On all-order higher-point Dp–D̄p̄ effective actions

Abstract

In this paper we derive a class of contributions to all orders in α to the effective action of D-braneanti D-brane systems in Type II String Theory, considering an amplitude involving a closed-string Ramond-Ramond state and four open-string states: two tachyons, a scalar and a gauge boson. This type of amplitude arises in both Type IIA and Type IIB strings, and reveals a number of new effective couplings. Furthermore, we derive a series representation for the result that goes beyond a factorized limit that was recently studied, and which is expected to apply to more general six-point amplitudes of superstrings, including external fermions. * Electronic address: riccardo.antonelli@sns.it † Electronic address: ivano.basile@sns.it ‡ Electronic address: ehsan.hatefi@sns.it 1 For in-depth discussions of open strings, see [1]. 2 For earlier detailed treatments, see [2-4]. 3 Similar corrections can also be found in the case of S-branes [7]. 3 are not present. Perturbative scattering amplitudes involve structures that are largely constrained, which makes it possible to reconstruct them, up to an overall coefficient, via Effective Field Theory (EFT) analyses of poles and symmetries in various channels. On the other hand, ab-initio computations of the corresponding string amplitudes have the virtue of fixing the α expansion, and thus the EFT couplings, to all orders. This procedure has been followed systematically in the literature [33-38], yielding generalizations of the standard Dirac-Born-Infeld (DBI), Myers [39] and Wess-Zumino (WZ) terms 4 [40]. The crucial interplay between D-branes and RR potentials has been thoroughly studied in the literature [42], but theirrole is yet to be fully dissected.The paper is organized as follows. In Section 2 we summarize a number of results that were obtained in earlier works, which provides a starting point for our considerations.Specifically, we discuss all-order α corrections to couplings that originate from amplitudes a single closed-string mode and less than four open-string ones. We focus on RR closed-string states, and thus on couplings related to WZ terms. In Section 3 we present the new result on the five-string scattering amplitude under consideration. From the point of view of the (open) world-sheet CFT, this is akin to a six-point correlator, whose vertex operators are to be integrated accordingly. The result is organized in terms of a class of integrals, whose detailed study is postponed to Section 4. In Section 3.3 we briefly discuss a factorized limit in which the integrals can be evaluated in closed form. In sections 3.4 and 3.5, after a proper discussion of bulk singularities, selection rules [43] and EFT methods, we recover the result from the low-energy perspective. In Section 4 we go beyond the factorized limit of Section 3.3, obtaining an expansion for the integrals, whose leading term reproduces it.While the resulting expansion entails a limit of series with decreasing convergence rate, weshow that the procedure is well-defined. We conclude in Section 5 with a su...

All-order quartic couplings in highly symmetric D-brane-anti-D-brane systems

“…whose properties were described in detail in [90]. As explained in [90], one can work with the soft limit of the six point function as 4k 2 • p → 1 which gives an analytic expression for the amplitude, and some of the integrals can be found in appendix B of [88]. They are subject to the on-shell condition…”

“…Other contact terms can be reproduced by properly adding higher derivative corrections; for more details see [90]. The amplitude has infinitely many massless poles in the C p−3 case, and there are infinitely many tachyon poles in the C p−1 case, where, for the sake of obtaining correct higher derivative corrections, it is sufficient to reconstruct the infinite set of gauge field poles.…”

“…where N 3 , N 4 are the multiplications of various Gamma functions; for their explicit forms, see appendix B of [90].…”

“…The S-matrix element for scattering of one RR particle and four tachyons on a DD-brane is given in[91], and its relation to the Veneziano amplitude[92] is spelled out in there as well. Moreover, the allorder corrections to fermionic couplings[93] as well as a power series representation of the corresponding string amplitudes were obtained well beyond the factorized limit in[90] 5. If D is a differential operator acting in an algebra of functions, then we use the convention Df g ≡ (Df )g.…”

Supersymmetry breaking, brane dynamics and Swampland conjectures

“…Aside from cases where the leading contribution vanishes, one can expect that couplings of this type be required to all orders, at least in α , in order to circumvent a Dine-Seiberg-like argument [121]. Some progress along these lines has been achieved via all-order string-amplitude computations (see, e.g., [122,123]) and via T-duality in the context of cosmology [124][125][126][127][128][129][130][131][132][133]. Furthermore, from the perspective of holography, it would be interesting to understand whether the IR fixed-point structure exhibited by the JHEP10(2021)080 near-horizon AdS throats discussed in section 3 can be reproduced via strong-coupling effects in the putative dual gauge theory.…”