We study the brane/flux annihilation in the double-throat system in which the corresponding cycles of two throats are homologically equivalent. When we put $\overline{\rm D3}$-branes at only one of throat tips, two throats are no longer identical. Then the brane/flux annihilation can be interpreted as the process for reducing the difference between two throat geometries through the transition to the supersymmetric vacuum. To see this, we describe the changes in the amounts of the NSNS 3-form flux supporting the B-cycle contained in two throat regions during the brane/flux annihilation. We also compare our analysis with the recently proposed thraxion scenario, which also describes the inequivalence of two throats caused by the different NSNS 3-form flux distributions in two throat regions.
We discuss the properties of a class of exact dynamical solutions of the DBI action in various dimensions. They can be interpreted as shock waves of the nonlinear theory. They can also describe two parallel branes connected by a throat within a Minkowski bulk. We analyze issues related to the conservation of energy in these systems. We also discuss possible applications in particle physics and cosmology.
We analyze behaviour of D3-branes in BGMPZ throat geometry. We show that although single brane has some of the moduli stabilized multi-brane system tends to expand and form a bound state. Such a system loses non-abelian gauge symmetry.
Dynamics of D3-branes in models of warped D3-D7 inflationary set up is studied where perturbative $α'$ correction to the Kähler potential and the nonperturbative corrections to the superpotential are included. It is shown that a dS minimum can be obtained without introducing anti-branes. Some specific configurations of D7-branes embedding were studied. After stabilizing the angular directions, it is shown that the resulting D3-D7 potential of the radial position of the D3-brane is too steep to allow slow-roll inflation. Depending on D7-branes embedding and the stabilized angular directions, th…
We exhibit bound states in the spectrum of non-compact D-branes in N=2 Liouville conformal field theory. We interpret these states in the study of D-branes in the near-horizon limit of Neveu-Schwarz five-branes spread on a topologically trivial circle. We match semi-classical di-electric and repulsion effects with exact conformal field theory results and describe the fate of D-branes hitting NS5-branes. We also show that the bound states can give rise to massless vector and hyper multiplets in a low-energy gauge theory on D-branes deep inside the throat.
We first briefly present a consistent world-volume Lagrangian description of lightlike p-branes (LL-branes) in two equivalent forms - a Polyakov-type and a dual to it Nambu-Goto-type formulations. The most important characteristic features of LL-brane dynamics are: (i) the brane tension appears as a non-trivial additional dynamical degree of freedom; (ii) consistency of LL-brane dynamics in a spherically or axially symmetric gravitational background of codimension one requires the presence of an event horizon which is automatically occupied by the LL-brane ("horizon straddling"). Next we consi…
We compute the force between a stack of smeared antibranes at the bottom of a warped throat and a stack of smeared branes at some distance up the throat, both for anti-D3 branes and for anti-M2 branes. We perform this calculation in two ways: first, by treating the antibranes as probes in the background sourced by the branes and second, by treating the branes as probes in the candidate background sourced by the antibranes. These two very different calculations yield exactly the same expression for the force, for all values of the brane-antibrane separation. This indicates that the force betwee…
We investigate the 3-form singularities that are typical to anti-brane solutions in supergravity and check whether they can be cloaked by a finite temperature horizon. For anti-D3-branes in the Klebanov-Strassler background, this was already shown numerically to be impossible when the branes are partially smeared. In this paper, we present analytic arguments that also localised branes remain with singular 3-form fluxes at both zero and finite temperature. These results may have important, possibly fatal, consequences for constructions of meta-stable de Sitter vacua through uplifting.
We compute the imaginary self-dual (ISD) and imaginary anti-self-dual (IASD) fluxes for the Klebanov-Strassler background perturbed by a stack of p anti-D3 branes. We show that, at linear order in p, they both have a singularity in the near-brane region. While one can argue that the IASD flux may disappear at full non-linear level, no such argument exists for the ISD mode. An analogy with anti-D6 backreaction suggests that such singularity may survive once full backreaction is taken into account and may be a universal feature of anti-brane solutions.
In a previous work, we have shown that, like BPS Dp branes, bulk gravity gets decoupled from the brane even for the non-susy Dp branes of type II string theories indicating a possible extension of AdS/CFT correspondence for the non-supersymmetric case. In that work, the decoupling of gravity on the non-susy Dp branes has been shown numerically for the general case as well as analytically for some special case. Here we discuss the decoupling limit and the throat geometry of the non-susy D3 brane when the charge associated with the brane is very large. We show that in the decoupling limit the th…
We generalize the swampland criterion forbidding stable non-supersymmetric AdS vacua and propose a new swampland conjecture forbidding stable non-supersymmetric "locally AdS" warped throats. The conjecture is motivated by the properties of systems of fractional D3-branes at singularities, and can be used to rule out large classes of warped throats with supersymmetry breaking ingredients, and their possible application to de Sitter uplift. In particular, this allows to reinterpret the runaway instabilities of the gravity dual of fractional branes in the dP$_1$ theory, and to rule out warped thr…
We embed the supersymmetry breaking mechanism in N=1 SQCD of hep-th/0602239 in a smooth superstring theory using D-branes in the background R^4 \times SL(2)_{k=1}/U(1) which smoothly captures the throat region of an intersecting NS5-brane configuration. A controllable deformation of the supersymmetric branes gives rise to the mass deformation of the magnetic SQCD theory on the branes. The consequent instability on the open string worldsheet can be followed onto a stable non-supersymmetric configuration of D-branes which realize the metastable vacuum configuration in the field theory. The new b…
We study rolling radion dynamics of electrified D-brane in NS5-brane background, both in effective field theory and in full open string theory. We construct exact boundary states and, from them, extract conserved Noether currents. We argue that T-duality and Lorentz boost offer an intuitive approach. In the limit of large number of NS5-branes, both boundary wave functions and conserved currents are sharply peaked and agree with those deduced from the effective field theory. As the number of NS5-branes is reduced, width around the peak becomes wider by string corrections. We also study radiativ…
This article discusses model-building scenarios including anti-D3-/D7-branes, in which supersymmetry is broken spontaneously, despite having no scale at which sparticles appear and standard supersymmetry is restored. If the branes are placed on singularities at the tip of warped throats in Calabi-Yau orientifold flux compactifications, they may give rise to realistic particle spectra, closed- and open-string moduli stabilisation with a Minkowski/de Sitter uplift, and a geometrical origin for the scale hierarchies. The paper derives the low-energy effective field theory description for such sce…
We describe duality cascades and their infrared behavior for systems of D3-branes at singularities given by complex cones over del Pezzo surfaces (and related examples), in the presence of fractional branes. From the gauge field theory viewpoint, we show that D3-branes probing the infrared theory have a quantum deformed moduli space, given by a complex deformation of the initial geometry to a simpler one. This implies that for the dual supergravity viewpoint, the gauge theory strong infrared dynamics smoothes out the naked singularities of the recently constructed warped throat solutions with …
We consider the Penrose limit of the solution of D5-brane given in the Anti-de Sitter space and analyse the shape of the D5-brane in the pp-wave background. We find that the D5-brane leads to the branes and the throats connecting the branes. The branes spread on R^4 with periodic values of the light-cone time x^+ and the throats lie along x^+. We also give some comments on holography.
We present a scenario where brane inflation arises more generically. We start with D3 and anti-D3-branes at the infrared ends of two different throats. This setup is a natural consequence of the assumption that in the beginning we have a multi-throat string compactification with many wandering anti-D3-branes. A long period of inflation is triggered when D3-branes slowly exit the highly warped infrared region, under a potential generically arising from the moduli stabilization. In this scenario, the usual slow-roll conditions are not required, and a large warping is allowed to incorporate the R…
An interesting feature of type IIB flux compactifications is the natural presence of strongly warped regions or `throats'. These regions allow for a 5d Randall-Sundrum model interpretation with a large hierarchy between the UV and IR brane. We show that, in the 5d description, the flux stabilization of this hierarchy (or, equivalently, of the brane-to-brane distance) can be understood as an implementation of the Goldberger-Wise mechanism. This mechanism relies on the non-trivial bulk profile of the so-called Goldberger-Wise scalar, which in addition has fixed expectation values at the boundari…
We investigate a novel mechanism of dynamical tuning of a flat potential in the open string landscape within the context of warped brane-antibrane inflation in type IIB string theory. Because of competing effects between interactions with the moduli stabilizing D7-branes in the warped throat and anti-D3-branes at the tip, a stack of branes gives rise to a local minimum of the potential, holding the branes high up in the throat. As branes successively tunnel out of the local minimum to the bottom of the throat the potential barrier becomes lower and is eventually replaced by a flat inflection p…
We argue that brane anti-brane inflation in string theory de-Sitter vacua of Kachru-Kallosh-Linde-Trivedi (KKLT) is captured by the dynamics of a D3-brane probe in the local KKLT model constructed in hep-th/0203041. This provides a framework to study in a controllable way corrections to the inflationary slow roll parameter ηdue to conformal symmetry breaking in a warped geometry throat. We compute the leading correction to ηfor the inflation in the Klebanov-Tseytlin throat geometry. We find that in certain regime this correction tends to decrease η. Computations in a different regime suggest h…
We discuss various realizations of the four dimensional braneworld inflation in warped geometries of string theory. In all models the inflaton field is represented by a Dp probe brane scalar specifying its position in the warped throat of the compactification manifold. We study existing inflationary throat local geometries, and construct a new example. The inflationary brane is either a D3- or a D5-brane of type IIB string theory. In the latter case the inflationary brane is wrapping a two-cycle of the compactification manifold. We discuss some phenomenological aspects of the model where slow-…
Two recent results indicate that the addition of supersymmetry-breaking ingredients can destabilize the Klebanov-Strassler warped deformed conifold throat. The first comes from an analytic treatment of the interaction between anti-D3 branes and the complex-structure modulus corresponding to the deformation of the conifold [arXiv:1809.06861]. The second comes from the numeric construction of Klebanov-Strassler black holes [arXiv:1809.08484], which stop existing above a certain value of the non-extremality. We show that in both calculations the destabilization energies have the same parametric d…
We calculate the (p,q) string spectrum in a warped deformed conifold using the dielectric brane method. The spectrum is shown to have the same functional form as in the dual picture of a wrapped D3-brane with electric and magnetic fluxes on its world volume. The agreement is exact in the limit where q is large. We also calculate the dielectric spectrum in the S-dual picture. The spectrum in the S-dual picture has the same form as in the original picture but it is not exactly S-dual invariant due to an interchange of Casimirs of the non-Abelian gauge symmetries. We argue that in order to restor…
We present a variant of warped D-brane inflation by incorporating multiple sets of holomorphically-embedded D7-branes involved in moduli stabilization with extent into a warped throat. The resultant D3-brane motion depends on the D7-brane configuration and the relative position of the D3-brane in these backgrounds. The non-perturbative moduli stabilization superpotential takes the racetrack form, but the additional D3-brane open string moduli dependence provides more flexibilities in model building. For concreteness, we consider D3-brane motion in the warped deformed conifold with the presence…
We propose a mechanism of reheating after inflation in multi-throat scenarios of warped extra dimensions. Validity of an effective field theory on the standard model (SM) brane requires that the position of the SM brane during inflation be different from the position after inflation. The latter is supposed to be near the tip of the SM throat but the former is not. After inflation, when the Hubble expansion rate becomes sufficiently low, the SM brane starts moving towards the tip and eventually oscillates. The SM fields are excited by the brane motion and the universe is reheated. Since interac…
We examine how reheating occurs after brane-antibrane inflation in warped geometries, such as those which have recently been considered for Type IIB string vacua. We adopt the standard picture that the energy released by brane annihilation is dominantly dumped into massive bulk (closed-string) modes which eventually cascade down into massless particles, but argue that the this need not mean that the result is mostly gravitons with negligible visible radiation on the Standard Model brane. We show that if the inflationary throat is not too strongly warped, and if the string coupling is sufficien…
Towards the end of brane inflation, the brane pair annihilation produces massive closed strings. The transfer of this energy to Standard Model (SM) open string modes depends on where the SM branes and the brane annihilation are located: in the bulk, in the same throat or in different throats. We find that, in all cases as long as the brane annihilation and the SM branes are not both in the bulk, the transfer of energy to start the hot big bang epoch can be efficient enough to be compatible with big bang nucleosynthesis. The suppression of the abundance of the graviton and its Kaluza-Klein (KK)…
We construct analytically a perturbative supergravity solution that captures the backreaction of a metastable state of anti-branes in the background of a particular modification of the Klebanov-Strassler throat in a long-wavelength approximation. Our solution, which has no unphysical singularities, describes how non-supersymmetric spherical NS5-branes with dissolved anti-D3 brane charge backreact in a fluxed throat geometry. It supports previous claims that there is a well-behaved supergravity description of the metastable state of wrapped NS5-branes proposed years ago by Kachru, Pearson, and …
We construct a simple explicit local geometry providing a `bifid throat' for 5-brane axion monodromy. A bifid throat is a throat that splits into two daughter throats in the IR, containing a homologous 2-cycle family reaching down into each daughter throat. Our example consists of a deformed $\mathbb{Z}_3\times\mathbb{Z}_2$ orbifold of the conifold, which provides us with an explicit holographic dual of the bifid throat including D3-branes and fractional 5-branes at the toric singularities of our setup. Having the holographic description in terms of the dual gauge theory allows us to address t…
We investigate in some quantitative details the viability of reheating in multi-throat brane inflationary scenarios by estimating and comparing the time scales for the various processes involved. We also calculate within perturbative string theory the decay rate of excited closed strings into KK modes and compare with that of their decay into gravitons; we find that in the inflationary throat the former is preferred. We also find that over a small but reasonable range of parameters of the background geometry, these KK modes will preferably tunnel to another throat (possibly containing the Stan…
In this paper we study non-perturbative instabilities in Anti de-Sitter vacua arising from flux compactifications of string models with broken supersymmetry. In the semi-classical limit, these processes drive the vacua towards lower fluxes, which translate into higher curvatures and higher string couplings. In order to shed some light on this regime, we provide evidence for a description in terms of branes, which generate near-horizon AdS throats. To this end, we study the attractor properties of the geometries near the throat, and we also characterize their asymptotics away from it. We also d…
We show that it is possible to define Majorana (s)pinor fields on M-branes which have been identified under the action of the antipodal map on the adS factor of the throat geometry, or which have been wrapped on two-cycles of arbitrary genus. This is an important consistency check, since it means that one may still take the generators of supertranslations in superspace to transform as Majorana fermions under the adjoint action of $Spin(10,1)$, even though the antipodally identified M2-brane is {\it not} space-orientable. We point out that similar conclusions hold for any p-branes which have th…
Generic classes of string compactifications include ``brane throats'' emanating from the compact dimensions and separated by effective potential barriers raised by the background gravitational fields. The interaction of observers inside different throats occurs via tunnelling and is consequently weak. This provides a new mechanism for generating small numbers in Nature. We apply it to the hierarchy problem, where supersymmetry breaking near the unification scale causes TeV sparticle masses inside the standard model throat. We also design naturally long-lived cold dark matter which decays withi…
We present a curvaton model from type IIB string theory compactified on a warped throat with approximate isometries. Considering an (anti-)D3-brane sitting at the throat tip as a prototype standard model brane, we show that the brane's position in the isometry directions can play the role of curvatons. The basic picture is that the fluctuations of the (anti-)D3-brane in the angular isometry directions during inflation eventually turns into the primordial curvature perturbations, and subsequently the brane's oscillation excites other open string modes on the brane and reheat the universe. We fi…
Using the tachyon DBI action proposal for the effective theory of non-coincident D$_p$-brane-anti-D$_p$-brane system, we study the decay of this system in the tachyon channel. We assume that the branes separation is held fixed, i.e. no throat formation, and then find the bounce solution which describe the decay of the system from false to the true vacuum of the tachyon potential. We shall show that due to the non-standard form of the kinetic term in the effective action, the thin wall approximation for calculating the bubble nucleation rate gives a result which is independent of the branes sep…
Back-reaction effects can modify the dynamics of mobile D3 branes moving within type IIB vacua, in a way which has recently become calculable. We identify some of the ways these effects can alter inflationary scenarios, with the following three results: (1) By examining how the forces on the brane due to moduli-stabilizing interactions modify the angular motion of D3 branes moving in Klebanov-Strassler type throats, we show how previous slow-roll analyses can remain unchanged for some brane trajectories, while being modified for other trajectories. These forces cause the D3 brane to sink to th…
We study the inflationary dynamics in a model of slow-roll inflation in warped throat. Inflation is realized by the motion of a D-brane along the radial direction of the throat, and at later stages instabilities develop in the angular directions. We closely investigate both the single field potential relevant for the slow-roll phase, and the full multi-field one including the angular modes which becomes important at later stages. We study the main features of the instability process, discussing its possible consequences and identifying the vacua towards which the angular modes are driven.
We revisit necessary conditions for gluing local (anti-)D3 throats into flux throats with opposite charge. These consistency conditions typically reveal singularities in the three-form fluxes whose meaning is being debated. In this note we prove, under well-motivated assumptions, that unphysical singularities can potentially be avoided when the anti-branes polarise into spherical NS5 branes with a specific radius. If a consistent solution can then indeed be found, our analysis seems to suggests a rather large correction to the radius of the polarization sphere compared to the probe result. We …
The implications of brane motion in angular directions of Calabi-Yau flux compactifications are discussed from the point of view of an observer living on the worldvolume of the brane and from the point of view of an observer living elsewhere in the three non-compact dimensions. The brane observer can experience cosmological bounces and cyclic behavior of the scale factor induced by centrifugal angular momentum barriers. Observers living elsewhere in the compactification experience marginally prolonged periods of inflation due to large angular momentum (spinflation). The presence of spinflaton …
We consider de Sitter vacua realised in concrete type IIB Calabi-Yau compactifications with an anti D3-brane at the tip of a warped throat of Klebanov-Strassler type. The Kähler moduli are stabilised together with the complex structure modulus of the warped throat. The volume is exponentially large as in the large volume scenario (LVS). We analyse the conditions on the parameters of the EFT such that they are in the region of validity of our approximations, there are no runaway problems and the vacua satisfy all consistency constraints, such as tadpole cancellation. We illustrate our results w…
We describe the construction of string theory models with semirealistic spectrum in a sector of (anti) D3-branes located at an orbifold singularity at the bottom of a highly warped throat geometry, which is a generalisation of the Klebanov-Strassler deformed conifold. These models realise the Randall-Sundrum proposal to naturally generate the Planck/electroweak hierarchy in a concrete string theory embedding, and yielding interesting chiral open string spectra. We describe examples with Standard Model gauge group (or left-right symmetric extensions) and three families of SM fermions, with corr…
The time-varying density of D-branes and anti-D-branes in an expanding universe is calculated. The D-brane anti-brane annihilation rate is shown to be too small to compete with the expansion rate of a FRW type universe and the branes over-close the universe. This brane problem is analogous to the old monopole problem. Interestingly however, it is shown that small dimension D-branes annihilate more slowly than high dimension branes. Hence, an initially brany universe may be filled with only low dimension branes at late times. When combined with an appropriate late inflationary theory this leads…
Fluxes can decay via the nucleation of Brown-Teitelboim bubbles, but when the decaying fluxes induce D-brane charges this process must be accompanied with an annihilation of D-branes. This occurs via dynamics inside the bubble wall as was well described for (anti-)D3 branes branes annihilating against 3-form fluxes. In this paper we extend this to the other Dp branes with p smaller than seven. Generically there are two decay channels: one for the RR flux and one for the NSNS flux. The RR channel is accompanied by brane annihilation that can be understood from the Dp branes polarising into D(p+…
In this paper we study a curvaton model obtained by considering a probe anti-D3-brane with angular motion at the bottom of a KS throat with approximate isometries. We calculate the spectrum of curvature perturbations and the non-Gaussianities of this model. Specifically, we consider the limit of relativistic rotation of the curvaton brane which leads to a small sound speed, and thus it can be viewed as an implementation of the DBI-curvaton mechanism. We find that the primordial power spectrum is nearly scale-invariant while the non-Gaussianity of local type is sizable and that of equilateral t…
We present exact classical solutions of the higher-derivative theory that describes the dynamics of the position modulus of a probe brane within a five-dimensional bulk. The solutions can be interpreted as static or time-dependent throats connecting two parallel branes. In the nonrelativistic limit the brane action is reduced to that of the Galileon theory. We derive exact solutions for the Galileon, which reproduce correctly the shape of the throats at large distances, but fail to do so for their central part. We also determine the parameter range for which the Vainshtein mechanism is reprodu…
Despite their consequential applications, metastable states of antibranes in warped throats are not yet fully understood. In this thesis, we provide new information on various aspects of these metastable antibranes through applications of the blackfold effective theory for higher-dimensional black holes. As concrete examples, we study the conjectured metastable state of polarised anti-D3 branes at the tip of the Klebanov-Strassler (KS) throat in type IIB supergravity and the analogous state of polarised anti-M2 branes at the tip of the Cvetic-Gibbons-Lu-Pope (CGLP) throat in eleven-dimensional…
The Einstein-Rosen "bridge" wormhole solution proposed in the classic paper [1] does not satisfy the vacuum Einstein equations at the wormhole throat. We show that the fully consistent formulation of the original Einstein-Rosen "bridge" requires solving Einstein equations of bulk D=4 gravity coupled to a lightlike brane with a well-defined world-volume action. The non-vanishing contribution of Einstein-Rosen "bridge" solution to the right hand side of Einstein equations at the throat matches precisely the surface stress-energy tensor of the lightlike brane which automatically occupies the thro…
String theory compactification involves manifolds with multiple warp factors. For cosmological applications, one often introduces a short, high-energy inflationary throat, and a long,low-energy Standard Model throat. It is assumed that at the end of inflation,the excited Kaluza-Klein modes from the Inflationary throat tunnel to the SM throat and reheat Standard Model degrees of freedom, which are attached to probe brane(s). However, the huge hierarchy of energy scales can result in a highly dynamic transition of the throat geometry. We point out that in such a cosmological scenario the Standar…
We study the complex deformations of orientifolds of D3-branes at toric CY singularities, using their description in terms of dimer diagrams. We describe orientifold quotients that have fixed lines or fixed points in the dimer, and characterize the possibilities to deform them in terms of the behaviour of zig-zag paths under the orientifold symmetry. The resulting models are holographic duals to warped throats with orientifold planes. Our systematic construction provides a general class of configurations which includes models recently appeared in the context of de Sitter uplift by nilpotent go…
In this note $D9$- and anti-$D9$-brane annihilation in type I string theory is probed by a $D1$-brane. We consider the covariant Green-Schwarz or twistor formulation of the probe theory. We expect the theory to be $κ$-invariant after the annihilation is completed. Conditions of the $κ$-invariance of the theory impose constraints on the background tachyon field. Solutions to the constraints define tachyon values which correspond to type I $D5$-branes as remnants of the annihilation. As a byproduct we get a theory which lies in the same universality class as the non-linear $σ$-model for the Atiy…
In this paper we point out the inevitability of an explosive production of gauge field and gravity wave during an open string tachyon condensation in a cosmological setting. We will be particularly studying an example of brane-anti-brane inflation in a warped throat where inflation ends via tachyon condensation. We point out that a tachyonic instability helps fragmenting the homogeneous tachyon and excites gauge field and contributes to the stress energy tensor which also feeds into the gravity waves.
We study the potential governing D3-brane motion in a warped throat region of a string compactification with internal fluxes and wrapped D-branes. If the Kahler moduli of the compact space are stabilized by nonperturbative effects, a D3-brane experiences a force due to its interaction with D-branes wrapping certain four-cycles. We compute this interaction, as a correction to the warped four-cycle volume, using explicit throat backgrounds in supergravity. This amounts to a closed-string channel computation of the loop corrections to the nonperturbative superpotential that stabilizes the volume.…
Born-Infeld theory admits finite energy point particle solutions with $δ$-function sources, BIons. I discuss their role in the theory of Dirichlet $p$-branes as the ends of strings intersecting the brane when the effects of gravity are ignored. There are also topologically non-trivial electrically neutral catenoidal solutions looking like two $p$-branes joined by a throat. The general solution is a non-singular deformation of the catenoid if the charge is not too large and a singular deformation of the BIon solution for charges above that limit. The intermediate solution is BPS and Coulomb-lik…
We derive the low energy absorption cross section of minimal scalars for a very generic class of geometries, that includes, among others, black holes, strings, $p$-branes, as well as intersecting brane configurations. The scalar field can be absorbed across a regular surface (a horizon) of finite area, or across a zero area throat, which may be singular or regular. Then we focus on some particular cases and compare with the results obtained using microscopic models at weak coupling. Exact agreement is found for the absorption by the non-degenerate ground state of effective strings. For geometr…
A generic F-theory compactification containing many D3 branes develops multiple brane throats. The interaction of observers residing inside different throats involves tunneling suppression and, as a result, is very weak. This suggests a new mechanism for generating small numbers in Nature. One application is to the hierarchy problem: large supersymmetry breaking near the unification scale inside a shallow throat causes TeV-scale SUSY-breaking inside the standard-model throat. Another application, inspired by nuclear-decay, is in designing naturally long-lived particles: a cold dark matter part…
