D3-brane loop amplitudes from M5-brane tree amplitudes

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 D3brane 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.

Propagators, BCFW recursion and new scattering equations at one loop

“…However, in contrast to the maximally supersymmetric case, the half-integrand I (1) NS does not vanish for tadpole-like worldsheet geometries, 34 and we thus expect the worldsheet formulas to lead to unphysical poles in the loop integrand. Contributions from similar poles in the 'linear' 32 We prove these statements in section 8.2. 33 This construction does indeed give the pure Yang-Mills integrand in the 'linear' formalism, i.e., with the 'old' one-loop scattering equations [24].…”

“…Both have been fruitful for studying theories of massless particles, most importantly gauge theory and gravity, and have brought numerous insights. They have also been extended to loop level, in various approaches; see, e.g., [11][12][13][14][15][16][17][18][19][20] for the BCFW recursion relations and [21][22][23][24][25][26][27][28][29][30][31][32][33] for the scattering equations.…”

Electromagnetic duality and D3-brane scattering amplitudes beyond leading order

“…Recently, a beautiful CHY formula based on polarized scattering equations, appeared for the complete tree-level S-matrix of the N = 4 probe D3-brane (N f = 4 and N s = 6), as well as similar formulae for the 6d parent theories describing probe N = (1, 1) D5-and N = (2, 0) M5-branes [16]. Such higher-dimensional constructions have recently been used to obtain 1-loop integrands for the D3-brane theory in dimensional regularization [17].…”

“…Then, at z = 1, the shifted momenta are projected onto the 3d subspace normal to N µ : p µ i N µ z=1 = 0. We implement this shift in terms of spinor-helicity brackets via the holomorphic shift 17) where N = N µ σ µ and a i are constants constrained by momentum conservation,…”

Quantum corrections to generic branes: DBI, NLSM, and more

“…A study of one-loop corrections to specific brane models with additional fields can be found in[86][87][88].…”