We study the stability of vacua with spontaneously broken supersymmetry in N=2 supergravity theories with only hypermultiplets. Focusing on the projection of the scalar mass matrix along the sGoldstino directions, we are able to derive a universal upper bound on the lowest mass eigenvalue. This bound only depends on the gravitino mass and the cosmological constant, but not on the details of the quaternionic manifold spanned by the scalar fields. Comparing with the Breitenlohner-Freedman bound shows that metastability requires the cosmological constant to be smaller than a certain negative critical value. Therefore, only AdS vacua with a sufficiently negative cosmological constant can be stable, while Minkowski and dS vacua necessarily have a tachyonic direction.
We analyze the gauging of Abelian isometries on the hypermultiplet scalar manifolds of N = 2 supergravity in four dimensions. This involves a study of symmetric special quaternionic-Kähler manifolds, building on the work of de Wit and Van Proeyen. In particular we compute the general set of Killing prepotentials and associated compensators for these manifolds manifolds. This allows us to glean new insights about AdS 4 vacua which preserve the full N = 2 supersymmetry as well as BPS static black hole horizons.
The hypermultiplet moduli space M_H in type II string theories compactified on a Calabi-Yau threefold X is largely constrained by supersymmetry (which demands quaternion-Kählerity), S-duality (which requires an isometric action of SL(2, Z)) and regularity. Mathematically, M_H ought to encode all generalized Donaldson-Thomas invariants on X consistently with wall-crossing, modularity and homological mirror symmetry. We review recent progress towards computing the exact metric on M_H, or rather the exact complex contact structure on its twistor space.
By analyzing qualitative aspects of NS5-brane instanton corrections, we determine the topology of the hypermultiplet moduli space M_H in Calabi-Yau compactifications of type II string theories at fixed value of the dilaton and of the Calabi-Yau metric. Specifically, we show that for fivebrane instanton couplings to be well-defined, translations along the intermediate Jacobian must induce non-trivial shifts of the Neveu-Schwarz axion which had thus far been overlooked. As a result, the Neveu-Schwarz axion parametrizes the fiber of a circle bundle, isomorphic to the one in which the fivebrane pa…
We determine the conditions for maximally supersymmetric AdS_5 vacua of five-dimensional gauged N=2 supergravity coupled to vector-, tensor- and hypermultiplets charged under an arbitrary gauge group. In particular, we show that the unbroken gauge group of the AdS_5 vacua has to contain an U(1)_R-factor. Moreover we prove that the scalar deformations which preserve all supercharges form a Kahler submanifold of the ambient quaternionic Kahler manifold spanned by the scalars in the hypermultiplets.
We study the geometric interpretation of metastable vacua for systems of D3 branes at non isolated toric deformable singularities. Using the L^{aba} examples, we investigate the relations between the field theoretic susy breaking and restoration and the complex deformations of the CY singularities.
We investigate membrane instanton effects in type IIA strings compactified on rigid Calabi-Yau manifolds. These effects contribute to the low-energy effective action of the universal hypermultiplet. In the absence of additional fivebrane instantons, the quaternionic geometry of this hypermultiplet is determined by solutions of the three-dimensional Toda equation. We construct solutions describing membrane instantons, and find perfect agreement with the string theory prediction. In the context of flux compactifications we discuss how membrane instantons contribute to the scalar potential and th…
We argue that tachyon-free type I string vacua with supersymmetry breaking in the open sector at the string scale can be interpreted, via S and T-duality arguments, as metastable vacua of supersymmetric type I superstring. The dynamics of the process can be partially captured via nucleation of brane-antibrane pairs out of the non-supersymmetric vacuum and subsequent tachyon condensation.
We construct Abelian brane models with metastable vacua which are obtained from deformations of ${\cal N}=2$ supersymmetric brane configurations. One such model lives on a D4 brane stretched between two displaced and rotated NS5 branes. Another one lives on a D5 brane wrapped on a deformed and fibered $A_2$ singularity.
We use the non-normalizable complex deformations to describe the stringy realizations of the metastable vacua in N = 1, SU(N_c) SUSY theories with N_f > N_c massive fundamental flavors. The consideration of the non-normalizable deformations requires a modified Toric duality. The new approach considers the tachyon condensation between pairs of wrapped D5 branes and anti D5 branes and the resulting mixing between some cycles in the geometry. We enlarge the class of metastable vacua to the case of branes-antibranes wrapped on cycles of deformed A_n singularities.
We prove the impossibility of resonant decay of a metastable vacuum in a theory of a scalar field coupled to a gauge field. Our result extends to gauge theories of scalar fields a recent no go theorem for resonant tunneling in a pure scalar field theory.
Massive hypermultiplets admit degenerate discrete vacua only if they form nonlinear sigma models or have gauge interaction. We discuss BPS domain walls in these theories. This talk is based on the original papers hep-th/0307274 and hep-th/0211103.
Typical de Sitter (dS) vacua of gauged supergravity correspond to saddle points of the potential and often the unstable mode runs into a singularity. We explore the possibility to obtain dS points where the unstable mode goes on both sides into a supersymmetric smooth vacuum. Within N=2 gauged supergravity coupled to the universal hypermultiplet, we have found a potential which has two supersymmetric minima (one of them can be flat) and these are connected by a de Sitter saddle point. In order to obtain this potential by an Abelian gauging, it was important to include the recently proposed qua…
Models of spontaneous supersymmetry breaking generically have an R-symmetry, which is problematic for obtaining gaugino masses and avoiding light R-axions. The situation is improved in models of metastable supersymmetry breaking, which generically have only an approximate R-symmetry. Based on this we argue, with mild assumptions, that metastable supersymmetry breaking is inevitable. We also illustrate various general issues regarding spontaneous and explicit R-symmetry breaking, using simple toy models of supersymmetry breaking.
We find non-supersymmetric metastable vacua in four dimensional N=2 gauge theories softly broken to N=1 by a superpotential term. First we study the simplest case, namely the SU(2) gauge theory without flavors. We study the spectrum and lifetime of the metastable vacuum and possible embeddings of the model in UV complete theories. Then we consider larger gauge group theories with flavors. We show that when we softly break them to N=1, the potential induced on specific submanifolds of their moduli space is identical to the potential in lower rank gauge theories. Then we show that the potential …
It has been shown that four dimensional N=2 gauge theories, softly broken to N=1 by a superpotential term, can accommodate metastable non-supersymmetric vacua in their moduli space. We study the SU(2) theory at high temperatures in order to determine whether a cooling universe settles in the metastable vacuum at zero temperature. We show that the corrections to the free energy because of the BPS dyons are such that may destroy the existence of the metastable vacuum at high temperatures. Nevertheless we demonstrate the universe can settle in the metastable vacuum, provided that the following tw…
We study dynamical supersymmetry breaking in vector-like superconformal N=1 gauge theories. We find appropriate deformations of the superpotential to overcome the problem of the instability of the non supersymmetric vacuum. The request for long lifetime translates into constraints on the physical couplings which in this regime can be controlled through efficient RG analysis.
We conjecture that all vacua in string theory decay. More precisely, non-supersymmetric vacua in string theory are at most metastable and eventually decay, while supersymmetric vacua are only marginally stable. All de Sitter vacua with small cosmological constant are metastable to decay via a process that occurs on scales small compared to the horizon size.
We consider the geometrical engineering of the non-supersymmetric metastable vacua of N = 1 super Yang-Mills proposed in hep-th/0602239 and hep-th/0610249. By T-duality they become N = 1 brane configurations. The identifications between gluino condensation and the geometry sizes for the configurations of hep-th/0610249 are studied by proceeding through the usual MQCD transitions. The geometrical description of the Seiberg dualities for the theories of hep-th/0602239 involves new types of modifications of the complex structure for the resolutions of N = 2 singularities.
In a recent paper [1] we showed that N=1 supersymmetric QCD in the presence of certain superpotential deformations has a rich landscape of supersymmetric and non-supersymmetric vacua. In this paper we embed this theory in string theory as a low energy theory of intersecting NS and D-branes. We find that in the region of parameter space of brane configurations that can be reliably studied using classical string theory, the vacuum structure is qualitatively similar to that in the field theory regime. Effects that in field theory come from one loop corrections arise in string theory as classical …
We study maximally supersymmetric Anti-de Sitter backgrounds in consistent N=2 truncations of type IIB supergravity compactified on the Sasaki-Einstein manifold $T^{1,1}$. In particular, we focus on truncations that contain fields coming from the nontrivial second and third cohomology forms on $T^{1,1}$. These give rise to N=2 supergravity coupled to two vector- and two hypermultiplets (Betti-vector truncation) or one vector- and three hypermultiplets (Betti-hyper truncation), respectively. We find that both truncations admit AdS$_5$ backgrounds with the gauge group always being broken but con…
We consider quiver gauge theories arising on D-branes at simple Calabi-Yau singularities (quotients of the conifold). These theories have metastable supersymmetry breaking vacua. The field theoretic mechanism is basically the one exhibited by the examples of Intriligator, Seiberg and Shih in SUSY QCD. In a dual description, the SUSY breaking is captured by the presence of anti-branes. In comparison to our earlier related work, the main improvements of the present construction are that we can reach the free magnetic range of the SUSY QCD theory where the existence of the metastable vacua is on …
We consider O'Raifeartaigh-like models with explicit R-symmetry breaking and analyze the vacuum landscape. Taking such models as candidates for the hidden sector, we analyze the gauge mediation of the supersymmetry breaking, focusing on the effects produced by R-symmetry breaking. First, we construct families of non-R-symmetric models containing only singlet chiral superfields, and determine the conditions under which SUSY vacua, runaway directions and (longlived) metastable vacua exist. We then extend the results to the case in which some of the chiral fields are in a non-trivial representati…
We analyze the conditions to have no-scale supersymmetry breaking solutions of type IIA and IIB supergravity compactified on manifolds of SU(3)-structure. The supersymmetry is spontaneously broken by the intrinsic torsion of the internal space. For type IIB orientifolds with O9 and O5-planes the mass of the gravitino is governed by the torsion class W_1, and the breaking is mediated through F-terms associated to descendants of the original N=2 hypermultiplets. For type IIA orientifolds with O6-planes we find two families of solutions, depending on whether the breaking is mediated exclusively b…
We construct a simple class of N=2 gauged supergravity theories that admit metastable de Sitter vacua, generalizing the recent work done in the context of rigid supersymmetry. The setup involves one hypermultiplet and one vector multiplet spanning suitably curved quaternionic-Kahler and special-Kahler geometries, with an Abelian gauging based on a single triholomorphic isometry, but neither Fayet-Iliopoulos terms nor non-Abelian gauge symmetries. We construct the most general model of this type and show that in such a situation the possibility of achieving metastable supersymmetry breaking vac…
In this paper, we present a series of supersymmetric models exhibiting an entirely new vacuum structure: towers of metastable vacua with higher and higher energies. As the number of vacua grows towards infinity, the energy of the highest vacuum remains fixed while the energy of the true ground state tends towards zero. We study the instanton-induced tunneling dynamics associated with such vacuum towers, and find that many distinct decay patterns along the tower are possible: these include not only regions of vacua experiencing direct collapses and/or tumbling cascades, but also other regions o…
We study the possibility of achieving metastable de Sitter vacua in general N=2 to N=1 truncated supergravities without vector multiplets, and compare with the situations arising in N=2 theories with only hypermultiplets and N=1 theories with only chiral multiplets. In N=2 theories based on a quaternionic manifold and a graviphoton gauging, de Sitter vacua are necessarily unstable, as a result of the peculiar properties of the geometry. In N=1 theories based on a Kahler manifold and a superpotential, de Sitter vacua can instead be metastable provided the geometry satisfies some constraint and …
We demonstrate that, in an appropriate limit, the off-shell M5-brane worldvolume action effectively captures the scalar potential of Seiberg-Witten theory perturbed by a small superpotential and, consequently, any nonsupersymmetric vacua that it describes. This happens in a similar manner to the emergence from M5's of the scalar potential describing certain type IIB flux configurations [arXiv:0705.0983]. We then construct exact nonholomorphic M5 configurations in the special case of SU(2) Seiberg-Witten theory deformed by a degree six superpotential which correspond to the recently discovered …
By implementing an error function on a Machine Learning algorithm we look for minimal conditions to construct stable Anti de Sitter and de Sitter vacua from dimensional type IIB String theory compactifcation on Kähler manifolds with torsion. This allows to have contributions to the scalar potential from the five-form flux and from D-branes wrapping torsional cycles, interpreted as non-BPS states. The former implies the possibility to construct stable AdS vacua while the later constitutes a mechanism to uplift AdS to dS vacua. Particularly we consider $\hat{D5}$ non-BPS states to uplift the sta…
We construct an M-theory background dual to the metastable state recently discussed by Klebanov and Pufu, which corresponds to placing a stack of anti-M2 branes at the tip of a warped Stenzel space. With this purpose we analytically solve for the linearized non-supersymmetric deformations around the warped Stenzel space, preserving the SO(5) symmetries of the supersymmetric background, and which interpolate between the IR and UV region. We identify the supergravity solution which corresponds to a stack of $\bar{N}$ backreacting anti-M2 branes by fixing all the 12 integration constants in terms…
We analyze vacuum decay in brane world setups, where a free scalar field in five dimensions has a localized potential admitting metastable vacua. We study in particular the bounce solution and its properties in flat and warped spaces. In the latter case, placing into a deeply warped region the term in the potential that lifts the vacuum degeneracy, can increase indefinitely the lifetime of the false vacuum. We discuss the application to metastable vacua in supersymmetric brane-world constructions.
In this paper we consider quiver gauge theories with fractional branes whose infrared dynamics removes the classical supersymmetric vacua (DSB branes). We show that addition of flavors to these theories (via additional non-compact branes) leads to local meta-stable supersymmetry breaking minima, closely related to those of SQCD with massive flavors. We simplify the study of the one-loop lifting of the accidental classical flat directions by direct computation of the pseudomoduli masses via Feynman diagrams. This new approach allows to obtain analytic results for all these theories. This work e…
In the context of flux compactifications, metastable vacua with a small positive cosmological constant are obtained by combining a sector where supersymmetry is broken dynamically with the sector responsible for moduli stabilization, which is known as the F-uplifting. We analyze this procedure in a model-independent way and study phenomenological properties of the resulting vacua.
The scalar potential of recombination fields of magnetized branes in Type IIB orientifold compactifications is analyzed in the absence of any closed string fluxes. Considering its perturbative F and D-term contributions in a quadratic approximation, we present the conditions for which its minima are supersymmetric. We show that for reasonable conditions on the spectrum, both metric moduli and recombination fields can be stabilized. We then provide explicit examples of compact manifolds where a Minkowski vacuum is realized in a Higgs phase. The vacuum energy is zero and some charged scalars acq…
Anomalously small gaugino masses are a common feature of various models of direct gauge mediation. This problem is closely related to the vacuum structure of the theory. In this paper we show that massive SQCD can have SUSY-breaking vacua which are qualitatively different from the ISS vacuum. These novel vacua are metastable with respect to decay to the ISS vacuum. We demonstrate the possibility of addressing the gaugino mass problem in this framework. We study the properties of these vacua and construct an example of a model of direct gauge mediation.
Continuing the programme of constructing the backreacted solution corresponding to smeared anti-D3 branes in the warped deformed conifold, we solve analytically the equations governing the space of first-order deformations around this solution. We express the results in terms of at most three nested integrals. These are the simplest expressions for the space of $SU(2) \times SU(2) \times \ZZ_2$-invariant deformations, in which the putative solution for smeared anti-D3 branes must live. We also explain why one cannot claim to identify this solution without fully relating the coefficients of the…
We construct a model with long-lived metastable vacua in which all the relevant parameters, including the supersymmetry breaking scale, are generated dynamically by dimensional transmutation. The metastable vacua appear along a pseudo-runaway direction near a point of enhanced symmetry as a result of a balance between non-perturbative and perturbative quantum effects. We show that metastable supersymmetry breaking is a rather generic feature near certain enhanced symmetry points of gauge theory moduli spaces.
We study the scenario that conformal dynamics leads to metastable supersymmetry breaking vacua. At a high energy scale, the superpotential is not R-symmetric, and has a supersymmetric minimum. However, conformal dynamics suppresses several operators along renormalization group flow toward the infrared fixed point. Then we can find an approximately R-symmetric superpotential, which has a metastable supersymmetry breaking vacuum, and the supersymmetric vacuum moves far away from the metastable supersymmetry breaking vacuum. We show a 4D simple model. Furthermore, we can construct 5D models with …
We show that the perturbation of an N=2 supersymmetric gauge theory by a superpotential linear in the Kahler normal coordinates of the Coulomb branch, discussed in arXiv:0704.3613, is equivalent to the perturbation by Fayet-Iliopoulos terms. It follows that the would-be meta-stable vacuum at the origin of the normal coordinates in fact preserves N=1 supersymmetry unless the superpotential is truncated to a finite-degree polynomial of the adjoint scalar fields. We examine the criteria for supersymmetry breaking under a perturbation by Fayet-Iliopoulos terms and present a general classification …
Until recently, dynamical supersymmetry breaking seemed an exceptional phenomenon, involving chiral gauge theories with a special structure. Recently it has become clear that requiring only metastable states with broken supersymmetry leads to a far broader class of theories. In this paper, we extend these constructions still further, finding new classes which, unlike earlier theories, do not have unbroken, approximate $R$ symmetries. This allows construction of new models with direct gauge mediation. These theories permit a relatively compact solution to the $μ$ problem.
We study supersymmetry breaking in metastable vacua on the Coulomb branch of perturbed N=2 gauge theories, with gauge group SU(2) and different matter content (N_f=0,2,4). The theory is deformed with a superpotential which is a cubic polynomial in u=Tr Φ^2, where Φis the adjoint superfield. The allowed region of the perturbation parameters in this N=1 theory is plotted as a function of the moduli space coordinate. In the asymptotically free cases a significant fine-tuning in the perturbation parameters is needed to achieve metastable vacua in the weakly coupled region of the moduli space; a lo…
We study the conditions under which a generic supergravity model involving chiral and vector multiplets can admit viable metastable vacua with spontaneously broken supersymmetry and realistic cosmological constant. To do so, we impose that on the vacuum the scalar potential and all its first derivatives vanish, and derive a necessary condition for the matrix of its second derivatives to be positive definite. We study then the constraints set by the combination of the flatness condition needed for the tuning of the cosmological constant and the stability condition that is necessary to avoid uns…
Much has been learned about metastable vacua and R-symmetry breaking in O'Raifeartaigh models. Such work has largely been done from the perspective of the superpotential and by including Coleman-Weinberg corrections to the scalar potential. Instead, we consider these ideas from the perspective of the one loop effective Kahler potential. We translate known ideas to this framework and construct convenient formulas for computing individual terms in the expanded effective Kahler potential. We do so for arbitrary R-charge assignments and allow for small R-symmetry violating terms so that both spont…
The decay rates of metastable SQCD vacua in ISS-type models, both towards supersymmetric vacua as well as towards other nonsupersymmetric configurations arising in theories with elementary spectators, are estimated numerically in the semiclassical approximation by computing the corresponding multifield bounce configurations. The scaling of the bounce action with respect to the most relevant dimensionless couplings and ratios of scales is analyzed. In the case of the decays towards the susy vacua generated by nonperturbative effects, the results confirm previous analytical estimations of this s…
We study the existence of metastable vacua in cascades based on fractional brane configurations at non-isolated singularities preserving N = 1 supersymmetry. We find that in a large class of models the extra moduli typically generated along such cascades may be stabilized by utilizing special monopole points found recently. We illustrate this in detail for cascades based on the SPP singularity. The supergravity interpretation of these constructions in terms of warped throats with supersymmetry breaking localized near their tips as well as applications to string compactification is discussed. O…
We consider partial supersymmetry breaking in ${\cal N}=2$ supergravity coupled to a single vector and a single hypermultiplet. This breaking pattern is in principle possible if the quaternion-Kähler space of the hypermultiplet admits (at least) one pair of commuting isometries. For this class of manifolds, explicit metrics exist and we analyse a generic electro-magnetic (dyonic) gauging of the isometries. An example of partial breaking in Minkowski spacetime has been found long ago by Ferrara, Girardello and Porrati, using the gauging of two translation isometries on $SO(4,1)/SO(4)$. We demon…
We study the compatibility of spontaneous breaking of parity and successful cosmology in a left-right symmetric model where supersymmetry breaking is achieved in metastable vacua. We show that domain walls formed due to this breaking can be removed due to Planck scale suppressed terms, provided the parity breaking scale $M_R$ is constrained to remain smaller than $10^{10}-10^{11}$ GeV. Ensuring metastability is achieved naturally even if the entire mechanism operates at low scales, within a few orders of magnitude of the TeV scale. Taking $M_R$ as high as permitted, close to the acceptable reh…
We show that, for a generic choice of a point on the Coulomb branch of any N=2 supersymmetric gauge theory, it is possible to find a superpotential perturbation which generates a metastable vacuum at the point. For theories with SU(N) gauge group, such a superpotential can be expressed as a sum of single-trace terms for N=2 and 3. If the metastable point is chosen at the origin of the moduli space, we can show that the superpotential can be a single-trace operator for any N. In both cases, the superpotential is a polynomial of degree 3N of the vector multiplet scalar field.
I discuss conceptual issues associated with the presence of metastable AdS vacua in the string landscape. The geometry of the decay from one AdS to another is presented in detail, and various subtleties that are not present for flat or dS vacua are demonstrated and analyzed. I use mostly semiclassical gravity, but I will consider the implications for recent attempts to construct field theory duals of metastable AdS vacua and also possible relevance to the study of eternal inflation.
We reexamine the vacuum structure of three-dimensional quantum chromodynamics (QCD$_3$) with gauge group $SU(N)$, $N_f$ fundamental quark flavors, and a level-$k$ Chern-Simons term. This analysis can be reliably carried out in the large-$N$, fixed $N_f, k$ limit of the theory, up to certain assumptions that we spell out explicitly. At leading order in the large-$N$ expansion we find $N_f + 1$ distinct, exactly degenerate vacuum superselection sectors with different patterns of flavor-symmetry breaking. The associated massless Nambu-Goldstone bosons are generically accompanied by topological Ch…
I put metastable supersymmetry breaking in a cosmological context. I argue that under reasonable assumptions, the cooling down early Universe favors metastable SUSY-breaking vacua over the stable supersymmetric vacua. To illustrate the general argument, I analyze the early-Universe history of the Intriligator-Seiberg-Shih model.
We demonstrate that the problems of finding stable or metastable vacua in a low energy effective field theory requires solving nested NP-hard and co-NP-hard problems, while the problem of finding near-vacua is in P. Multiple problems relevant for computing effective potential contributions from string theory are shown to be instances of NP-hard problems. If P $\neq$ NP, the hardness of finding string vacua is exponential in the number of scalar fields. Cosmological implications, including for rolling solutions, are discussed in light of a recently proposed measure.
We study a four-dimensional effective theory of the five-dimensional (5D) gauged supergravity with a universal hypermultiplet and perturbative superpotential terms at the orbifold fixed points. Among eight independent isometries of the scalar manifold, we focus on three directions for gauging by the graviphoton. The class of models we consider includes the 5D heterotic M-theory and the supersymmetric Randall-Sundrum model as special limits of the gauging parameters. We analyze the vacuum structure of such models, especially the nature of moduli stabilization, from the viewpoint of the effectiv…
We consider "Orientifold field theories", namely SU(N) gauge theories with Dirac fermions in the two-index representation at high temperature. When N is even these theories exhibit a spontaneously broken Z2 centre symmetry. We study aspects of the domain wall that interpolates between the two vacua of the theory. In particular we calculate its tension to two-loop order. We compare its tension to the corresponding domain wall in a SU(N) gauge theory with adjoint fermions and find an agreement at large-N, as expected from planar equivalence between the two theories. Moreover, we provide a non-pe…
We study the stability of supersymmetry breaking metastable vacua and supersymmetric vacua in the presence of solitons. The metastable vacua of supersymmetric QCD and those found elsewhere such as in models based on the SU(5) grand unified group support the existence of topological solitons. The vacua containing such topological defects can become unstable against decay into lower energy configurations. We show for a specific model that a finite region of the available parameter space of couplings becomes disallowed due to the presence of monopoles. In a manner similar to previous studies base…
We clarify under what conditions slow-roll inflation can continue almost undisturbed, while briefly evolving through a (semi-classically) metastable false vacuum. Furthermore, we look at potential signatures in the primordial power spectrum that could point towards the existence of traversed metastable false vacua. Interestingly, the theoretical constraints for the existence of traversable metastable vacua imply that Planck should be able to detect the resulting features in the primordial power spectrum. In other words, if Planck does not see features this immediately implies the non-existence…
We investigate the recent suggestion that a Minkowski vacuum is either absolutely stable, or it has a divergent decay rate and thus fails to have a locally Minkowski description. The divergence comes from boost integration over momenta of the vacuum bubbles. We point out that a prototypical example of false-vacuum decay is pair production in a uniform electric field, so if the argument leading to the divergence is correct, it should apply to this case as well. We provide evidence that no catastrophic vacuum instability occurs in a constant electric field, indicating that the argument cannot be…
We argue that the vast majority of flux vacua with small cosmological constant are unstable to rapid decay to a big crunch. Exceptions are states with large compactification volume and supersymmetric and approximately supersymmetric states. Neither weak string coupling, warping, or the existence of very light particles are, by themselves, enough to render states reasonably metastable. We speculate, as well, about states which might be cosmological attractors.
In theories with multiple vacua, reheating to a temperature greater than the height of a barrier can stimulate transitions from a desirable metastable vacuum to a lower energy state. We discuss the constraints this places on various theories and demonstrate that in a class of supersymmetric models this transition does not occur even for arbitrarily high reheating temperature.
