Perturbative gauge theory as a string theory in twistor space

Communications in Mathematical Physics

Volumn 252, Issue 1-3, 2004, Pages 189-258

  Witten, Edward ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 11244344133     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1187-3     Document Type: Article

References (92)

1. Parke, S., Taylor, T.: An Amplitude for N Gluon Scattering. Phys. Rev. Lett. 56, 2459 (1986)
2. Berends, F.A., Giele, W.T.: Recursive Calculations for Processes with N. Gluons. Nucl. Phys. B306, 759 (1988)
3. DeWitt, B.: Quantum Theory of Gravity. III: Applications of the Covariant Theory. Phys. Rev. 162, 1239 (1967)
4. Bern, Z., Dixon, L., Kosower, D.: Progress in One-Loop QCD Computations. Ann. Rev. Nucl. Part. Sci. 46, 109 (1996)
5. Brink, L., Scherk, J., Schwarz, J.H.: Supersymmetric Yang-Mills Theories. Nucl. Phys. B121, 77 (1977)
6. Anastasiou, C., Bern, Z., Dixon, L., Kosower, D.: Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory. Phys. Rev. Lett. 91, 251-602 (2003); Bern, Z., De Freitas, A., Dixon, L.: Two Loop Helicity Amplitudes for Quark Gluon Scattering in QCD and Gluino Gluon Scattering in Supersymmetric Yang-Mills Theory. JHEP 0306, 028 (2003)
7. Anastasiou, C., Bern, Z., Dixon, L., Kosower, D.: Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory. Phys. Rev. Lett. 91, 251-602 (2003); Bern, Z., De Freitas, A., Dixon, L.: Two Loop Helicity Amplitudes for Quark Gluon Scattering in QCD and Gluino Gluon Scattering in Supersymmetric Yang-Mills Theory. JHEP 0306, 028 (2003)
8. Penrose, R.: Twistor Algebra. J. Math. Phys. 8. 345 (1967)
9. Penrose, R.: The Central Programme of Twistor Theory. Chaos, Solitons, and Fractals 10, 581 (1999)
10. Ferber, A.: Supertwistors and Conformal Supersymmetry. Nucl. Phys. B132, 55 (1978)
11. Witten, E.: An Interpretation of Classical Yang-Mills Theory. Phys. Lett. B77, 394 (1978)
12. Isenberg, J., Yasskin, P.B., Green, P.S.: Nonselfdual Gauge Fields. Phys. Lett. B78, 464 (1978)
13. Nair, V.: A Current Algebra for Some Gauge Theory Amplitudes. Phys. Lett. B214, 215 (1988)
14. Maldacena, J.: The Large N Limit of Superconformal Field Theories and Supergravity. Adv. Theor. Math. Phys. 2, 231 (1998)
15. 't Hooft, G.: A Planar Diagram Theory for Strong Interactions. Nucl. Phys. B72, 461 (1974)
16. MacCallum, M.A.H., Penrose, R.: Twistor Theory: An Approach to the Quantization of Fields and Space-Time. Phys. Rept. 6C, 241 (1972)
17. Hodges, A.P., Huggett, S.: Twistor Diagrams. Surveys in High Energy Physics 1, 333 (1980); Hodges, A.: Twistor Diagrams. Physica 114A, 157 (1982); Twistor Diagrams. In: S.A. Huggett, et al. (eds.), The Geometric Universe: Science, Geometry, and the Work of Roger Penrose, Oxford: Oxford University Press, 1998
18. Hodges, A.P., Huggett, S.: Twistor Diagrams. Surveys in High Energy Physics 1, 333 (1980); Hodges, A.: Twistor Diagrams. Physica 114A, 157 (1982); Twistor Diagrams. In: S.A. Huggett, et al. (eds.), The Geometric Universe: Science, Geometry, and the Work of Roger Penrose, Oxford: Oxford University Press, 1998
19. Hodges, A.P., Huggett, S.: Twistor Diagrams. Surveys in High Energy Physics 1, 333 (1980); Hodges, A.: Twistor Diagrams. Physica 114A, 157 (1982); Twistor Diagrams. In: S.A. Huggett, et al. (eds.), The Geometric Universe: Science, Geometry, and the Work of Roger Penrose, Oxford: Oxford University Press, 1998
20. Bjorken, J.D., Chen, M.C.: High Energy Trident Production with Definite Helicities. Phys. Rev. 154, 1335 (1966)
21. Reading Henry, G.: Trident Production with Nuclear Targets. Phys. Rev. 154, 1534 (1967)
22. Berends, F.A., Kleiss, R., De Causmaecker, P., Gastmans, R., Wu, T.T.: Single Bremsstrahlung Processes in Gauge Theory. Phys. Lett. 103B, 124 (1981); De Causmaecker, P., Gastmans, R., Troost, W., Wu, T.T.: Helicity Amplitudes for Massless QED. Phys. Lett. B105, 215 (1981); Nucl. Phys. B206, 53 (1982); Berends, F.A., Kleiss, R., De Causmaecker, P., Gastmans, R., Troost, W., Wu, T.T.: Multiple Bremsstrahlung in Gauge Theories at High-Energies. 2. Single Bremsstrahlung. Nucl. Phys. B206, 61 (1982)
23. Berends, F.A., Kleiss, R., De Causmaecker, P., Gastmans, R., Wu, T.T.: Single Bremsstrahlung Processes in Gauge Theory. Phys. Lett. 103B, 124 (1981); De Causmaecker, P., Gastmans, R., Troost, W., Wu, T.T.: Helicity Amplitudes for Massless QED. Phys. Lett. B105, 215 (1981); Nucl. Phys. B206, 53 (1982); Berends, F.A., Kleiss, R., De Causmaecker, P., Gastmans, R., Troost, W., Wu, T.T.: Multiple Bremsstrahlung in Gauge Theories at High-Energies. 2. Single Bremsstrahlung. Nucl. Phys. B206, 61 (1982)
24. Berends, F.A., Kleiss, R., De Causmaecker, P., Gastmans, R., Wu, T.T.: Single Bremsstrahlung Processes in Gauge Theory. Phys. Lett. 103B, 124 (1981); De Causmaecker, P., Gastmans, R., Troost, W., Wu, T.T.: Helicity Amplitudes for Massless QED. Phys. Lett. B105, 215 (1981); Nucl. Phys. B206, 53 (1982); Berends, F.A., Kleiss, R., De Causmaecker, P., Gastmans, R., Troost, W., Wu, T.T.: Multiple Bremsstrahlung in Gauge Theories at High-Energies. 2. Single Bremsstrahlung. Nucl. Phys. B206, 61 (1982)
25. Berends, F.A., Kleiss, R., De Causmaecker, P., Gastmans, R., Wu, T.T.: Single Bremsstrahlung Processes in Gauge Theory. Phys. Lett. 103B, 124 (1981); De Causmaecker, P., Gastmans, R., Troost, W., Wu, T.T.: Helicity Amplitudes for Massless QED. Phys. Lett. B105, 215 (1981); Nucl. Phys. B206, 53 (1982); Berends, F.A., Kleiss, R., De Causmaecker, P., Gastmans, R., Troost, W., Wu, T.T.: Multiple Bremsstrahlung in Gauge Theories at High-Energies. 2. Single Bremsstrahlung. Nucl. Phys. B206, 61 (1982)
26. Kleis, R., Stirling, W.J.: Spinor Techniques for Calculating Proton Anti-Proton to W or Z Plus Jets. Nucl. Phys. B262, 235 (1985)
27. Gunion, J.F., Kunzst, Z.: Improved Analytic Techniques for Tree Graph Calculations and the ggqq̄ll̄ Process. Phys. Lett. 161B, 333 (1985)
28. Berends, F.A., Giele, W-T.: The Six Gluon Process as an Example of Weyl-van der Waerden Spinor Calculus. Nucl. Phys. B294, 700 (1987)
29. Xu, Z., Zhang, D.-H., Chang, L.: Helicity Amplitudes for Multiple Bremsstrahlung in Massless Nonabelian Gauge Theories. Nucl. Phys. B291, 392 (1987)
30. Chalmers, G., Siegel, W.: Simplifying Algebra in Feynman Graphs, Part I: Spinors. Phys. Rev. D59, 045012 (1999), Part II: Spinor Helicity from the Light Cone. Phys. Rev. D59, 045013 (1999), Part III: Massive Vectors. Phys. Rev. D63, 125027 (2001)
31. Chalmers, G., Siegel, W.: Simplifying Algebra in Feynman Graphs, Part I: Spinors. Phys. Rev. D59, 045012 (1999), Part II: Spinor Helicity from the Light Cone. Phys. Rev. D59, 045013 (1999), Part III: Massive Vectors. Phys. Rev. D63, 125027 (2001)
32. Chalmers, G., Siegel, W.: Simplifying Algebra in Feynman Graphs, Part I: Spinors. Phys. Rev. D59, 045012 (1999), Part II: Spinor Helicity from the Light Cone. Phys. Rev. D59, 045013 (1999), Part III: Massive Vectors. Phys. Rev. D63, 125027 (2001)
33. Mangano, M.L., Parke, S.J.: Multiparton Amplitudes in Gauge Theories. Phys. Rept. 200, 301 (1991)
34. Dixon, L.: Calculating Scattering Amplitudes Efficiently. TASI Lectures, 1995, http:// arxiv.org/abs/hep-ph/9601359, 1996
35. Witten, L.: Invariants of General Relativity and the Classification of Spaces. Phys. Rev. (2) 113, 357 (1959)
36. Penrose, R., Rindler, W.: Spinors and Space-Time: Volume 1. Two-Spinor Calculus and Relativistic Fields, Volume 2, Spinor and Twistor Methods in Spacetime Geometry. Cambridge: Cambridge University Press, 1986
37. Ward, R.S., Wells, R.O.Jr.: Twistor Geometry and Field Theory. Cambridge: Cambridge University Press, 1991
38. Hughston, L.P.: Twistors and Particles. Lecture Notes in Physics 97, Berlin: Springer-Verlag, 1989
39. Bailey, T.N., Baston, R.J. (eds.): Twistors in Mathematics and Physics. London: London Mathematical Society Lecture Notes Series, 156, 1990
40. Huggett, S.A., Tod, K.P.: An Introduction to Twistor Theory. London Mathematical Society Student Texts 4, New York: Cambridge Univ. Press, 1985
41. Penrose, R.: The Nonlinear Graviton. Gen. Rel. Grav. 7, 171 (1976)
42. Ward, R.: On Self-Dual Gauge Fields. Phys. Lett. 61A, 81 (1977)
43. Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Self-Duality in Four-Dimensional Riemannian Geometry. Proc. Roy. Soc. London Ser. A 362, 425 (1978)
44. Atiyah, M.F.: Geometry of Yang-Mills Fields. Lezioni Fermiane, Pisa: Academia Nazionale dei Lincei and Scuola Normale Superiore, 1979
45. Penrose, R.: Twistor Quantization and Curved Spacetime. Int. J. Theor. Phys. 1, 61 (1968)
46. Mangano, M., Parke, S., Xu, Z.: Duality and Multi-Gluon Scattering. Nucl. Phys. B298, 653 (1988)
47. Berends, F.A., Giele, W.T., Kuijf, H.: Exact and Approximate Expressions for Multi-Gluon Scattering. Nucl. Phys. B333, 120 (1990)
48. Bern, Z., Dixon, L., Dunbar, D., Kosower, D.A.: One-Loop N-Point Gauge Theory Amplitudes. Unitarity and Collinear Limits, hep-ph/9403226
49. Bern, Z., Dixon, L., Kosower, D.: One Gluon Corrections to Five Gluon Amplitudes. Phys. Rev. Lett. 70, 2677 (1993)
50. Bern, Z., Dixon, L., Kosower, D.A.: In: M.B. Halpern, et al. (eds.), Strings 1993, Singapore: World Scientific, 1995; Bern, Z., Chalmers, G., Koxon, L., Kosower, D.A.: Phys. Rev. Lett. 72, 2134 (1994)
51. Bern, Z., Dixon, L., Kosower, D.A.: In: M.B. Halpern, et al. (eds.), Strings 1993, Singapore: World Scientific, 1995; Bern, Z., Chalmers, G., Koxon, L., Kosower, D.A.: Phys. Rev. Lett. 72, 2134 (1994)
52. Mahlon, G.: Multigluon Helicity Amplitudes Involving a Quark Loop. Phys. Rev. D49, 4438 (1994)
53. Mahlon, G., Yan, T.-M.: Multi-Photon Production at High Energies in the Standard Model: I. Phys. Rev. D47, 1776 (1993)
54. Bern, Z., Kosower, D.: The Computation of Loop Amplitudes in Gauge Theories. Nucl. Phys. B379, 451 (1992)
55. Bern, Z., Dixon, L., Dunbar, D.C., Kosower, D.A.: One-loop Gauge Theory Amplitudes with an Arbitrary Number of External Legs, hep-ph/9405248
56. Berends, F.A., Giele, W.T., Kuijf, H.: On Relations Between Multi-Gluon and Multi-Graviton Scattering. Phys. Lett. 211B, 91 (1988)
57. Witten, E.: Mirror Manifolds and Topological Field Theory. hep-th/9112056, In: S.-T. Yau, (ed.), Mirror Symmetry, Cambridge, MA: International Press, 1998
58. Hori, K., et al. (eds.): Mirror symmetry. Providence, RI: American Mathematical Society, 2003
59. Witten, E.: Chern-Simons Gauge Theory as a String Theory. Prog. Math. 133, 637 (1995)
60. Dijkgraaf, R., Vafa, C.: Matrix Models, Topological Strings, and Supersymmetric Gauge Theories. Nucl. Phys. B644, 3 (2002)
61. Aganagic, M., Dijkgraaf, R., Klemm, A., Marino, M., Vafa, C.: Topological Strings and Integrable Hierarchies. hep-th/0312085
62. N-1 Models with Quarks. Nucl. PHys. B152, 125 (1979)
63. Witten. E.: Instantons, the Quark Model, and the 1/N Expansion. Nucl. Phys. B149, 285 (1979)
64. Zumino, B.: Supersymmetry and Kahler Manifolds. Phys. Lett. B87, 203 (1979)
65. Movshev, M., Schwarz, A.: On Maximally Supersymmetric Yang-Mills Theory. hep-th/0311132
66. Bershadsky, M., Cecotti, S., Ooguri, H., Vafa, C.: Holomorphic Anomalies in Topological Field Theories. Nucl. Phys. B405, 279 (1993); Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes. Commun. Math. Phys. B165, 311 (1994)
67. Bershadsky, M., Cecotti, S., Ooguri, H., Vafa, C.: Holomorphic Anomalies in Topological Field Theories. Nucl. Phys. B405, 279 (1993); Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes. Commun. Math. Phys. B165, 311 (1994)
68. Grisaru, M., Rocek, M., Siegel, W.: Superloops 3, Beta 0: A Calculation in N = 4 Yang-Mills Theory. Phys. Rev. Lett. 45, 1063 (1980)
69. Avdeev, L.V., Tarasov, O.V.: The Three Loop Beta Function in the N = 1, N = 2, N = 4 Super-symmetric Yang-Mills Theories. Phys. Lett. B112, 356 (1982)
70. Mandelstam, S.: Light Cone Superspace and the Ultraviolet Finiteness of the N = 4 Model. Nucl. Phys. B213, 149 (1983)
71. Krasnov, K.: Twisters, CFT, and Holography. hep-th/0311162
72. Atiyah, M.F., Hitchin, N.: The Geometry and Dynamics of Magnetic Monopoles. Princeton, NJ: Princeton University Press, 1988
73. Polchinski, J.: Dirichlet Branes and Ramond-Ramond Charges. Phys. Rev. Lett. 75, 4724 (1995)
74. Lazaroiu, C.: Holomorphic Matrix Models. hep-th/0303008.
75. Siegel, W.: The N = 2(4) String is Self-Dual N = 4 Yang-Mills. Phys. Rev. D46, R3235 (1992); Self-Dual N = 8 Supergravity as Closed N = 2(4) Strings, hep-th/9207043
76. Siegel, W.: The N = 2(4) String is Self-Dual N = 4 Yang-Mills. Phys. Rev. D46, R3235 (1992); Self-Dual N = 8 Supergravity as Closed N = 2(4) Strings, hep-th/9207043
77. Chalmers, G., Siegel, W.: The Self-Dual Sector of QCD Amplitudes. hep-th/9606061
78. Witten, E.: Small Instantons in String Theory. Nucl. Phys. B460, 541 (1996)
79. Douglas, M.R.: Gauge Fields and D-Branes. J. Geom. Phys. 28, 255 (1998)
80. Fradkin, E.S., Tseytlin, A.A.: Conformal Supergravity. Phys. Rept. 119, 233 (1985)
81. Salam, A., Sezgin, E.: Supergravities in Diverse Dimensions. Vol. 2, Singapore: World Scientific, 1989
82. 5 Superstring. hep-th/0305116
83. Dolan, L., Nappi, C.R., Witten, E.: A Relation Among Approaches to Integrability in Superconformal Yang-Mills Theory. JHEP 0310, 017 (2003)
84. Luscher, M., Pohlmeyer, K.: Scattering of Massless Lumps and Nonlocal Charges in the Two-Dimensional Classical Non-Linear Sigma Model. Nucl. Phys. B137, 46 (1978)
85. de Vega, H.J., Eichenherr, H., Maillet, J.M.: Yang-Baxter Algebras of Monodromy Matrices in Integrable Quantum Field Theories. Nucl. Phys. B240, 377 (1984)
86. Berg, B., Weisz, P.: Exact S Matrix of the Adjoint SU (N) Representation. Commun. Math. Phys. 67, 241 (1979)
87. Goldschmidt, Y., Witten, E.: Conservation Laws in Some Two-Dimensional Models. Phys. Lett. 91B, 392 (1980)
88. Abdalla, E.: In: N. Sanchez, (ed.), Non-linear Equations in Classical and Quantum Field Theory. Springer Lectures in Physics, Vol. 226, Berlin-Heidelberg-New York: Springer, 1985, p. 140; Abdalla, E., Abdalla, M.C.B., Gomes, M.: Phys. Rev. D25, 452 (1982), D27, 825 (1983)
89. Abdalla, E.: In: N. Sanchez, (ed.), Non-linear Equations in Classical and Quantum Field Theory. Springer Lectures in Physics, Vol. 226, Berlin-Heidelberg-New York: Springer, 1985, p. 140; Abdalla, E., Abdalla, M.C.B., Gomes, M.: Phys. Rev. D25, 452 (1982), D27, 825 (1983)
90. Abdalla, E.: In: N. Sanchez, (ed.), Non-linear Equations in Classical and Quantum Field Theory. Springer Lectures in Physics, Vol. 226, Berlin-Heidelberg-New York: Springer, 1985, p. 140; Abdalla, E., Abdalla, M.C.B., Gomes, M.: Phys. Rev. D25, 452 (1982), D27, 825 (1983)
91. Berkovits, N.: Super Poincaré Covariant Quantization of the Superstring. JHEP 0004, 018 (2000), hep-th/0001035, Covariant Quantization of the Superparticle Using Pure Spinors. hep-th/0105050, JHEP 0109, 016 (2001)
92. Berkovits, N.: Super Poincaré Covariant Quantization of the Superstring. JHEP 0004, 018 (2000), hep-th/0001035, Covariant Quantization of the Superparticle Using Pure Spinors. hep-th/0105050, JHEP 0109, 016 (2001)