F5 contributions to the non-Abelian Born–Infeld action from a supersymmetric Yang–Mills five-point function

Abstract

We consider the N = 4 supersymmetric Yang-Mills theory in four dimensions. We compute the one-loop contributions to the effective action with five external vector fields and compare them with corresponding results in open superstring theory. Our calculation determines the structure of the F 5 terms that appear in the nonabelian generalization of the Born Infeld action. The trace operation on the gauge group indices receives contributions from the symmetric as well as the antisymmetric part. We find that in order to study corrections to the symmetrized trace prescription one has to consistently take into account derivative contributions not only with antisymmetrized products ∇ [µ ∇ ν] but also with symmetrized ones ∇ (µ ∇ ν) .

Derivative corrections in 10-dimensional super-Maxwell theory

“…In principle, there are now two possibilities: they can either be cancelled separately, or not. In the latter case we need both contributions at the same time, and then there must be relations between the coefficients a (4,4) a (4,4) and a (2,0) a (6,8) . So it is indeed possible that a priori independent invariants are related to each other at higher orders in the iteration.…”

Supersymmetric Yang-Mills theory at order α′ 3

“…This method also yields an effective action at α ′ 3 , now directly in d = 10. Although [12] and [13] find the same (DF ) 2 F 2 terms, they disagree on the F 5 contributions.…”

Revisiting the S-matrix approach to the open superstring low energy effective lagrangian

“…They can be calculated in terms of Beta and Hypergeometric functions. Although not immediately, the coefficients of the first terms of their α expansion can be obtained 13 , for example [16] …”

“…Also, it is clear that the Symmetrized Trace prescription does not work already at α 3 order since the usual Born-Infeld lagrangian only contains even powers of α and it is known that the α 3 terms are not zero in the nonabelian low energy effective action [11][12][13][14][15][16].…”

“…Before the work in [16], the S-matrix approach for the α correction terms in the low energy effective action had been only used with knowledge of 4-point amplitudes [12], which was already insufficient to determine all the α 3 terms. Alternative methods, mainly based on Supersymmetry, arised to obtain the complete list of nonabelian terms at each order in α , whenever possible [13,15,[27][28][29][30][31][32][33][34]. In some cases these methods obtained the complete superinvariant at a given order in α , either in component fields [29,30,33,34] or in terms of superfields [28,31] (in the case of D=4).…”