209.
J. Isenberg, P.B. Yasskin and P.S. Green, Nonselfdual Gauge Fields, Phys. Lett. 78B (1978) 462 [INSPIRE].
R.J. Baston and L.J. Mason, Conformal Gravity, the Einstein Equations and Spaces of Complex Null Geodesics, Class. Quant. Grav. 4 (1987) 815 [INSPIRE].
C. LeBrun, Thickenings and conformal gravity, Commun. Math. Phys. 139 (1991) 1 [INSPIRE].
L.J. Mason and D. Skinner, Heterotic twistor-string theory, Nucl. Phys. B 795 (2008) 105 [arXiv:0708.2276] [INSPIRE].
R.A. Reid-Edwards, On Closed Twistor String Theory, arXiv:1212.6047 [INSPIRE].
E. Casali and P. Tourkine, On the null origin of the ambitwistor string, JHEP 11 (2016) 036 [arXiv:1606.05636] [INSPIRE].
P. Di Vecchia, R. Nakayama, J.L. Petersen, J.R. Sidenius and S. Sciuto, Covariant N string amplitude, Nucl. Phys. B 287 (1987) 621 [INSPIRE].
R.A. Reid-Edwards, Ambitwistor String Theory in the Operator Formalism, JHEP 06 (2016) 084 [arXiv:1511.08406] [INSPIRE].
L. Álvarez-Gaumé, C. Gomez, G.W. Moore and C. Vafa, Strings in the Operator Formalism, Nucl. Phys. B 303 (1988) 455 [INSPIRE].
C. Vafa, Operator Formulation on Riemann Surfaces, Phys. Lett. B 190 (1987) 47 [INSPIRE].
A. LeClair, M.E. Peskin and C.R. Preitschopf, String Field Theory on the Conformal Plane. 1. Kinematical Principles, Nucl. Phys. B 317 (1989) 411 [INSPIRE].
E. Witten, Superstring Perturbation Theory Revisited, arXiv:1209.5461 [INSPIRE].
E. Witten, Noncommutative Geometry and String Field Theory, Nucl. Phys. B 268 (1986) 253 [INSPIRE].
A. LeClair, M.E. Peskin and C.R. Preitschopf, String Field Theory on the Conformal Plane. 2. Generalized Gluing, Nucl. Phys. B 317 (1989) 464 [INSPIRE].
M. Saadi and B. Zwiebach, Closed String Field Theory from Polyhedra, Annals Phys. 192 (1989) 213 [INSPIRE].
H. Sonoda and B. Zwiebach, Closed String Field Theory Loops With Symmetric Factorizable Quadratic Differentials, Nucl. Phys. B 331 (1990) 592 [INSPIRE].
R. Saroja and A. Sen, Picture changing operators in closed fermionic string field theory, Phys. Lett. B 286 (1992) 256 [hep-th/9202087] [INSPIRE].
S.B. Giddings and E.J. Martinec, Conformal Geometry and String Field Theory, Nucl. Phys. B 278 (1986) 91 [INSPIRE].
M. Peskin, unpublished.
J. Lykken and S. Raby, unpublished.
M. Kaku and J.D. Lykken, Modular invariant closed string field theory, Phys. Rev. D 38 (1988) 3067 [INSPIRE].
M. Kaku, Geometric Derivation of String Field Theory From First Principles: Closed Strings and Modular Invariance, Phys. Rev. D 38 (1988) 3052 [INSPIRE].
H. Sonoda and B. Zwiebach, Covariant closed string theory cannot be cubic, Nucl. Phys. B 336 (1990) 185 [INSPIRE].
M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. London A 173 (1939) 211.
T. Ortin, Gravity and Strings, second edition, Cambridge University Press, Cambridge U.K. (2015).
R.P. Feynman, F.B. Morinigo, W.G. Wagner, B. Hatfield and D. Pines, Feynman lectures on gravitation, Westview Press, Boulder U.S.A. (2002).
Y. Geyer, L. Mason, R. Monteiro and P. Tourkine, Loop Integrands for Scattering Amplitudes from the Riemann Sphere, Phys. Rev. Lett. 115 (2015) 121603 [arXiv:1507.00321] [INSPIRE].
E. Casali, Y. Herfray and P. Tourkine, The complex null string, Galilean conformal algebra and scattering equations, arXiv:1707.09900 [INSPIRE].
Y. Li and W. Siegel, Chiral Superstring and CHY Amplitude, arXiv:1702.07332 [INSPIRE].
M. Ademollo et al., Dual String Models with Nonabelian Color and Flavor Symmetries, Nucl. Phys. B 114 (1976) 297 [INSPIRE].
M. Ademollo et al., Supersymmetric Strings and Color Confinement, Phys. Lett. 62B (1976) 105 [INSPIRE].
N. Marcus, A Tour through N = 2 strings, in International Workshop on String Theory, Quantum Gravity and the Unification of Fundamental Interactions Rome Italy (1992) [hep-th/9211059] [INSPIRE].
D. Friedan, E.J. Martinec and S.H. Shenker, Conformal Invariance, Supersymmetry and String Theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].
E.P. Verlinde and H.L. Verlinde, Multiloop Calculations in Covariant Superstring Theory, Phys. Lett. B 192 (1987) 95 [INSPIRE].
R. Donagi and E. Witten, Supermoduli Space Is Not Projected, Proc. Symp. Pure Math. 90 (2015) 19 [arXiv:1304.7798] [INSPIRE].
C. Wendt, Scattering Amplitudes and Contact Interactions in Witten’s Superstring Field Theory, Nucl. Phys. B 314 (1989) 209 [INSPIRE].
T. Erler, S. Konopka and I. Sachs, Resolving Witten’s superstring field theory, JHEP 04 (2014) 150 [arXiv:1312.2948] [INSPIRE].
T. Erler, S. Konopka and I. Sachs, NS-NS Sector of Closed Superstring Field Theory, JHEP 08 (2014) 158 [arXiv:1403.0940] [INSPIRE].
L. Álvarez-Gaumé, C. Gomez, P.C. Nelson, G. Sierra and C. Vafa, Fermionic Strings in the Operator Formalism, Nucl. Phys. B 311 (1988) 333 [INSPIRE].
P.V. Collins and K.A. Friedman, Off-Shell Amplitudes and Currents in the Dual Resonance Model, Nuovo Cim. A 28 (1975) 173 [INSPIRE].
S. Samuel, Off-shell conformal field theory, Nucl. Phys. B 308 (1988) 317 [INSPIRE].
O. Lechtenfeld and S. Samuel, Off-shell Conformal Methods for the Superstring, Nucl. Phys. B 310 (1988) 254 [INSPIRE].
A. Sen, Off-shell Amplitudes in Superstring Theory, Fortsch. Phys. 63 (2015) 149 [arXiv:1408.0571] [INSPIRE].
A. Sen and E. Witten, Filling the gaps with PCO’s, JHEP 09 (2015) 004 [arXiv:1504.00609] [INSPIRE].
A. Sen, Covariant Action for Type IIB Supergravity, JHEP 07 (2016) 017 [arXiv:1511.08220] [INSPIRE].
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Reid-Edwards, R., Riccombeni, D. A superstring field theory for supergravity. J. High Energ. Phys. 2017, 103 (2017). https://doi.org/10.1007/JHEP09(2017)103
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DOI: https://doi.org/10.1007/JHEP09(2017)103