Some properties of scattering amplitudes in supersymmetric theories

Grisaru, Marcus T.; Pendleton, Hugh

doi:10.1016/0550-3213(77)90277-2

Cited by 236 publications

(214 citation statements)

References 13 publications

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“…At the level of the amplitude this is of course in complete agreement with the appropriate supersymmetric Ward identity [14].…”

supporting

confidence: 52%

“…So in fact both of these fermion amplitudes are zero independent of our choice for x. This can also be seen as a consequence of supersymmetric Ward identities [14].…”

mentioning

confidence: 84%

“…Since the second order rules bear such a close resemblance to the Feynman rules for a scalar interacting with a gauge field, it is worth investigating whether they shed light on the the supersymmetric Ward identities [14,13]. We shall, for the sake of example, consider the simple relationship between the A(−+; + .…”

mentioning

confidence: 99%

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Second order fermions in gauge theories

Morgan

1995

Physics Letters B

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The second order formalism for fermions provides a description of fermions that is very similar to that of scalars. We demonstrate that this second order formalism is equivalent to the standard Dirac formalism. We do so in terms of the conventional fermionic Feynman rules. The second order formalism has previously proven useful for the computation of fermion loops, here we describe how the corresponding rules can be applied to the calculation of amplitudes involving external fermions, including tree-level processes and processes with more than one fermion line. We comment on the supersymmetric identities relating fermions and scalars and the associated simplifications to perturbative calculations that are then more transparent.

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“…At the level of the amplitude this is of course in complete agreement with the appropriate supersymmetric Ward identity [14].…”

supporting

confidence: 52%

“…So in fact both of these fermion amplitudes are zero independent of our choice for x. This can also be seen as a consequence of supersymmetric Ward identities [14].…”

mentioning

confidence: 84%

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Second order fermions in gauge theories

Morgan

1995

Physics Letters B

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“…The one-loop relation (5.19) is a direct consequence of the supersymmetry Ward identities for S-matrix elements first obtained by Grisaru, Pendleton and van Nieuwenhuizen [69,70]. Those identities hold for massive as well as for massless supermultiplets in the loop.…”

Section: The All '+' Helicity Amplitudes In the Euler-heisenberg Apprmentioning

confidence: 76%

Two-loop self-dual Euler-Heisenberg Lagrangians (I): Real part and helicity amplitudes

Dunne¹,

Schubert²

2002

J. High Energy Phys.

117

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We show that, for both scalar and spinor QED, the two-loop Euler-Heisenberg effective Lagrangian for a constant Euclidean self-dual background has an extremely simple closed-form expression in terms of the digamma function. Moreover, the scalar and spinor QED effective Lagrangians are very similar to one another. These results are dramatic simplifications compared to the results for other backgrounds. We apply them to a calculation of the low energy limits of the two-loop massive N-photon 'all +' helicity amplitudes. The simplicity of our results can be related to the connection between self-duality, helicity and supersymmetry.

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“…In particular, the supersymmetric Ward identities determine in these four dimensions [19] A(+ + · · · +) = 0 , 12) with an exception only for the three particle A(+ + −) and A(− − +) amplitude which vanish generically only for all momenta in R (1,3) . The input in this argument is nothing more than simple representation theory of on-shell N = 1 space-time supersymmetry and the absence of helicity-violating fermion amplitudes.…”

Section: Effective Supersymmetrymentioning

confidence: 99%

MHV, CSW and BCFW: field theory structures in string theory amplitudes

Boels

Larsen

Obers³

et al. 2008

J. High Energy Phys.

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Motivated by recent progress in calculating field theory amplitudes, we study applications of the basic ideas in these developments to the calculation of amplitudes in string theory. We consider in particular both non-Abelian and Abelian open superstring disk amplitudes in a flat space background, focusing mainly on the four-dimensional case. The basic field theory ideas under consideration split into three separate categories. In the first, we argue that the calculation of α ′ -corrections to MHV open string disk amplitudes reduces to the determination of certain classes of polynomials. This line of reasoning is then used to determine the α ′3 -correction to the MHV amplitude for all multiplicities. A second line of attack concerns the existence of an analog of CSW rules derived from the Abelian Dirac-Born-Infeld action in four dimensions. We show explicitly that the CSW-like perturbation series of this action is surprisingly trivial: only helicity conserving amplitudes are non-zero. Last but not least, we initiate the study of BCFW on-shell recursion relations in string theory. These should appear very naturally as the UV properties of the string theory are excellent. We show that all open four-point string amplitudes in a flat background at the disk level obey BCFW recursion relations. Based on the naturalness of the proof and some explicit results for the five-point gluon amplitude, it is expected that this pattern persists for all higher point amplitudes and for the closed string.

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Some properties of scattering amplitudes in supersymmetric theories

Cited by 236 publications

References 13 publications

Second order fermions in gauge theories

Second order fermions in gauge theories

Two-loop self-dual Euler-Heisenberg Lagrangians (I): Real part and helicity amplitudes

MHV, CSW and BCFW: field theory structures in string theory amplitudes

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