Abstract
We study loop corrections to scattering amplitudes in the world-volume theory of a probe D3-brane, which is described by the supersymmetric Dirac-Born-Infeld theory. We show that the D3-brane loop superamplitudes can be obtained from the tree-level superamplitudes in the world-volume theory of a probe M5-brane (or D5-brane). The M5-brane theory describes self-interactions of an abelian tensor supermultiplet with (2, 0) supersymmetry, and the tree-level superamplitudes are given by a twistor formula. We apply the construction to the maximally-helicity-violating (MHV) amplitudes in the D3- brane theory at one-loop order, which are purely rational terms (except for the four-point amplitude). The results are further confirmed by generalised unitarity methods. Through a supersymmetry reduction on the M5-brane tree-level superamplitudes, we also construct one-loop corrections to the non-supersymmetric D3-brane amplitudes, which agree with the known results in the literature.
Highlights
The tree-level superamplitudes in the M5-brane theory and D5-brane theory are described by twistor formulations either based on rational maps [7,8,9], or based on the polarised scattering equations [10, 11]1
We study loop corrections to scattering amplitudes in the world-volume theory of a probe D3-brane, which is described by the supersymmetric Dirac-Born-Infeld theory
We show that the D3-brane loop superamplitudes can be obtained from the tree-level superamplitudes in the world-volume theory of a probe M5-brane
Summary
The tree-level amplitudes in the D3-brane theory are obtained through a dimension reduction by setting all the external momenta of the M5-brane amplitudes in 4D [7]. At four points, from (2.31), we find the superamplitude with two massive and two massless states is given by. At six points, the factorisation terms of the tree-level amplitude with two massive states are shown, where each diagram takes the form of d4ηK δ8(QL). This is consistent with the known fact that a six-point supersymmetric contact term with six derivatives is not allowed by (2, 0) (and (1, 0)) supersymmetry [44] This is in agreement with what was found in [40] for the all-plus and single-minus amplitudes (with two additional massive scalars).. Consider the eight-point superamplitudes, for which the factorisation terms schematically take the form of d4ηPK1
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