On the KKLT goldstino

Abstract

We construct general asymptotically Klebanov-Strassler solutions of a five dimensional SU (2)× SU (2) × Z 2 × Z 2R truncation of IIB supergravity on T 1,1 , that break supersymmetry. This generalizes results in the literature for the SU (2) × SU (2) × Z 2 × U (1) R case, to a truncation that is general enough to capture the deformation of the conifold in the IR. We observe that there are only two SUSY-breaking modes even in this generalized set up, and by holographically computing Ward identities, we confirm that only one of them corresponds to spontaneous breaking: this is the mode triggered by smeared anti-D3 branes at the tip of the warped throat. Along the way, we address some aspects of the holographic computation of one-point functions of marginal and relevant operators in the cascading gauge theory. Our results strengthen the evidence that if the KKLT construction is meta-stable, it is indeed a spontaneously SUSY-broken (and therefore bona fide) vacuum of string theory. 1 bulk supersymmetry, the corresponding state in the dual theory should be one where SUSY is spontaneously broken, which means that it should be characterized by a goldstino mode. Such a mode was indeed identified in [13] and later in [14] within the context of a certain five dimensional SU (2) × SU (2) × Z 2 × U (1) R truncation of IIB supergravity on T 1,1 using the holographic renormalization technology developed by [15].In this paper, our goal is to extend these results to an SU (2)×SU (2)×Z 2 ×Z 2R truncation by including supergravity fields which are not neutral under the R-symmetry: the previous constructions [13,14] were working with Klebanov-Tseytlin (KT) [16] asymptotics, whereas we will deal with the full Klebanov-Strassler. Klebanov-Tseytlin geometry is singular in the IR and cannot incorporate the deformation of the conifold, while Klebanov-Strassler is a fully regular solution. The (implicit or explicit) hope of the calculations in [13,14] was that since the deformation parameter is a supersymmetric perturbation, it is unlikely to destroy the claims about the SUSY-breaking perturbations. But it must be borne in mind that to discuss this question adequately, one must work with a fully consistent truncation that allows the deformation in the first place, and see whether (a) such a truncation allows for more SUSYbreaking parameters in the UV asymptotic solution 5 , and (b) whether the holographic Ward identities [14,17] get modified in any substantive way. We will answer both these questions in the negative in this paper, by working with the SU (2) × SU (2) × Z 2 × Z 2R truncation.The price we pay for working with a more realistic truncation is that there are extra fields in the system which make the problem more complicated. More conceptually, we will see that the extra fields that we turn on correspond to relevant sources, and that the mixing 6 of fields that they cause on the supergravity side needs to be suitably taken care of. In the U (1) case, only marginal sources were present and their mixing was dealt with [14] by defin...

Supersymmetric embedding of antibrane polarization

“…For example, before adding anti-D3-branes to the KS geometry, the holographic dual of KS is given by a nonconformal N = 1 cascading gauge theory [48]. The effect of antibranes can then be included by adding a particular nonsupersymmetric perturbation to the cascading gauge theory [57] and it was shown in subsequent work [58,59] that the resulting gauge theory indeed contains a massless fermion, as expected if the supersymmetry breaking was spontaneous. Although this is suggestive, in these approaches the perturbations describing anti-D3-branes still explicitly break supersymmetry.…”

Bounds on slow roll and the de Sitter Swampland

“…Our discussion in this paper clarifies this point by noting that the bound should be understood as a bound on single field slow roll itself, and therefore a high number of e-folds is pretty much in direct contradiction with it. 14 Inflation in many situations is known to have problems due to trans-Planckian field ranges during slow roll, and it has often been suggested (eg., [28,[36][37][38]) that one way to avoid this is to have a large number of (axionic?) fields like in N-flation.…”

Supersymmetric anti-D3-brane action in the Kachru-Kallosh-Linde-Trivedi setup

“…All of these developments have broadened into a variety of different research directions and led to many interesting related results during the last few years; see, e.g., Refs. [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. However, so far nobody has succeeded in writing down the full four-dimensional low-energy effective supergravity action that includes all anti-D3-brane world-volume fields in the KKLT background.…”