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

Abstract

The conventional S-matrix approach to the (tree level) open string low energy effective lagrangian assumes that, in order to obtain all its bosonic α N order terms, it is necessary to know the open string (tree level) (N +2)-point amplitude of massless bosons, at least expanded at that order in α . In this work we clarify that the previous claim is indeed valid for the bosonic open string, but for the supersymmetric one the situation is much more better than that: there are constraints in the kinematical bosonic terms of the amplitude (probably due to Spacetime Supersymmetry) such that a much lower open superstring n-point amplitude is needed to find all the α N order terms. In this 'revisited' S-matrix approach we have checked that, at least up to α 4 order, using these kinematical constraints and only the known open superstring 4-point amplitude, it is possible to determine all the bosonic terms of the low energy effective lagrangian. The sort of results that we obtain seem to agree completely with the ones achieved by the method of BPS configurations, proposed about ten years ago. By means of the KLT relations, our results can be mapped to the NS-NS sector of the low energy effective lagrangian of the type II string theories implying that there one can also find kinematical constraints in the N -point amplitudes and that important informations can be inferred, at least up to α 4 order, by only using the (tree level) 4-point amplitude.

Ambitwistor formulations of R2 gravity and (DF)2 gauge theories

“…We should perhaps note that Lagrangians with similar operators have previously been studied for phenomenological reasons in [13][14][15][16][17][18] and because the operators arise as corrections in the α expansion of bosonic open string theory [19][20][21]. It is however the specific theory introduced in [6] that interests us as it satisfies color-kinematics duality and gives conformal gravity through the double copy.…”

“…After gauge-fixing e = χ = 0, one gets the BRST charge 18) whose cohomology contains the vertex operator 19) together with corresponding picture-number-zero or integrated versions, where µ 1 , ν 2 combine to form the graviton, Kalb-Ramond and dilaton polarizations. Restricting to gravitons, one can show that the tree-level n-point correlation function of these vertex operators gives rise to the CHY formula (4.19).…”

Remarks on the mixed Ramond–Ramond, open string scattering amplitudes of BPS, non-BPS and brane–anti-brane

“…23 Replacing the vertex operators and performing all the correlators by using the Wick theorem, one can investigate the whole of the amplitudes as follows: …”

“…Here we are working with a five point function and to the best of our knowledge the best 23 The following vertices with their correct Chan-Paton factor for Dbrane-anti-D-brane are taken into account:…”

“…Having set up this formalism, one may end up obtaining several new couplings for all BPS branes in the RNS formalism [18][19][20][21][22][23] and eventually one could investigate a proposal for the corrections to some of the couplings [24]. In particular it is shown that some of these couplings must be employed to be able to work with some of the applications of either M-theory [25,26] or gauge-gravity duality [27].…”