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## Perturbative gauge theory as a string theory in twistor space (2003)

Venue: | COMMUN. MATH. PHYS |

Citations: | 384 - 1 self |

### Citations

5611 | The Large N Limit of Superconformal Field Theories and Supergravity, Adv.Theor.Math.Phys - Maldacena - 1998 |

556 |
Hooft, “A Planar Diagram Theory for Strong Interactions
- ’t
- 1974
(Show Context)
Citation Context ...y possibly give some version of N = 4 conformal supergravity, in which case the string theory considered here is equivalent to super Yang-Mills theory only in the planar limit (large N with fixed g2N =-=[14]-=-), in which the closed strings decouple. (If so, as conformal supergravity is generally assumed to have negative energies and ghosts, the B model of CP 3|4 may be physically sensible only in the plana... |

545 | Chern-Simons gauge theory as a string theory,” Prog
- Witten
- 1995
(Show Context)
Citation Context ...helpful to have more familiarity that we can convey here with the topological B model and its extension to open strings. For reviews of the B model, see [48,49], for the extension to open strings see =-=[50]-=-, and for some recent applications of the B model, see [51,52]. Some of the basics about the Penrose transform that are needed for this analysis are explained in an appendix, but the reader will proba... |

384 | Mirror manifolds and topological field theory,” arXiv:hep-th/9112056
- Witten
(Show Context)
Citation Context ...of the paper. The reader will probably find it helpful to have more familiarity that we can convey here with the topological B model and its extension to open strings. For reviews of the B model, see =-=[48,49]-=-, for the extension to open strings see [50], and for some recent applications of the B model, see [51,52]. Some of the basics about the Penrose transform that are needed for this analysis are explain... |

383 |
The geometry and dynamics of magnetic monopoles
- Atiyah, Hitchin
- 1988
(Show Context)
Citation Context ...losest analog of twistor space in a different dimension is probably the “mini-twistor space,” a complex line bundle over CP 1 that is used to solve the equations for BPS monopoles in three dimensions =-=[62]-=-. This construction is naturally obtained by dimensional reduction from the twistor correspondence in four dimensions. 53Indeed, CP 3|4 has a U(1) symmetry which does not leave invariant the holomorp... |

326 |
Matrix models, topological strings, and supersymmetric gauge theories
- Dijkgraaf, Vafa
- 2002
(Show Context)
Citation Context ...˜ λi, ˜ λj]. 1 + 2 + 3 + 4 − 5 − 6 − 1 + 2 + 3 − 4 + 5 − 6 − 1 + 2 − 3 + 4 − 5 + 6 − X = 1 + 2 + 3 Y = 1 + 2 + 4 Z = 1 + 3 + 5 α 0 −[12]〈56〉〈4|Y |3〉 [13]〈46〉〈5|Z|2〉 β [23]〈56〉〈1|X|4〉 [24]〈56〉〈1|Y |3〉 =-=[51]-=-〈24〉〈3|Z|6〉 γ [12]〈45〉〈3|X|6〉 [12]〈35〉〈4|Y |6〉 [35]〈62〉〈1|Z|4〉 Our conjecture says again that these amplitudes should be supported on configurations in which all six points Pi labeling the external pa... |

306 |
Super Poincare Covariant Quantization of the Superstring
- Berkovits
- 2000
(Show Context)
Citation Context ...to super Yang-Mills theory in roughly the same way that Q is. Their motivation was in part to understand the covariant quantization of the Green-Schwarz superparticle and superstring via pure spinors =-=[78]-=-, which in some ways is a cousin of twistor constructions. Many of their examples have nonzero first Chern class and hence no topological B model, but their method of construction of the measure may b... |

223 |
Dirichlet Branes and Ramond-Ramond charges,” Phys.Rev.Lett
- Polchinski
- 1995
(Show Context)
Citation Context ...y conditions that do this are Neumann boundary conditions. We introduce Chan-Paton factors of the gauge group GL(N, C) (a real form of which is U(N)). In modern language, this construction amounts to =-=[63]-=- introducing N space-filling D-branes wrapped on X. The branes are endowed by a vector bundle E with structure group GL(N, C). As is also explained in [50], the only physical open string field in this... |

155 |
A current algebra for some gauge theory amplitudes,” Phys. Lett. B214
- Nair
- 1988
(Show Context)
Citation Context ...] long ago. 1 From the string theory, we recover the tree level MHV amplitudes of gauge theory. They arise from a one-instanton computation that leads to a formalism similar to that suggested by Nair =-=[12]-=-. This representation of weakly coupled N = 4 super-Yang-Mills theory as a string theory is an interesting counterpoint to the by now familiar description of the strongly coupled regime of the same th... |

127 |
Planar amplitudes in maximally supersymmetric Yang-Mills theory
- Anastasiou, Bern, et al.
(Show Context)
Citation Context ...mmetric case. For a sampling of one-loop results, see the review [4], and for some recent two-loop results for the theory with maximal or N = 4 supersymmetry (which was first constructed in [5]), see =-=[6]-=-. N = 4 super Yang-Mills theory is an important test case for perturbative gauge theory, since it is the simplest case and, for example, has the same gluonic tree amplitudes as pure Yang-Mills theory.... |

111 | Calculating scattering amplitudes efficiently
- Dixon
(Show Context)
Citation Context ...and not just products of twistor spaces. In section 2, we review Yang-Mills helicity amplitudes and their description via spinors [17-24] and the MHV amplitudes. For expositions of this material, see =-=[25,26]-=-. For the use of spinors in relativity, see [27,28]. Then we describe the Fourier transform to twistor space. For general reviews of twistor theory, see [8,15,29-32]; for the twistor transform of the ... |

92 | One-Loop n-Point Gauge Theory Amplitudes
- Bern, Dixon, et al.
- 1994
(Show Context)
Citation Context ...udes to look at first are the planar MHV amplitudes with precisely two negative helicity gluons in N = 4 super Yang-Mills theory. General and relatively simple formulas are known for these amplitudes =-=[40]-=-. Until this point, it has not generally mattered if we contemplate pure Yang-Mills theory or a supersymmetric extension thereof. The reason is that so far we have mainly limited ourselves to tree amp... |

85 |
Gauge Fields and D-branes
- Douglas
(Show Context)
Citation Context ...e fermions. Under appropriate conditions, α and β will have zero modes. If α and 71β are bosons, the zero modes will lead to flat directions which by analogy with phenomena in critical string theory =-=[67,68]-=- will represent the deformation of the D1-brane into a smooth holomorphic bundle on CP 3|4 with second Chern class nonzero (and Poincaré dual to C). By the twistor transform of the anti-selfdual Yang-... |

84 | cone superspace and the ultraviolet finiteness of the N=4 - Mandelstam, Light - 1983 |

82 |
Twistor Algebra
- Penrose
- 1967
(Show Context)
Citation Context ...t paper, we will offer a new perspective on explaining these results. We will study what happens when the usual momentum space scattering amplitudes are Fourier transformed to Penrose’s twistor space =-=[7]-=-. We argue that the perturbative amplitudes in twistor space are supported on certain holomorphic curves. Results such as the holomorphy of the tree-level MHV amplitudes, as well as more complicated (... |

69 |
W.: Spinors and space-time. Volume 1. Two-spinor calculus and relativistic fields
- Penrose, Rindler
- 1984
(Show Context)
Citation Context ... 2, we review Yang-Mills helicity amplitudes and their description via spinors [17-24] and the MHV amplitudes. For expositions of this material, see [25,26]. For the use of spinors in relativity, see =-=[27,28]-=-. Then we describe the Fourier transform to twistor space. For general reviews of twistor theory, see [8,15,29-32]; for the twistor transform of the selfdual Einstein and Yang-Mills equations, see res... |

63 |
Helicity Amplitudes for Multiple Bremsstrahlung
- Xu, Zhang, et al.
- 1987
(Show Context)
Citation Context ...ed for 〈λi, λj〉, and [i j] for [ ˜ λi, ˜ λj]. 1 + 2 + 3 + 4 − 5 − 6 − 1 + 2 + 3 − 4 + 5 − 6 − 1 + 2 − 3 + 4 − 5 + 6 − X = 1 + 2 + 3 Y = 1 + 2 + 4 Z = 1 + 3 + 5 α 0 −[12]〈56〉〈4|Y |3〉 [13]〈46〉〈5|Z|2〉 β =-=[23]-=-〈56〉〈1|X|4〉 [24]〈56〉〈1|Y |3〉 [51]〈24〉〈3|Z|6〉 γ [12]〈45〉〈3|X|6〉 [12]〈35〉〈4|Y |6〉 [35]〈62〉〈1|Z|4〉 Our conjecture says again that these amplitudes should be supported on configurations in which all six p... |

58 |
Twistor theory: An approach to the quantization of fields and space-time
- Penrose, MacCallum
- 1972
(Show Context)
Citation Context ...pergravity is generally assumed to have negative energies and ghosts, the B model of CP 3|4 may be physically sensible only in the planar limit.) In twistor theory, it has been a longstanding problem =-=[15,16]-=- to understand how to use twistors to describe perturbative field theory amplitudes. Our proposal in the present paper differs from previous attempts mainly in that we consider families of holomorphic... |

58 | Twistor geometry and field theory. Cambridge Univ - Ward, Jr - 1988 |

53 |
Scattering Of massless lumps and nonlocal charges in the two-dimensional classical nonlinear sigma model,” Nucl
- Luscher, Pohlmeyer
- 1978
(Show Context)
Citation Context ... was first found in strong coupling in [71] and has also been found for weak coupling [72]. We therefore should look for such symmetry in the present framework. Along with many two-dimensional models =-=[73]-=-, the two-dimensional sigma model with target space CP M−1 has nonlocal symmetries that generate a Yang-Baxter or Yangian algebra, as investigated in [74]. However (in contrast to similar models in wh... |

50 |
Multiparton Amplitudes
- Mangano, Parke
- 1991
(Show Context)
Citation Context ...lly helicity violating (MHV) can be expressed in terms of a simple holomorphic or antiholomorphic function. This was first conjectured by Parke and Taylor based on computations in the first few cases =-=[1]-=-; the general case was proved by Berends and Giele [2]. (Unexpected simplicity and selection rules in Yang-Mills and gravitational helicity amplitudes were first found, as far as I know, by DeWitt [3]... |

40 |
The six gluon process as an example of Weyl-van der Waerden spinor calculus Nucl.Phys. B294
- Berends, Giele
- 1987
(Show Context)
Citation Context ...al complex line bundle which is the square of the Hopf bundle.) Suppose though that instead of being given only a lightlike vector pa˙a one is given a λ, that is a decomposition pa˙a = λa ˜ λ˙a. Then =-=[22,24]-=- we do have enough information to determine a polarization vector, up to a gauge transformation. To get a negative helicity polarization vector, we pick any positive helicity spinor ˜µ˙a that is not a... |

37 |
On selfdual gauge
- Ward
- 1977
(Show Context)
Citation Context ...the Fourier transform to twistor space. For general reviews of twistor theory, see [8,15,29-32]; for the twistor transform of the selfdual Einstein and Yang-Mills equations, see respectively [33] and =-=[34]-=-, as well as [35,36] for the Euclidean signature case. In section 3, we investigate the behavior of the perturbative Yang-Mills amplitudes in twistor space. We demonstrate (in various examples of tree... |

33 | Improved Analytic Techniques for Tree Graph Calculations and the G g q anti-q Lepton anti-Lepton Subprocess, Phys.Lett. B161 - Gunion, Kunszt - 1985 |

29 | Single bremsstrahlung processes in gauge theories - Berends, Kleiss, et al. - 1981 |

20 |
Multi - gluon helicity amplitudes involving a quark loop, Phys. Rev. D49
- Mahlon
- 1994
(Show Context)
Citation Context ...e one-loop diagrams with all gluons of the same helicity are non-zero in general. Indeed, they are given by a simple formula that was conjectured by Bern, Dixon, and Kosower [42] and proved by Mahlon =-=[43]-=-, following some early computations in special cases [44-45]. For a useful summary, see [46]. Interestingly, these amplitudes are polynomial (and in fact quartic) in ˜ λ, and hence are supported on a ... |

19 |
Quantum theory of gravity. iii. applications of the covariant theory, Phys. Rev
- DeWitt
- 1967
(Show Context)
Citation Context ...[1]; the general case was proved by Berends and Giele [2]. (Unexpected simplicity and selection rules in Yang-Mills and gravitational helicity amplitudes were first found, as far as I know, by DeWitt =-=[3]-=- for four particle amplitudes.) These unexpected simplifications have echoes, in many cases, in loop amplitudes, especially in the supersymmetric case. For a sampling of one-loop results, see the revi... |

17 |
An Interpretation of Classical Yang-Mills Theory
- Witten
- 1978
(Show Context)
Citation Context ... instantons. The string theory is the topological B model whose target space is the Calabi-Yau supermanifold CP 3|4 . This is the supersymmetric version of twistor space, as defined [9] and exploited =-=[10]-=- long ago. 1 From the string theory, we recover the tree level MHV amplitudes of gauge theory. They arise from a one-instanton computation that leads to a formalism similar to that suggested by Nair [... |

17 |
Atiyah, Geometry of Yang-Mills Fields (Lezioni Fermiane
- F
- 1979
(Show Context)
Citation Context ...form to twistor space. For general reviews of twistor theory, see [8,15,29-32]; for the twistor transform of the selfdual Einstein and Yang-Mills equations, see respectively [33] and [34], as well as =-=[35,36]-=- for the Euclidean signature case. In section 3, we investigate the behavior of the perturbative Yang-Mills amplitudes in twistor space. We demonstrate (in various examples of tree level and one-loop ... |

15 |
The Central programme of twistor theory
- Penrose
- 1999
(Show Context)
Citation Context .... For expositions of this material, see [25,26]. For the use of spinors in relativity, see [27,28]. Then we describe the Fourier transform to twistor space. For general reviews of twistor theory, see =-=[8,15,29-32]-=-; for the twistor transform of the selfdual Einstein and Yang-Mills equations, see respectively [33] and [34], as well as [35,36] for the Euclidean signature case. In section 3, we investigate the beh... |

13 |
Confinement And Chiral Symmetry Breaking
- D’Adda, Vecchia, et al.
- 1979
(Show Context)
Citation Context ...eet Supersymmetry The next step is to introduce world-sheet supersymmetry. Because CP M−1|P is a Kahler manifold, a supersymmetric sigma model with this target space (first constructed and studied in =-=[53,54]-=- in the case P = 0) will automatically have N = 2 worldsheet supersymmetry. We thus replace C with a super Riemann-surface with N = 2 supersymmetry, the fermionic coordinates being a complex spinor θ ... |

11 |
Yang-Baxter algebras of monodromy matrices in integrable quantum field theories”, Nucl. Phys. B240
- Vega, Eichenherr, et al.
- 1984
(Show Context)
Citation Context ...ework. Along with many two-dimensional models [73], the two-dimensional sigma model with target space CP M−1 has nonlocal symmetries that generate a Yang-Baxter or Yangian algebra, as investigated in =-=[74]-=-. However (in contrast to similar models in which the target space is, for example, a sphere), the quantum version of this model is believed to not be integrable [75]; presumably, the nonlocal symmetr... |

10 |
the quark model, and the 1/N expansion,” Nucl. Phys. B149
- Witten, “Instantons
- 1979
(Show Context)
Citation Context ...eet Supersymmetry The next step is to introduce world-sheet supersymmetry. Because CP M−1|P is a Kahler manifold, a supersymmetric sigma model with this target space (first constructed and studied in =-=[53,54]-=- in the case P = 0) will automatically have N = 2 worldsheet supersymmetry. We thus replace C with a super Riemann-surface with N = 2 supersymmetry, the fermionic coordinates being a complex spinor θ ... |

10 |
Comments on the Holomorphic Anomaly
- Cook, Ooguri, et al.
(Show Context)
Citation Context ... one, one encounters analytic torsion, and for higher genus one meets less familiar invariants, to whose study powerful methods including mirror symmetry and the holomorphic anomaly have been applied =-=[57]-=-. In our example of CP M−1|P , we want to take M = 4, because it is CP 3 (and its supersymmetric extensions), and not some other CP M−1 , that is related to four-dimensional 12 In this discussion, we ... |

9 | Twistor Quantization And Curved Space-Time - Penrose - 1968 |

8 |
Holomorphic matrix models
- Lazaroiu
(Show Context)
Citation Context ...able and the action is a holomorphic function, one must try to understand this path integral as a contour integral for each mode of A. (See [51] for matrix models based on such contour integrals, and =-=[64]-=- for a thorough discussion of the contours in that context.) In general, the result of the path integral may depend on the choice of contour. How to make sense of the path integral as a contour integr... |

6 |
The N = 2 (4) string is selfdual
- Siegel
(Show Context)
Citation Context ...L(4|4) symmetry. Moreover, the field content is almost recognizable (and will be altogether recognizable to readers familiar with investigations by Siegel of a chiral limit of super Yang-Mills theory =-=[65]-=-). A ′ is the gauge field of the N = 4 theory, while χ ′ and ˜χ ′ are the usual positive and negative chirality fermions, and φ ′ are the usual scalars. We still have to interpret G ′ , as well as the... |

5 |
Invariants of General Relativity and the Classification of Spaces,” Phys
- Witten
- 1959
(Show Context)
Citation Context ... 2, we review Yang-Mills helicity amplitudes and their description via spinors [17-24] and the MHV amplitudes. For expositions of this material, see [25,26]. For the use of spinors in relativity, see =-=[27,28]-=-. Then we describe the Fourier transform to twistor space. For general reviews of twistor theory, see [8,15,29-32]; for the twistor transform of the selfdual Einstein and Yang-Mills equations, see res... |

5 |
The Nonlinear Graviton,” Gen
- Penrose
- 1976
(Show Context)
Citation Context ...describe the Fourier transform to twistor space. For general reviews of twistor theory, see [8,15,29-32]; for the twistor transform of the selfdual Einstein and Yang-Mills equations, see respectively =-=[33]-=- and [34], as well as [35,36] for the Euclidean signature case. In section 3, we investigate the behavior of the perturbative Yang-Mills amplitudes in twistor space. We demonstrate (in various example... |

4 |
Selfduality
- Atiyah, Hitchin, et al.
- 1978
(Show Context)
Citation Context ...form to twistor space. For general reviews of twistor theory, see [8,15,29-32]; for the twistor transform of the selfdual Einstein and Yang-Mills equations, see respectively [33] and [34], as well as =-=[35,36]-=- for the Euclidean signature case. In section 3, we investigate the behavior of the perturbative Yang-Mills amplitudes in twistor space. We demonstrate (in various examples of tree level and one-loop ... |

4 | Superloops 3, Beta 0: A Calculation - Grisaru, Roček, et al. - 1981 |

4 |
Conservation Laws
- Goldschmidt, Witten
- 1980
(Show Context)
Citation Context ...the target space is, for example, a sphere), the quantum version of this model is believed to not be integrable [75]; presumably, the nonlocal symmetries are anomalous, as the local ones appear to be =-=[76]-=-. The supersymmetric CP M−1 model also has Yangian symmetry classically. Quantum mechanically, it is believed to be integrable with a factorizable S-matrix, and anomaly-free Yangian symmetry [77]. Gra... |

3 | Spinor techniques for calculating proton anti-proton to W or Z plus jets - Kleiss, Stirling - 1985 |

3 |
Simplifying algebra
- Chalmers, Siegel
- 1999
(Show Context)
Citation Context ...al complex line bundle which is the square of the Hopf bundle.) Suppose though that instead of being given only a lightlike vector pa˙a one is given a λ, that is a decomposition pa˙a = λa ˜ λ˙a. Then =-=[22,24]-=- we do have enough information to determine a polarization vector, up to a gauge transformation. To get a negative helicity polarization vector, we pick any positive helicity spinor ˜µ˙a that is not a... |

3 | One Loop Amplitudes for - Bern, Dixon, et al. - 1998 |

2 | Multi-Photon Production At High Energies - Mahlon, Yan - 1993 |

1 |
Twistor Diagrams,” Surveys
- Hodges, Huggett
- 1998
(Show Context)
Citation Context ...pergravity is generally assumed to have negative energies and ghosts, the B model of CP 3|4 may be physically sensible only in the planar limit.) In twistor theory, it has been a longstanding problem =-=[15,16]-=- to understand how to use twistors to describe perturbative field theory amplitudes. Our proposal in the present paper differs from previous attempts mainly in that we consider families of holomorphic... |

1 | Trident Production With Nuclear Targets,” Phys. Rev - Henry - 1967 |

1 | eds., Twistors - Bailey, Baston - 1990 |

1 |
One Gluon Corrections To Five Gluon Amplitudes
- Bern, Dixon, et al.
- 1993
(Show Context)
Citation Context ...only of λ and not ˜ λ (times a delta function of energy-momentum conservation). Denoting the corresponding one-loop amplitudes as Â1, the relation between them is Â1 = g 2 Â0(L1 + L2), (3.39) 42with =-=[41]-=- L1 = − 1 ǫ 2 L2 = 5∑ ln i=1 5∑ ( 2 µ −si,i+1 i=1 ( −si,i+1 −si+1,i+2 )ǫ ) ln ( −si+2,i+3 −si−2,i−1 ) + 5π2 6 . (3.40) Here si,j = (pi + pj) 2 . These amplitudes have been computed with dimensional re... |

1 | One-Loop Gauge Theory Amplitudes With An Arbitrary Number Of External Legs,” hep-ph/9405248
- Bern, Dixon, et al.
(Show Context)
Citation Context ...ey are given by a simple formula that was conjectured by Bern, Dixon, and Kosower [42] and proved by Mahlon [43], following some early computations in special cases [44-45]. For a useful summary, see =-=[46]-=-. Interestingly, these amplitudes are polynomial (and in fact quartic) in ˜ λ, and hence are supported on a degree one curve of genus zero, by the same argument that we give momentarily for General Re... |

1 | The Three Loop Beta Function - Avdeev, Tarasov - 1982 |

1 |
A Relation Among Approaches To Integrability
- Dolan, Nappi, et al.
- 2003
(Show Context)
Citation Context ...eems to have an extended infinitedimensional symmetry group that can be described as Yangian symmetry. This result was first found in strong coupling in [71] and has also been found for weak coupling =-=[72]-=-. We therefore should look for such symmetry in the present framework. Along with many two-dimensional models [73], the two-dimensional sigma model with target space CP M−1 has nonlocal symmetries tha... |

1 |
in Non-linear Equations in Classical and Quantum Field Theory
- Abdalla
- 1982
(Show Context)
Citation Context ...o be [76]. The supersymmetric CP M−1 model also has Yangian symmetry classically. Quantum mechanically, it is believed to be integrable with a factorizable S-matrix, and anomaly-free Yangian symmetry =-=[77]-=-. Granted this, Yangian symmetry will also hold for CP M−1|P , as the anomalies generated by Feynman diagrams really only depend on M − P. If we set M − P = 0, even more anomalies (such as the beta fu... |