Twistors and the Amplitudes in the Integrable Sector of Superstring Theory

Authors

  • Simon Davis Research Foundation of Southern California, La Jolla, California, U.S.A.

DOI:

https://doi.org/10.48165/

Keywords:

Transport, Periodic, Doped, Metallic, Nanotube, Ballistic, Symmetry

Abstract

 Twistors can represent the spin in superstring theory and provide a theoretical explanation of  the two-dimensional spherical model of elementary particles together with the surface  distributions of the charges. The integrability of certain matter sectors of the strong  interactions also may be traced to the action of the conformal group on collinear trajectories  that occur in a twistor formulation. The amplitudes for these scattering processes in four  dimensions have a representation with quantum states in a nonsupersymmetric theory defined  by the low-energy limit of a solution to the N = 2 string equations with a Wick rotation of the  metric with (2, 2) signature. The twistor form of an N = 2 scattering amplitude is given.

References

. E. Witten, Twistor-Like Transform in Ten Dimensions, Nucl. Phys. B266 (1986) 245-264. [2]. I. V. Volovich, Super-selfduality for Supersymmetric Yang-Mills Theory, Phys. Lett. B123 (1983) 329- 331.

. C. Devchand, Integrability on Lightlike Lines in Six-Dimensional Superspace, Z. Phys. C32 (1986) 233-236.

. I. Kaplansky, Three-Dimensional Division Algebras, J. Algebra 40 (1976) 384- 391. [5]. R. E. McRae, On the Theory of Division Algebras, Lin. Alg. Appl. 119 (1989) 121-128. [6]. D. G. Glynn, On Finite Division Algebras, J. Comb. Theory Ser. A 44 (1987) 253-266. [7]. M. Koca and N. Ozdes, Division Algebras with Integral Elements, J. Phys. A22 (1989) 1469-1493. [8]. L. Brink, M. Cederwall and C. R. Preitschopf, N=8 Superconformal Algebra and the Superstring, Phys. Lett. B311 (1993) 76-82.

. N. Berkovits, A Geometrical Interpretation for the Symmetries of the GreenSchwarz Superstring, Phys. Lett. B241 (1990) 497-502.

. F. Delduc, A. Galperin, P. Howe and E. Sokatchev, A Twistor Formulation of the Heterotic D = 10 Superstring with Manifest (8,0) Worldsheet Supersymmetry, Phys. Rev. D47 (1993) 578-593. [11]. S. Davis, String Compactifications and Regge Trajectories for the Resonances of the Strong Interactions, Int. J. Pure Appl. Math. 70 (2011) 25-38.

. S. Davis, A Constraint on the Geometry of Yang-Mills Theory, J. Geom. Phys. 4 (1987) 405-415. [13]. M. Cederwall, Introduction to Division Algebras, Sphere Algebras and Twistors, Talk presented at the Theoretical Physics Network Meeting at NORDITA, Copenhagen, September, 1993, hep-th/9310115. [14]. G. Landi and G. Marmo, Extensions of Lie Superalgebras and Supersymmetric Abelian Gauge Fields, Phys. Lett. 193 (1987) 61-66.

. J. M. Evans, Supersymmetric Yang-Mills Theories and Division Algebras, Nucl. Phys. B298 (1988) 92-108.

. S. Davis, The Group E6 and the Formulation of String Theory, Bull. Pure and Appl. Sci., Section E: Math. and Stat. 32 (2013) 141-159.

. D. L¨ust and S. Theisen, Exceptional Groups in String Theory, Int. J. Mod. Phys. A4 (1989) 4513- 4533.

. M. Green, J. Schwarz and E. Witten, Superstring Theory, Vol. 2, Cambridge University Press, Cambridge, 1987.

. A. P. Balachandran, G. Marmo, B.-S. Skagerstam and A. Stern, Gauge Symmetries and Fibre Bundles, Lect. Notes Phys., Vol. 188, Springer-Verlag, Berlin, 1983.

. W. Siegel, Untwisting the Twistor Superstring, hep-th/0404255.

. A. Ferber, Supertwistors and Superconformal Supersymmetry, Nucl. Phys. B132 (1978) 55-64. [22]. I. A. Bandos, J. A. de Azcarraga and C. Miguel-Espanya, Superspace Formulations of the (Super)twistor String, J. High Energy Phys. 0607 (2006) 005:1-23.

. G. Chalmers and W. Siegel, The Self-Dual Sector of QCD Amplitudes, Phys. Rev. D54 (1996) 7628. [24]. E. Witten, Perturbative Gauge Theory as a Theory in Twistor Space, Commun. Math. Phys. 252 (2004) 189.

. S. W. Hawking, The Boundary Conditions for Gauged Supergravity, Phys. Lett. B126 (1983) 175-177. [26]. S. Vidussi, Some Remarks on the Cohomology of SU(3) Gauge Orbit Space, Diff. Geom. Appl. 7 (1997) 29-33.

. J. Harnad, J. Hurtubise, M. Legare and S. Shnider, Constraint Equations and Field Equations in Supersymmetric N = 3 Yang-Mills Theory, Nucl. Phys. B256 (1985) 609-620.

. L. Brink, J. H. Schwarz and J. Scherk, Supersymmetric Yang-Mills Theory, Nucl. Phys. B121 (1977) 77-92.

. [29] B. Grossman, T. Kephart and J. Stasheff, Solutions to Yang-Mills Field Equations in Eight Dimensions and the Last Hopf Map, Commun. Math. Phys. 96 (1984) 431-437.

. S. Fubini and H. Nicolai, The Octonionic Instanton, Phys. Lett. B155 (1985) 369-372. [31]. S. Davis, The Unification of Symmetries in the Bosonic and Fermionic Sectors of the Strong Interactions, RFSC-14-37.

. J. M. Evans, Auxiliary Fields for Super-Yang-Mills from Division Algebras, Lect. Notes Phys. 447 (1995) 218-223.

. S. Davis, Connections and Generalized Gauge Transformations, Int. J. Geom. Meth. Mod. Phys. 2 (2005) 505-542.

. M. Eastwood, Supersymmetry, Twistors, and the Yang-Mills Equations, Trans. Amer. Math. Soc. 301 (1987) 615-635.

. V. P. Nair, Chern-Simons, WZW Models, Twistors and Multigluon Scattering Amplitudes, Lecture Notes, 2005.

. M. Wolf, A Connections between Twistors and Superstring Sigma Models on Coset Superspaces, J. High Energy Phys. 0909 (2009) 071:1-18.

. F. Delduc, A. Galperin, P. Howe and E. Sokatchev, A Twistor Formulation of the Heterotic D = 10 Superstring with Manifest (8, 0) Worldsheet Supersymmetry, Phys. Rev. D47 (1993) 578-593. [38]. M. de Roo, H. Suelmann and A. Wiedemann, The Supersymmetric Effective Action of the Heterotic String in Ten Dimensions, Nucl. Phys. B405 (1993) 326-366.

. A. Belitsky, V. M. Braun, A. S. Gorsky and G. P. Korchemsky, Integrability in QCD and Beyond, Int. J. Mod. Physics A19 (2004) 4715-4788.

. T. Adamo and L. Mason, MHV Diagrams in Twistor Space and the Twistor Action,. Phys. Rev. D86 (2012) 065019:1-30.

. W. Siegel, N=2(4) String Theory is Selfdual N = 4 Yang-Mills Theory, Phys. Rev. D46 (1992) 3235- 3238.

. O. Lechtenfeld and A. D. Popov, Supertwistors and Cubic String Field Theory for Open Strings, Phys. Lett. B598 (2004) 113-120.

. E. Witten, Perturbative Gauge Theory as a String Theory in Twistor Space, Commun. Math. Phys. 252 (2004) 189-258.

. W. Siegel, “ N = 2(4) String Theory is Selfdual N = 4 Yang-Mills Theory”, Phys. Rev. D46, pp.3235- 3238, 1992.

. O. Lechtenfeld and W. Siegel, N=2 Worldsheet Instantons yield Cubic Self-Dual Yang-Mills, Phys. Lett. B405 (1997) 49-54.

. N. Berkovits and W. Siegel, Covariant Field Theory for Self-Dual Strings, Nucl. Phys. B505 (1997) 139-152.

. S. K¨urkc¨o˘glu, Non-linear Sigma Model on the Fuzzy Supersphere, J. High Energy Phys. 0403 (2004) 062: 1-11.

. J. Fisher, Large-Order Estimates in Perturbative QCD and Non-BorelSummable Series, Fortschritte der Physik 42 (1994) 665-688.

. I. Caprini, J. Fisher, G. Abbas, B. Ananthanarayan, Perturbative Expansions in QCD Improved by Conformal Mappings of Borel Plane, Perturbation Theory: Advances in Research and Applications, Nova Science Publishers, Hauppauge, 2018.

. H.Ooguri and C. Vafa, N=2 Heterotic Strings, Nucl. Phys. B367 (1991) 83-104. [51]. G. Arutyunov and S. Frolov, Foundations of the AdS5xS5 Superstring, I, J. Phys. A: Math. Theor. 42 (2009) 254003: 1-121.

. F. Delduc, M. Magro and B. Vicedo, An Integrable Deformation of the AdS5xS5 Superstring Action, Phys. Rev. Lett. 112 (2014) 051601:1-5.

. N. Beisert, et. al. , Review of AdS/CFT Integrability: An Overiew, Lett. Math. Phys. 99 (2012) 3-32. [54]. H. A. Lorentz, Electromagnetic Phenomena in a System moving with any Velocity less than that of Light, Proc. Acad. Science Amsterdam IV (1904) 669-678.

Downloads

Published

2021-02-11

Issue

Vol. 40 No. 1 (2021): Bulletin of Pure and Applied Sciences Physics (Jan-Jun) 2021

Section

Articles

How to Cite

Twistors and the Amplitudes in the Integrable Sector of Superstring Theory . (2021). Bulletin of Pure and Applied Sciences – Physics, 40(1), 1–13. https://doi.org/10.48165/