One can define generalized models of gaugino condensation as theories which dynamically break a discrete R-symmetry, but do not break supersymmetry. We consider general examples consisting of gauge and matter fields, and the minimal number of gauge singlet fields to avoid flat directions in the potential. We explore which R-symmetries can arise, and their spontaneous breaking. In general, we find that the discrete symmetry is $\mathbb{Z}_{2b_0R}$ and the number of supersymmetric vacua is $b_0$, where $b_0$ is the coefficient of the one-loop beta function. Results are presented for various groups, including $SU(N_c), SO(N_c), Sp(2N_c)$, and $G_2$, for various numbers of flavors, $N_f$, by several methods. This analysis can also apply to the other exceptional groups, and thus all simple Lie groups. We also comment on model building applications where a discrete R-symmetry, broken by the singlet vevs, can account for $μ$-type terms and allow a realistic Higgs spectrum naturally.
In direct gauge mediation, gaugino masses often vanish at the leading order of supersymmetry breaking. Recently, this phenomenon is understood in connection with the global structure of vacua in O'Raifeartaigh-type models. In this note, we further explore a connection between gaugino masses and the landscape of vacua in more general situations, focusing on a few examples which demonstrate our idea. In particular, we present a calculable model with non-vanishing leading order gaugino masses on the lowest energy vacuum.
We clarify the role of approximate S-duality in effective supergravity theories that are the low energy limits of string theories, and show how this partial symmetry may be used to constrain effective lagrangians for gaugino condensation.
We review the mechanism of gaugino condensation in the framework of the $d=10$ heterotic string and its $d=11$ extension of Horava and Witten. In particular we emphasize the relation between the gaugino condensate and the flux of the antisymmetric tensor fields of higher dimensional supergravity. Its potential role for supersymmetry breakdown and moduli stabilization is investigated.
We study supersymmetry breaking by hidden-sector gaugino condensation in N=1 D=4 supergravity models with multiple dilaton-like moduli fields. Our work is motivated by Type I string theory, in which the low-energy effective Lagrangian can have different dilaton-like fields coupling to different sectors of the theory. We construct the effective Lagrangian for gaugino condensation and use it to compute the visible-sector gaugino masses. We find that the gaugino masses can be of order the gravitino mass, in stark contrast to heterotic string models with a single dilaton field.
We study dynamical gaugino condensation in superstring effective theories using the linear multiplet representation for the dilaton superfield. An interesting necessary condition for the dilaton to be stabilized, which was first derived in generic models of static gaugino condensation, is shown to hold for generic models of dynamical gaugino condensation. We also point out that it is stringy non-perturbative effects that stabilize the dilaton and allow dynamical supersymmetry breaking via the field-theoretical non-perturbative effect of gaugino condensation. As a typical example, a toy S-dual …
Supersymmetry breakdown via gaugino condensation in heterotic string theory can lead to models with a doubly suppressed gravitino mass. A TeV scale gravitino can emerge from a condensate as large as the grand unified scale. We analyze the properties of these models and discuss applications for particle physics and cosmology.
We find the complete chiral ring relations of the supersymmetric U(N) gauge theories with matter in adjoint representation. We demonstrate exact correspondence between the solutions of the chiral ring and the supersymmetric vacua of the gauge theory. The chiral ring determines the expectation values of chiral operators and the low energy gauge group. All the vacua have nonzero gaugino condensation. We study the chiral ring relations obeyed by the gaugino condensate. These relations are generalizations of the formula $S^N=Λ^{3N}$ of the pure ${\cal N} =1$ gauge theory.
We study gaugino condensation in the context of superstring effective theories using the linear multiplet formulation for the dilaton superfield. Including nonperturbative corrections to the Kähler potential for the dilaton may naturally achieve dilaton stabilization, with supersymmetry breaking and gaugino condensation; these three issues are interrelated in a very simple way. In a toy model with a single static condensate, a dilaton $vev$ is found within a phenomenologically interesting range. The effective theory differs significantly from condensate models studied previously in the chiral …
The hidden SU(5)' with one family, 10 and 5-bar, breaks supersymmetry dynamically. From the effective Lagrangian approach, we estimate the hidden sector gaugino candensation scale, the dilaton stabilization and the resulting gravitino mass. In some models, this gravitino mass can be smaller than the previous naive estimate. Then, it is possible to raise the SU(5)' confining scale above 10^{13} GeV.
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 examine the mechanism of gaugino condensation in supersymmetric theories within a Nambu-Jona-Lasinio type approach. We investigate the effective Lagrangian description of higher energy theories that include some moduli fields in the gauge coupling constant. First we consider supersymmetric QCD with and without a mass term. We can find a phase transition in massless theory, but when we add a mass term, such a phase transition disappears. We also examine a model with a dilaton dependent coupling constant and find that it is very similar to supersymmetric QCD. Application of our method to supe…
We investigate the formation of dynamical gaugino condensates and supersymmetry breaking in the compactifications of Horava-Witten theory with perturbative nonstandard embeddings. Specific models are considered where the underlying massless charged states of the condensing sector are determined by the spectra of $Z_2 \times Z_2 $ and $Z_4 $ orbifolds with nonstandard embeddings. We find among them viable examples where gaugino condensation is triggered on the wall with the weakest gauge coupling at $M_{GUT} $. In all these cases the magnitude of the condensate formed is below the energy scales…
Starting from the previously constructed effective supergravity theory below the scale of U(1) breaking in orbifold compactifications of the weakly coupled heterotic string, we study the effective theory below the scale of supersymmetry breaking by gaugino and matter condensation in a hidden sector. Issues we address include vacuum stability, soft supersymmetry-breaking masses in the observable sector, and the masses of the various moduli fields, including those associated with flat directions at the U(1)-breaking scale, and of their fermionic superpartners. The consistent treatment of U(1) br…
We study the effect of inflation on gaugino condensation in supergravity. Unless the Hubble scale H is significantly below the gaugino condensation scale, the gaugino condensate is a dynamical variable which cannot be integrated out. For a sufficiently high H, the gaugino condensate evolves to zero which in turn leads to dilaton/moduli destabilization. In practice, this often occurs at the Hubble rate about an order of magnitude below the gaugino condensation scale. This effect is independent of the specifics of moduli stabilization and thus places model independent constraints on inflationary…
We argue that supersymmetry breaking by gaugino condensation in the strongly coupled heterotic string can be described by an analogue of Scherk-Schwarz compactification on the eleventh dimension in M-theory. The M-theory scale is identified with the gauge coupling unification mass, whereas the radius of the eleventh dimension $ρ$ is at an intermediate scale $ρ^{-1}\sim 10^{12}$ GeV. At the lowest order, supersymmetry is broken only in the gravitational and moduli sector at a scale $m_{3/2}\simρ^{-1}$, while it is mediated by gravitational interactions to the observable world. Computation of th…
The status of gaugino condensation in low-energy string theory is reviewed. Emphasis is given to the determination of the efective action below condensation scale in terms of the 2PI and Wilson actions. We illustrate how the different perturbative duality symmetries survive this simple nonperturbative phenomenon, providing evidence for the believe that these are exact nonperturbative symmetries of string theory. Consistency with T duality lifts the moduli degeneracy. The $B_{μν}-axion$ duality also survives in a nontrivial way in which the degree of freedom corresponding to $B_{μν}$ is replace…
We analyze the gaugino condensation in the effective theory for N=1 SU(N) Supersymmetric QCD with $N_{f}$ flavors. It is known that taking the vacuum expectation value of the matter field to be infinite, we can show that gaugino condensation can occur. At such a limit we should consider only pure supersymmetric Yang-Mills theory. But when we include an interaction term of order $O(\frac{1}{v})$, the situation can change. We analyze the effect of this interaction term and examine the gaugino condensation in the low energy Yang-Mills theory by using the scheme of Nambu-Jona-Lasinio.
We study gaugino condensation in presence of an anomalous $U(1)$ gauge group and find that global supersymmetry is dynamically broken. An example of particular interest is provided by effective string models with 4-dimensional Green-Schwarz anomaly cancellation mechanism. The structure of the hidden sector is constrained by the anomaly cancellation conditions and the scale of gaugino condensation is shifted compared with the usual case. We explicitly compute the resulting soft supersymmetry breaking terms.
Using the linear multiplet formulation for the dilaton superfield, we construct an effective lagrangian for hidden-sector gaugino condensation in string effective field theories with arbitrary gauge groups and matter. Nonperturbative string corrections to the Kähler potential are invoked to stabilize the dilaton at a supersymmetry breaking minimum of the potential. When the cosmological constant is tuned to zero the moduli are stabilized at their self-dual points, and the vev's of their F-component superpartners vanish. Numerical analyses of one- and two-condensate examples with massless chira…
Gaugino condensation plays a crucial role in the formation of dS vacua. However, the theory of this effect is still incomplete. In 4d the perfect square nature of gaugino couplings follows from the square of auxiliaries in the supergravity action. We explain here why the supersymmetric non-Abelian Dp-brane action, which is the basis for the theory of 10d gaugino condensation, must have a 4-gaugino coupling. This term in the Einstein-Yang-Mills 10d supergravity is a part of the perfect square, mixing a 3-form with gaugino bilinear. The perfect square term follows from the superspace geometry, b…
The weakly-coupled heterotic string is known to have problems of dilaton/moduli stabilization, supersymmetry breaking (by hidden-sector gaugino condensation), gauge coupling unification (or the Newton's constant), QCD axion, as well as cosmological problems. We study these problems by adopting the viewpoint that they arise mostly due to our limited calculational power, little knowledge of the vacuum structure, and an inappropriate treatment of gaugino condensation. It turns out that these problems can be solved or are much less severe after a more consistent and complete treatment. There are t…
The duality-invariant gaugino condensation with or without massive matter fields is re-analysed, taking into account the dependence of the string threshold corrections on the moduli fields and recent results concerning one-loop corrected Kähler potentials. The scalar potential of the theory for a generic superpotential is also calculated.
Gaugino condensation is discussed in the context of a consistent new version of low energy heterotic M-theory. The four dimensional reduction of the theory is described, based on simple boson and fermion backgrounds. This is generalised to include gaugino condenstates and various background fluxes, some with non-trivial topology. It is found that condensate and quantised flux contributions to the four-dimensional superpotential contain no corrections due to the warping of the higher dimensional metric.
We present the potential energy due to flux and gaugino condensation in heterotic M-theory compactifications with anti-branes in the vacuum. For reasons which we explain in detail, the contributions to the potential due to flux are not modified from those in supersymmetric contexts. The discussion of gaugino condensation is, however, changed by the presence of anti-branes. We show how a careful microscopic analysis of the system allows us to use standard results in supersymmetric gauge theory in describing such effects - despite the explicit supersymmetry breaking which is present. Not surpris…
String effective theories with N=1 supersymmetry in four dimensions are subject of the discussion. Gaugino condensation in the chiral representation of the dilaton is reviewed in the truncated formalism in the $U_{K}(1)$-superspace. Using the supersymmetric duality of the dilaton the same investigation is made in the linear representation of the dilaton. We show that for the simple case of one gaugino condensate the results concerning supersymmtry breaking are independent of the representation of the dilaton.
This talk is a brief review of gaugino condensation in superstring effective field theories and some related issues (such as renormalization of the gauge coupling in the effective supergravity theories and modular anomaly cancellation). As a specific example, we discuss a model containing perturbative (1-loop) corrections to the Kähler potential and approximate S-duality symmetry.
We discuss compactifications of heterotic string theory to four dimensions in the presence of H-fluxes, which deform the geometry of the internal manifold, and a gaugino condensate which breaks supersymmetry. We focus on the compensation of the two effects in order to obtain vacua with zero cosmological constant and we comment on the effective superpotential describing these vacua.
We study in detail gaugino condensation in globally and locally supersymmetric Yang-Mills theories. We focus on models for which gauge-neutral matter couples to the gauge bosons only through nonminimal gauge kinetic terms, for the cases of one and several condensing gauge groups. Using only symmetry arguments, the low-energy expansion, and general properties of supersymmetry, we compute the low energy Wilson action, as well as the (2PI) effective action for the composite {\it classical} superfield $U\equiv\langle \Tr\WW \rangle$, with $W_α$ the supersymmetric gauge field strength. The 2PI effe…
The mechanism of gaugino condensation has emerged as a prime candidate for supersymmetry breakdown in low energy effective supergravity (string) models. One of the open questions in this approach concerns the size of the gauge coupling constant which is dynamically fixed through the vev of the dilaton. We argue that a nontrivial gauge kinetic function $f(S)$ could solve the potential problem of a runaway dilaton. The actual form of $f(S)$ might be constrained by symmetry arguments.
We present a mechanism able to generate the perturbatively absent up/down $<{\bf 10} \cdot {\bf 10} \cdot {\bf 5}^H>$ quark Yukawa couplings of SU(5)/flipped SU(5) GUTS in Type II orientifold compactifications with D-branes. The mechanism works when there are Sp(N) gauge groups involved. The ${\bf {\bar 5}}$'s get charged under the Sp(N) gauge groups and the generation of quark masses proceeds via the generation of the fermionic Sp(N) singlet condensate $<{\bf {\bar 5} \cdot {\bar 5} \cdot {\bar 5} \cdot {\bar 5}}>$ in the term $(1/{M_s^5}) {\bf 10} \cdot {\bf 10} \cdot < {\bf {\bar 5} \cdot {…
The existence of de Sitter solutions in string theory is strongly constrained by no-go theorems. We continue our investigation of corrections to the heterotic effective action, with the aim of either strengthening or evading the these constraints. We consider the combined effects of H-flux, gauge bundles, higher derivative corrections and gaugino condensation. The only consistent solutions we find with maximal symmetry in four dimensions are Minkowski spacetimes, ruling out both de Sitter and anti-de Sitter solutions constructed from these ingredients alone.
An effective lagrangian analysis of gaugino condensation is performed in a supersymmetric gauge theory with field-dependent gauge couplings described with a linear multiplet. An original aspect of this effective lagrangian is the use of a real vector superfield to describe composite gauge invariant degrees of freedom. The duality equivalence of this approach with the more familiar formulation using a chiral superfield is demonstrated. These results strongly suggest that chiral-linear duality survives nonperturbative effects in superstrings.
The principle of S-duality is used to incorporate gaugino condensates into effective supergravity (superstring) Lagrangians. We discuss two implementations of S-duality which differ in the way the coupling constant is transformed. Both solve the problem of the runaway dilaton and lead to satisfactory supersymmetry breaking in models with a {\em single} gaugino condensate. The breakdown of supersymmetry is intimately related to a nontrivial transformation of the condensate under T-duality.
The gaugino propagator is calculated by explicitly considering the propagation of a heterotic string between two different points in space-time using the non-trivial world-sheet conformal field theory for the fivebrane background. We find that there are no propagations of gaugino which is in the spinor representation of the non-trivial four-dimensional space of the fivebrane background. This result is consistent with the arguments on the fermion zero-modes of the fivebrane background in the low-energy heterotic supergravity theory. Furthermore, assuming the continuous limit to the flat space-t…
We discuss non-perturbative aspects of string effective field theories with N=1 supersymmetry in four dimensions. By the use of a scalar potential, which is on-shell invariant under the supersymmetric duality of the dilaton, we study gaugino condensation in (2,2) symmetric Z_{N} orbifold compactifications. The duality under consideration relates a two-form antisymmetric tensor to a pseudoscalar. We show, that our approach is independent of the superfield-representation of the dilaton and preserves the U(1)_{PQ} Peccei-Quinn symmetry exactly.
We present an additional test of the recent proposal for describing supersymmetry breaking due to gaugino condensation in the strong coupling regime, by a Scherk-Schwarz mechanism on the eleventh dimension of M-theory. An analysis of supersymmetric transformations in the infinite-radius limit reveals the presence of a discontinuity in the spinorial parameter, which coincides with the result found in the presence of gaugino condensation. The condensate is then identified with the quantized parameter entering the modification of the Scherk-Schwarz boundary conditions. This mechanism provides an …
We study a class of four-dimensional N=1 heterotic string theories which have nontrivial quantum dynamics arising from asymptotically free gauge groups. These models are obtained by orbifolding 4d N=2 heterotic/type II dual pairs by symmetries which leave unbroken products of nonabelian gauge groups (without charged matter) in a ``hidden sector'' on the heterotic side. Such models are expected to break supersymmetry through gaugino condensation in the hidden sector. We find a dual description of the effects of gaugino condensation on the type II side, where the corresponding superpotential ari…
The status of the gaugino condensation as the source of supersymmetry breaking is reexamined. It is argued that one cannot have stable minima with broken supersymmetry in models where the dilaton is coupled only linearly to the gaugino condensate. We show that the problems of the gaugino condensate mechanism can be solved by considering nonstandard gauge kinetic functions, created by nonperturbative effects. As an example we use the principle of S-duality to modify the coupling of the gaugino condensate to effective supergravity (superstring) Lagrangians. We show that such an approach can solv…
We study gaugino condensation in the presence of an intermediate mass scale in the hidden sector. S-duality is imposed as an approximate symmetry of the effective supergravity theory. Furthermore, we include in the Kähler potential the renormalization of the gauge coupling and the one-loop threshold corrections at the intermediate scale. It is shown that confinement is indeed achieved. Furthermore, a new running behaviour of the dilaton arises which we attribute to S-duality. We also discuss the effects of the intermediate scale, and possible phenomenological implications of this model.
We derive the explicit form, and discuss some properties of the moduli dependent effective potential arising from M-theory compactified on $M_4 \times X\times S^1 / Z_2 $, when one of the boundaries supports a strongly interacting gauge sector and induces gaugino condensation. We discuss the relation between the explicit gaugino condensate and effective superpotential formulations and find interesting differences with respect to the situation known from the weakly coupled heterotic string case. The moduli dependence of the effective potential turns out to be more complicated than expected, and…
I consider N=1 U(N) gauge theory with matter in the adjoint, fundamental and anti-fundamental representations. Focusing on the equations defining the Riemann surface that describes the quantum theory, the gaugino condensates (and related superpotentials) are calculated in the limit of SU(N) gauge group, both in the pure theory and in the presence of matter. In the case without fundamental matter it is investigated the structure of the space of vacua. In particular it is discussed how different vacua can be related, in a way which finally helps to count them.
We examine the one-loop vacuum structure of an effective theory of gaugino condensation coupled to the dilaton for string models in which the gauge coupling constant does not receive string threshold corrections. The new ingredients in our treatment are that we take into account the one-loop correction to the dilaton Kähler potential and we use a formulation which includes a chiral field $H$ corresponding to the gaugino bilinear. We find through explicit calculation that supersymmetry in the Yang-Mills sector is broken by gaugino condensation. The dilaton and $H$ field have masses on the order…
We extend the linearised solution of Polchinski and Strassler describing the supergravity dual of the N=1* gauge theory. By analysing the equations of motion of type IIB supergravity at cubic order in the mass perturbation parameter, we demonstrate the emergence of a 3-form flux of type (3,0) with respect to the natural complex structure. The generation of this flux can be associated to the dynamical formation of a gaugino condensate in the confining phase of the N=1* gauge theory. We also check that the supersymmetry conditions are satisfied, and we discuss how this (3,0)-form flux is tied to…
The phenomenon known as ``anomaly mediation" can be understood in a variety of ways. Rather than an anomaly, certain gaugino bilinear terms are required by local supersymmetry and gauge invariance (the derivation of these terms is in some cases related to anomalies in scale invariance or $R$ symmetries). We explain why the gaugino bilinear is required in supersymmetric gauge theories with varying number of colors and flavors. By working in the Higgs phase, gauging a flavor group, or working below the scale of gaugino condensation, each of these theories has a local effective description in whi…
We study heterotic backgrounds with non-trivial $H$-flux and non-vanishing expectation values of fermionic bilinears, often referred to as gaugino condensates. The gaugini appear in the low energy action via the gauge-invariant three-form bilinear $Σ_{MNP}={\rm tr}\:\barχΓ_{MNP}χ$. For Calabi-Yau compactifications to four dimensions, the gaugino condensate corresponds to an internal three-form $Σ_{mnp}$ that must be a singlet of the holonomy group. This condition does not hold anymore when an internal $H$-flux is turned on and ${\cal O}(α')$ effects are included. In this paper we study flux co…
Gaugino condensation on D-branes wrapping internal cycles gives a mechanism to stabilize the associated moduli. According to the effective field theory, this gives rise, when combined with fluxes, to supersymmetric AdS$_4$ solutions. In this paper we provide a ten-dimensional description of these vacua. We first find the supersymmetry equations for type II AdS$_4$ vacua with gaugino condensates on D-branes, in the framework of generalized complex geometry. We then solve them for type IIB compactifications with gaugino condensates on smeared D7-branes. We show that supersymmetry requires a (con…
We study dynamical moduli stabilization driven by gaugino condensation in supergravity. In the presence of background radiation, there exists a region of initial conditions leading to successful stabilization. We point out that most of the allowed region corresponds to initial Hubble rate H close to the scale of condensation Λ, which is the natural cutoff of the effective theory. We first show that including the condensate dynamics sets a strong bound on the initial conditions. We then find that (complete) decoupling of the condensate happens at H about two orders of magnitude below Λ. This bo…
It has been known that in a wide class of direct gauge mediation models, the gaugino masses vanish at leading order in SUSY breaking. Recently, this phenomenon is understood in connection with the global structure of vacua in O'Raifeartaigh-type models. We review recent developments on this topic.
In the first part of this note we argue that ten dimensional consistency requirements in the form of a certain tadpole cancellation condition can be satisfied by KKLT type vacua of type IIB string theory. We explain that a new term of non-local nature is generated dynamically once supersymmetry is broken and ensures cancellation of the tadpole. It can be interpreted as the stress caused by the restoring force that the stabilization mechanism exerts on the volume modulus. In the second part, we explain that it is surprisingly difficult to engineer sufficiently long warped throats to prevent dec…
It is argued that black hole condensation can occur at conifold singularities in the moduli space of type II Calabi--Yau string vacua. The condensate signals a smooth transition to a new Calabi--Yau space with different Euler characteristic and Hodge numbers. In this manner string theory unifies the moduli spaces of many or possibly all Calabi--Yau vacua. Elementary string states and black holes are smoothly interchanged under the transitions, and therefore cannot be invariantly distinguished. Furthermore, the transitions establish the existence of mirror symmetry for many or possibly all Cala…
The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the $B-L$ MSSM theory is reviewed, including a discussion of the "bundle" constraints that both the observable sector $SU(4)$ vector bundle and the a hidden sector bundle induced from a line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales …
In the low energy limit of for M-theory on S^1/Z_2, we calculate the gaugino condensate potential in four dimensions using the background solutions due to Horava. We show that this potential is free of delta-function singularities and has the same form as the potential in the weakly coupled heterotic string. A general flux quantization rule for the three-form field of M-theory on S^1/Z_2 is given and checked in certain limiting cases. This rule is used to fix the free parameter in the potential originating from a zero mode of the form field. Finally, we calculate soft supersymmetry breaking te…
We discuss some aspects of confinement and dynamical symmetry breaking in the so-called nonabelian Argyres-Douglas vacua, which occur very generally in supersymmetric theories. These systems are characterized by strongly-coupled nonabelian monopoles and dyons; confinement and dynamical symmetry breaking are caused by the condensation of monopole composites, rather than by condensation of single weakly-coupled monopoles. In general, there are strong constraints on which kind of monopoles can appear as the infrared degrees of freedom, related to the proper realization of the global symmetry of t…
There are two known sources of nonperturbative superpotentials for Kähler moduli in type IIB orientifolds, or F-theory compactifications on Calabi-Yau fourfolds, with flux: Euclidean brane instantons and low-energy dynamics in D7 brane gauge theories. The first class of effects, Euclidean D3 branes which lift in M-theory to M5 branes wrapping divisors of arithmetic genus 1 in the fourfold, is relatively well understood. The second class has been less explored. In this paper, we consider the explicit example of F-theory on $K3 \times K3$ with flux. The fluxes lift the D7 brane matter fields, an…
Coupling of bilinears of gauginos on D-branes to anti-symmetric tensor fields can be deduced by comparing F-theory compactified to 8 dimensions with the heterotic string on $R^8\times T^2$. Application to SUSY breaking in F-theory triggered by gaugino condensation is discussed. Compactification to four dimensions with a warp factor is briefly discussed. In this case some 3-branes whose world-volume coincides with the open spacetime must be introduced, in addition to 7-branes.
We present a new mechanism, the S-Track, to stabilize the volume modulus S in heterotic M-theory flux compactifications along with the orbifold-size T besides complex structure and vector bundle moduli stabilization. The key dynamical ingredient which makes the volume modulus stabilization possible, is M5-instantons arising from M5-branes wrapping the whole Calabi-Yau slice. These are natural in heterotic M-theory where the warping shrinks the Calabi-Yau volume along S^1/Z_2. Combined with H-flux, open M2-instantons and hidden sector gaugino condensation it leads to a superpotential W which st…
We investigate, at the microscopic level, the compatibility between D-term potentials from world-volume fluxes on D7-branes and non-perturbative superpotentials arising from gaugino condensation on a different stack of D7-branes. This is motivated by attempts to construct metastable de Sitter vacua in type IIB string theory via D-term uplifts. We find a condition under which the Kaehler modulus, T, of a Calabi-Yau 4-cycle gets charged under the anomalous U(1) on the branes with flux. If in addition this 4-cycle is wrapped by a stack of D7-branes on which gaugino condensation takes place, the q…
Within the ongoing debate about de Sitter (dS) vacua in string theory, different aspects of explicit dS proposals have come under intense scrutiny. One key ingredient is D7-brane gaugino condensation, which is usually treated using effective 4d supergravity. However, it is clearly more desirable to derive the relevant scalar potential directly from a local 10d Lagrangian. Such a local 10d description captures the interactions among the various localized sources and the background fields which are smeared in the 4d Lagrangian. While progress in this endeavour has recently been made, some form o…
