Tree and loop amplitudes in open twistor string theory

Dolan, L.; Goddard, Peter

doi:10.1088/1126-6708/2007/06/005

Cited by 36 publications

(83 citation statements)

References 29 publications

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“…In addition, there are ghost fields b, c, u, v, and world sheet gauge fields all summarized in [20]. The fields Z I have conformal spin zero and are relabeled as four boson fields λ a , µȧ, 1 ≤ a,ȧ ≤ 2 and four fermion fields ψ m , 1 ≤ m ≤ 4.…”

Section: Vertex Operators and Canonical Quantizationmentioning

confidence: 99%

“…to perform the k-integration, this becomes the vertex used by Berkovits and Witten, except they omit the A b , A bc , and A bcd terms [20,2,22,3]. In that form, it is easy to see that the…”

Section: Vertex Operatorsmentioning

confidence: 99%

“…We compute the conformal couplings in detail, as they should be important in further study of the loop calculation [20].…”

Section: Introductionmentioning

confidence: 99%

“…We use the twistor string canonical quantization described in [20,21] and follow their notation. In section 2, we give the vertex operators for all states in the conformal supergravity multiplets, as outlined by Berkovits and Witten [3].…”

Section: Introductionmentioning

confidence: 99%

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Conformal supergravity tree amplitudes from open twistor string theory

Dolan

Ihry

2009

Nuclear Physics B

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We display the vertex operators for all states in the conformal supergravity sector of the twistor string, as outlined by Berkovits and Witten. These include 'dipole' states, which are pairs of supergravitons that do not diagonalize the translation generators. We use canonical quantization of the open string version of Berkovits, and compute N -point tree level scattering amplitudes for gravitons, gluons and scalars. We reproduce the Berkovits-Witten formula for maximal helicity violating (MHV) amplitudes (which they derived using path integrals), and extend their results to the dipole pairs. We compare these trees with those of Einstein gravity field theory. email: ldolan, jihry@physics.unc.edu IntroductionWe pursue the tree amplitudes for graviton scattering in conformal gravity, described by twistor string theory. The twistor string Conformal gravity field theories [4,5] provided early examples of finite field theories of gravity [6,7]. They are not unitary theories, but have interesting structure and continue to provoke comments about possible uses [8]. Of course the conformal supergraviton states have zero norm, due to the lack of unitarity [9]. Nevertheless, the equivalence of the twistor string with this field theory system can be exploited to derive conformal gravity tree level scattering amplitudes hard to access in the field theory. We compute the gravity trees as a step toward learning how to decouple them in the twistor string. This would result in a perturbative string theory for super Yang-Mills (with no tower of massive states), and the computational advantage one hopes for in a string theory vs. field theory description.Various efforts towards a QCD string are discussed in [10].We work in a spinor helicity basis [11]- [13], and compare the conformal gravity tree amplitudes with those of Einstein gravity [14]- [19]. The conformal gravity trees have fewer poles.We compute the conformal couplings in detail, as they should be important in further study of the loop calculation [20].Computation is done in the Berkovits open string version [2]. We use the twistor string canonical quantization described in [20,21] and follow their notation. In section 2, we give the vertex operators for all states in the conformal supergravity multiplets, as outlined by Berkovits and Witten [3]. These include the dipole states, which form pairs of supergravitons, where one state in each pair does not diagonalize the translation generators, and is not a momentum eigenstate. We show all supergraviton states have zero norm in our basis.In section 3, three-point scattering amplitudes for gluons and gravitons and scalars, with both one and two negative helicities are calculated. We include cases for both members the dipoles, and find a momentum derivative appearing in amplitudes for states that do not diagonalize the translations generators. These amplitudes still have translational invariance.In section 4, we extend our results to N -point tree level amplitudes for these dipole pairs. We reproduce the Berkovits-Witte...

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Section: Vertex Operators and Canonical Quantizationmentioning

confidence: 99%

“…to perform the k-integration, this becomes the vertex used by Berkovits and Witten, except they omit the A b , A bc , and A bcd terms [20,2,22,3]. In that form, it is easy to see that the…”

Section: Vertex Operatorsmentioning

confidence: 99%

“…We compute the conformal couplings in detail, as they should be important in further study of the loop calculation [20].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Conformal supergravity tree amplitudes from open twistor string theory

Dolan

Ihry

2009

Nuclear Physics B

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“…The results of the paper and their implications are reviewed in section 9. The representations of amplitudes developed here may lead to simple explicit representations and diagrammatic rules for gluon tree amplitudes and approaches to studying loop amplitudes in twistor string theory [16]- [23].…”

Section: Introductionmentioning

confidence: 99%

Complete equivalence between gluon tree amplitudes in twistor string theory and in gauge theory

Dolan

Goddard

2012

J. High Energ. Phys.

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The gluon tree amplitudes of open twistor string theory, defined as contour integrals over the ACCK link variables, are shown to satisfy the BCFW relations, thus confirming that they coincide with the corresponding amplitudes in gauge field theory. In this approach, the integration contours are specified as encircling the zeros of certain constraint functions that force the appropriate relation between the link variables and the twistor string worldsheet variables. To do this, methods for calculating the tree amplitudes using link variables are developed further including diagrammatic methods for organizing and performing the calculations.

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