Vscape is an interactive tool for studying the one-loop effective potential of an ungauged supersymmetric model of chiral multiplets. The program allows the user to define a supersymmetric model by specifying the superpotential. The F-terms and the scalar and fermionic mass matrices are calculated symbolically. The program then allows you to search numerically for (meta)stable minima of the one-loop effective potential. Additional commands enable you to further study specific minima, by e.g. computing the mass spectrum for those vacua. Vscape combines the flexibility of symbolic software, with the speed of a numerical package.
We show that supersymmetric Abelian models that are obtained from deformations of those with ${\cal N}=2$ supersymmetry also contain metastable vacua for a wide range of parameters. The deformations we consider are combinations of masses for charged and singlet fields, a singlet F--term and an anomalous D--term. We find that, in all cases, the nonsupersymmetric vacua are parametrically far from the supersymmetric ones and therefore metastable. Using retrofitting, we show that these metastable vacua may lead to semi--realistic phenomenology.
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 …
Recently Murayama and Nomura proposed a simple scheme to construct the gauge mediation models, using metastable supersymmetry breaking vacua. It has a possibility to predict the ultra light gravitino mass m_{3/2} \lesssim 16 eV, while such a light gravitino may destabilize the metastable vacua. We investigate stability of the metastable vacuum of their model. The transition rate from the false vacuum to true ones is evaluated by numerical calculation, including the Coleman-Weinberg potential destabilizing the metastable vacuum. It is found that when the messenger sector is minimal, stability o…
We point out that, in a class of gauge mediation models using metastable supersymmetry breaking vacua, the minimum of the supersymmetry breaking field in the early universe is dynamically deviated from the one in the low energy. The deviation induces coherent oscillations of the supersymmetry breaking field, which decays into the gravitinos. For certain parameters, it can produce a right amount of the gravitinos to account for the observed dark matter.
In the Intriligator-Seiberg-Shih model, we parametrize spontaneous breaking of $U(1)_R$ symmetry with two gauge singlets with R-charges 1 and --1. These singlets can play the role of the messengers. The messenger scale is dynamically generated, and hence there is no hierarchy problem between the supersymmetry breaking scale and the messenger scale. In the gauge mediation scenario, supersymmetry breaking scale turns out to be around $\mathcal{O}(10^6)\textrm{GeV}$.
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.
We study the question whether a possible metastable vacuum state is actually populated in a phase transition in the early universe, as is usually assumed in the discussion of vacuum stability bounds e.g. for Standard Model parameters. A phenomenological (3+1)-dimensional Langevin equation is solved numerically for a toy model with a potential motivated by the finite temperature 1-loop effective potential of the Standard Model including additional non-renormalizable operators from an effective theory for physics beyond the Standard Model and a time dependent temperature. It turns out that wheth…
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.
We show how gauged flavour breaking and N = 1 supersymmetry breaking can be dynamically aligned to produce natural models. Supersymmetry is broken in a metastable vacuum, while a weakly gauged flavour symmetry is identified with an SU(3)_F subgroup of the global symmetry of the SQCD model. We find that alignment can easily occur either through strongly coupled flavour models, with SQCD bound states playing the role of flavons, or entirely weakly coupled and renormalizable models with elementary SU(3)_F adjoint flavons. In both cases it is essential that the SU(3)_F breaking, and hence all the …
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.
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 in (anomalous) U(1) gauge theories with the Fayet-Iliopoulos (FI) term and with generic interactions there are meta-stable vacua in which supersymmetry (SUSY) is spontaneously broken even without U(1)_R symmetry and various hierarchical structures, for example, Yukawa hierarchy, can be explained by the smallness of the FI parameter. When we introduce generic interactions, i.e., all interactions including higher dimensional interactions which are allowed by the symmetry of the theory with O(1) coefficients, various scales can be determined by the symmetry (U(1) charges of the intro…
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…
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 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.
We study the meson spectra in the excited QCD vacua, denominated replicas. We find all mesons have real masses, with no tachyons, thus showing the QCD replicas are indeed metastable.
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 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…
In this paper, we give a systematic procedure for building locally stable dS vacua in $\mathcal{N}=1$ supergravity models motivated by string theory. We assume that one of the superfields has a Kahler potential of no-scale type and impose a hierarchy of supersymmetry breaking conditions. In the no-scale modulus direction the supersymmetry breaking is not small, in all other directions it is of order $ε$. We establish the existence of an abundance of vacua for large regions in the parameter space spanned by $ε$ and the cosmological constant. These regions exist regardless of the details of the …
We study N=1 global and local supersymmetric theories with a continuous global $U(1)_R$ symmetry as models of dynamical supersymmetry (SUSY) breaking. We introduce explicit R-symmetry breaking terms into such models, in particular a generalized O'Raifeartaigh model. Such explicit R-symmetry breaking terms can lead to a SUSY preserving minimum. We classify explicit R-symmetry breaking terms by the structure of newly appeared SUSY stationary points as a consequence of the R-breaking effect, which could make the SUSY breaking vacuum metastable. We show that the R-breaking terms are basically divi…
If supersymmetry is broken in metastable vacua, it is not clear why we are now in there rather than supersymmetric vacua. Moreover, it is natural to expect that we were in supersymmetric vacua, which have higher symmetry than metastable vacua, in the early universe. In this paper, we reexamine and improve the previous analysis on the cosmological evolution of the vacuum structure in the ISS model of metastable supersymmetry breaking by taking into account constraints on the reheating temperature, which is needed to avoid the overproduction of gravitinos. It turns out that the desired phase tra…
We study the direct mediation of metastable supersymmetry breaking by a Φ^2-deformation to the ISS model and extend it by splitting both TrΦand TrΦ^2 terms in the superpotential and gauging the flavor symmetry. We find that with such an extension the enough long-lived metastable vacua can be obtained and the proper gaugino masses can be generated. Also, this allows for constructing a kind of models which can avoid the Landau pole problem. Especially, in our metastable vacua there exist a large region for the parameter m_3 which can satisfy the phenomenology requirements and allow for a low SUS…
We calculate the pair-annihilation cross section of real scalar singlet dark matter into two mono-energetic photons. We derive constraints on the theory parameter space from the Fermi limits on gamma-ray lines, and we compare with current limits from direct dark matter detection. We show that the new limits, albeit typically relevant only when the dark matter mass is close to half the Standard Model Higgs mass, rule out regions of the theory parameter space that are otherwise not constrained by other observations or experiments. In particular, the new excluded regions partly overlap with the p…
We discuss the coupling of heavy moduli fields to light fields when the dynamics of the latter, absent such couplings, yields metastable vacua. We show that the survival of the vacuum structure of the local model depends nontrivially on the cross-couplings of the two sectors. In particular we find that for "local" models (such as those realized by D-branes in type II string theories) with metastable vacua breaking supersymmetry via F-terms, cross-coupling of the two sectors at an intermediate scale can push the metastable vacuum outside of the regime of the effective field theory. We parametri…
We outline the construction of metastable de Sitter vacua of type IIB string theory. Our starting point is highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, one can make models with all moduli fixed, yielding a supersymmetric AdS vacuum. Inclusion of a small number of anti-D3 branes in the resulting warped geometry allows one to uplift the AdS minimum and make it a metastable de Sitter ground state. The lifetime of our metastable de Sitter vacua is …
Metastable vacua in supersymmetric QCD in the presence of single and multitrace deformations of the superpotential are explored, with the aim of obtaining an acceptable phenomenology. The metastable vacua appear at one loop, have a broken R-symmetry, and a magnetic gauge group that is completely Higgsed. With only a single trace deformation, the adjoint fermions from the meson superfield are approximately massless at one loop, even though they are massive at tree level and R-symmetry is broken. Consequently, if charged under the standard model, they are unacceptably light. A multitrace quadrat…
We study a SU(2) gauge theory with a classical complex modulus. Introducing a chemical potential for a conserved modulus hypercharge causes it to become unstable and start condensing. We show that the modulus condensation in turn generates homogeneous but anisotropic non-abelian field strength condensates. The existence of a stable vacuum at the end point of the condensation process depends on a modulus representation under the gauge group. For a modulus in the fundamental representation, the global vacuum of the theory is a state both with the rotational symmetry and the electromagnetic U(1) …
According to the KKLT scenario, metastable dS vacua are formed as a result of uplifting of supersymmetric AdS vacua by $\overline {D3}$ branes. I describe an extended version of this scenario where metastable dS vacua appear after an uplift from a state where the potential of the volume modulus in the absence of $\overline {D3}$ branes would be unbounded below. This mechanism may considerably strengthen vacuum stabilization in the early universe.
A new class of metastable de Sitter vacua is presented and analyzed in N =1 supergravity and string theory with tunable (infinitesimally small) value of the cosmological constant. They are based on a gauged R-symmetry and the minimal spectrum contains a vector and a linear multiplet of the string dilaton or of a compactification modulus. In the minimum of the scalar potential supersymmetry is broken by an expectation value of both a D- and F-term.
We construct an N=2 supersymmetric generalization of the N=1 supercurrent formalism of Komargodski and Seiberg (KS) and use it to show that N=2 theories with linear superconformal anomalies cannot break SUSY under certain broad assumptions. This result suggests that there are no metastable SUSY breaking vacua in a large class of theories that includes N=2 Super Yang-Mills (SYM).
We study the existence of Z(3) metastable states in the presence of the dynamical quarks within the ambit of Polyakov quark meson (PQM) model. Within the parameters of the model, it is seen that for temperatures $T_m$ greater than the chiral transition temperature $T_c$, Z(3) metastable states exist ( $T_{m} \sim 310$ MeV at zero chemical potential). At finite chemical potential $T_m$ is larger than the same at vanishing chemical potential. We also observe a shift of ($\sim 5^\circ$) in the phase of the metastable vacua at zero chemical potential. The energy density difference between true and…
We search for viable models of direct gauge mediation, where the SUSY-breaking sector is (generalized) SQCD, which has cosmologically favorable uplifted vacua even when the reheating temperature is well above the messenger scale. This requires a relatively large tadpole term in the scalar potential for the spurion field X and, consequently, we argue that pure (deformed) SQCD is not a viable model. On the other hand, in SQCD with an adjoint, which is natural e.g. in string theory, assuming an appropriate sign in the Kahler potential for X, such metastable vacua are possible.
We compute the effective potential for the phase of the Wilson line at high temperature in the standard model to one loop order. Besides the trivial vacua, there are metastable states in the direction of $U(1)$ hypercharge. Assuming that the universe starts out in such a metastable state at the Planck scale, it easily persists to the time of the electroweak phase transition, which then proceeds by an unusual mechanism. All remnants of the metastable state evaporate about the time of the $QCD$ phase transition.
We develop a method for constructing metastable de Sitter vacua in N=1 supergravity models describing the no-scale volume moduli sector of Calabi-Yau string compactifications. We consider both heterotic and orientifold models. Our main guideline is the necessary condition for the existence of metastable vacua coming from the Goldstino multiplet, which constrains the allowed scalar geometries and supersymmetry-breaking directions. In the simplest non-trivial case where the volume is controlled by two moduli, this condition simplifies and turns out to be fully characterised by the intersection n…
We investigate the dependence of the QCD vacuum structure on the $θ$-angle and quark mass, using the Di-Vecchia--Veneziano model. Although the Di-Vecchia--Veneziano model is a chiral effective model, it contains the topological properties of the pure Yang--Mills theory. It is shown that within this model, the ground state energies for all $θ$ are continuous functions of quark mass from the chiral limit to the quenched limit, even including the first order phase transition at $θ= π$. Based on this effective model, we discuss (i) how the ground state depends on quark mass, and (ii) why the phase…
It has been suggested recently that in a consistent theory any Minkowski vacuum must be exactly stable. As a result, a large class of theories that in ordinary treatment would appear sufficiently long-lived, in reality make no sense. In particular, this applies to supersymmetric models in which global supersymmetry is broken in a false vacuum. We show that in any such theory the dynamics of supersymmetry breaking cannot be decoupled from the Planck scale physics. This finding poses an obvious challenge for the idea of low-scale metastable (for example gauge) mediation.
It is becoming increasingly clear that metastable vacua may play a prominent role in supersymmetry-breaking. To date, however, this idea has been realized only in models where non-perturbative dynamics complicates the analysis of metastability. In this paper, we present a simple construction in which metastable vacua occur classically, i.e., at tree-level, and in which supersymmetry-breaking is sourced by both D-terms and F-terms. All relevant dynamics is perturbative, and hence calculations of vacuum energies and lifetimes can be performed explicitly. Moreover, we find that our construction c…
Supersymmetry breaking in a metastable vacuum is re-examined in a cosmological context. It is shown that thermal effects generically drive the Universe to the metastable minimum even if it begins in the supersymmetry-preserving one. This is a generic feature of the ISS models of metastable supersymmetry breaking due to the fact that SUSY preserving vacua contain fewer light degrees of freedom than the metastable ground state at the origin. These models of metastable SUSY breaking are thus placed on an equal footing with the more usual dynamical SUSY breaking scenarios.
The possibility of a landscape of metastable vacua raises the question of what fraction of vacua are truly long lived. Naively any would-be vacuum state has many nearby decay paths, and all possible decays must be suppressed. An interesting model of this phenomena consists of $N$ scalars with a random potential of fourth order. Here we show that the scaling of the typical minimal bounce action with $N$ is readily understood, and differs from statements in the literature. We discuss the extension to more realistic landscape models.
We present an extension of the mass sum rule that applies to renormalizable rigid supersymmetric field theories to the case of the N=1 supersymmetric effective action (the gauged non-linear sigma model) consisting of adjoint scalar superfields and vector superfields possessing a K"ahler potential, a set of gauge coupling functions (second prepotential derivatives) and a superpotential, which respectively set their energy scales. The mass sum rule derived is valid for any vacua, including the (metastable) one of broken supersymmetry with the condensates of D-term and/or F-term. We manage to ext…
Many models of high energy physics possess metastable vacua. It is conceivable that the universe can get trapped in such a false vacuum, irrespective of its origin and prior history, at an earlier stage during its evolution. The ensuing false vacuum inflation results in a cold and empty universe and has a generic graceful exit problem. We show that an inflection point inflation along the flat directions of the Minimal Supersymmetric Standard Model (MSSM) can resolve this graceful exit problem by inflating the bubble which nucleate out of a false vacuum. The important point is that the initial …
Taking into account the quadratic in mass terms in the effective chiral lagrangian, we show that, at θ\sim π, the theory with 2 light quarks of equal mass involves two degenerate vacuum states separated by a barrier. For three flavors, the energy barrier between two vacua appears already in the leading order in mass. This corresponds to the first order phase transition at θ= π. The surface energy density of the domain wall separating two different vacua is calculated. In the immediate vicinity of the phase transition point, two minima of the potential still exist, but one of them becomes metas…
It follows on general grounds that the theta dependence in QCD is more complicated than suggested by the large N_c approach or instanton arguments. Generically, the vacuum energy E_{vac}(θ) is a multi-valued function of θadmitting the existence of metastable states. We discuss decays of such metastable vacua in the theory with and without the axion, and point out the potential relevance of this and related phenomena for constraining a dark matter axion. Based on the analysis of the axion potential, an idea for a new axion search experiment at RHIC is suggested. It is noted that the false vacuu…
We perform a general algebraic analysis on the possibility of realising slow-roll inflation in the moduli sector of string models. This problem turns out to be very closely related to the characterisation of models admitting metastable vacua with non-negative cosmological constant. In fact, we show that the condition for the existence of viable inflationary trajectories is a deformation of the condition for the existence of metastable de Sitter vacua. This condition depends on the ratio between the scale of inflation and the gravitino mass and becomes stronger as this parameter grows. After pe…
Although the Higgs potential in the Standard Model (SM) contains only a simple electroweak symmetry breaking vacuum in the small field region, additional metastable or global vacua could exist in models beyond the SM. In this paper, we study one intriguing scenario with an additional electroweak symmetric vacuum that could be the global one. For the thermal universe ending at the current metastable vacuum, the electroweak symmetry should stay non-restored at high temperatures. We realize the scenario in a model with Higgs-portal couplings to SM singlet scalars with approximately global O(N) sy…
Large N gluodynamics was shown to have a set of metastable vacua with the gluonic domain walls interpolating between them. The walls may separate the genuine vacuum from an excited one, or two excited vacua which are unstable at finite N (here N is the number of colors). One may attempt to stabilize them by switching on the axion field. We study how the light quarks and the axion affect the structure of the domain walls. In pure gluodynamics (with the axion field) the axion walls acquire a very hard gluonic core. Thus, we deal with a wall "sandwich" which is stable at finite N. In the case of …
Finite density effects can destabilize the metastable vacua in relaxion models. Focusing on stars as nucleation seeds, we derive the conditions that lead to the formation and runaway of a relaxion bubble of a lower energy minimum than in vacuum. The resulting late-time phase transition in the universe allows us to set new constraints on the parameter space of relaxion models. We also find that similar instabilities can be triggered by the large electromagnetic fields around rotating neutron stars.
It was recently shown in hep-th/0610334 that in the context of the ISS models with a metastable supersymmetry breaking vacuum, thermal effects generically drive the Universe to the metastable vacuum even if it began after inflation in the supersymmetry-preserving one. We continue this programme and specifically take into account two new effects. First is the effect of the mass-gap of the gauge degrees of freedom in the confining supersymmetry preserving vacua, and second, is the effect of the back reaction of the MSSM sector on the SUSY breaking ISS sector. It is shown that, even though the ma…
Recently, the calculation of tunneling actions, that control the exponential suppression of the decay of metastable vacua, has been reformulated as an elementary variational problem in field space. This paper extends this formalism to include the effect of gravity. Considering tunneling potentials $V_t(ϕ)$ that go from the false vacuum $ϕ_+$ to some $ϕ_0$ on the stable basin of the scalar potential $V(ϕ)$, the tunneling action is the minimum of the functional $S_E[V_t]=6 π^2m_P^4\int_{ϕ_+}^{ϕ_0}(D+V_t')^2/(V_t^2D)dϕ$, where $D\equiv [(V_t')^2+6(V-V_t)V_t/m_P^2]^{1/2}$, $V_t'=dV_t/dϕ$ and $m_P$…
