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Distributions of flux vacua
 JHEP
"... Abstract: We give results for the distribution and number of flux vacua of various types, supersymmetric and nonsupersymmetric, in IIb string theory compactified on CalabiYau manifolds. We compare this with related problems such as counting attractor points. Contents ..."
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Cited by 165 (16 self)
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Abstract: We give results for the distribution and number of flux vacua of various types, supersymmetric and nonsupersymmetric, in IIb string theory compactified on CalabiYau manifolds. We compare this with related problems such as counting attractor points. Contents
Supersymmetry and Attractors
 Phys. Rev. D
, 1996
"... We find a general principle which allows one to compute the area of the horizon of N=2 extremal black holes as an extremum of the central charge. One considers the ADM mass equal to the central charge as a function of electric and magnetic charges and moduli and extremizes this function in the modul ..."
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Cited by 158 (14 self)
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We find a general principle which allows one to compute the area of the horizon of N=2 extremal black holes as an extremum of the central charge. One considers the ADM mass equal to the central charge as a function of electric and magnetic charges and moduli and extremizes this function in the moduli space (a minimum corresponds to a fixed point of attraction). The extremal value of the square of the central charge provides the area of the horizon, which depends only on electric and magnetic charges. The doubling of unbroken supersymmetry at the fixed point of attraction for N=2 black holes near the horizon is derived via conformal flatness of the BertottiRobinsontype geometry. These results provide an explicit model independent expression for the macroscopic BekensteinHawking entropy of N=2 black holes which is manifestly duality invariant. The presence of hypermultiplets in the solution does not affect the area formula. Various examples of the general formula are displayed. We outline the attractor mechanism in N=4,8 supersymmetries and the relation to the N=2 case. The entropyarea formula in five dimensions, recently discussed in the literature, is also seen to be obtained by extremizing the 5d central charge.
Nongeometric Flux Compactifications
, 2006
"... We investigate a simple class of type II string compactifications which incorporate nongeometric “fluxes” in addition to “geometric flux” and the usual Hfield and RR fluxes. These compactifications are nongeometric analogues of the twisted torus. We develop Tduality rules for NSNS geometric and ..."
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Cited by 129 (5 self)
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We investigate a simple class of type II string compactifications which incorporate nongeometric “fluxes” in addition to “geometric flux” and the usual Hfield and RR fluxes. These compactifications are nongeometric analogues of the twisted torus. We develop Tduality rules for NSNS geometric and nongeometric fluxes, which we use to construct a superpotential for the dimensionally reduced fourdimensional theory. The resulting structure is invariant under Tduality, so that the distribution of vacua in the IIA and IIB theories is identical when nongeometric fluxes are included. This gives a concrete framework in which to investigate the possibility that generic string compactifications may be nongeometric in any duality frame. The framework developed in this paper also provides some concrete hints for how mirror symmetry can be generalized to compactifications with arbitrary Hflux, whose mirrors are generically nongeometric.
Ftheory flux, destabilization of orientifolds and soft terms on D7branes,” arXiv:hepth/0501139
"... We use Ftheory to derive a general expression for the flux potential of type II compactifications with D7/D3 branes, including open string moduli and 2form fluxes on the branes. Our main example is Ftheory on K3 × K3 and its orientifold limit T 2 /Z2 × K3. The full scalar potential cannot be deri ..."
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Cited by 65 (13 self)
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We use Ftheory to derive a general expression for the flux potential of type II compactifications with D7/D3 branes, including open string moduli and 2form fluxes on the branes. Our main example is Ftheory on K3 × K3 and its orientifold limit T 2 /Z2 × K3. The full scalar potential cannot be derived from the bulk superpotential W = ∫ Ω ∧ G3 and generically destabilizes the orientifold. Generically all open and closed string moduli are fixed, except for a volume factor. An alternative formulation of the problem in terms of the effective supergravity is given and we construct an explicit map between the Ftheory fluxes and gaugings. We use the superpotential to compute the effective action for flux compactifications on orbifolds, including the µterm and softbreaking terms on the D7brane worldvolume. January
The scaling of the noscale potential and de Sitter model building
"... We propose a variant of the KKLT (A)dS flux vacuum construction which does not require an antibrane to source the volume modulus. The strategy is to find nonzero local minima of the noscale potential in the complex structure and dilaton directions in moduli space. The corresponding noscale potenti ..."
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Cited by 61 (3 self)
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We propose a variant of the KKLT (A)dS flux vacuum construction which does not require an antibrane to source the volume modulus. The strategy is to find nonzero local minima of the noscale potential in the complex structure and dilaton directions in moduli space. The corresponding noscale potential expanded about this point sources the volume modulus in the same way as does the antibrane of the KKLT construction. We exhibit explicit examples of such nonzero local minima of the noscale potential in a simple toroidal orientifold model.
An open string landscape
 JHEP
, 2005
"... Abstract: The effect of fluxes on open string moduli is studied by analyzing the constraints imposed by supersymmetry on Dbranes in type IIB flux backgrounds. We show that generically the conditions of supersymmetry cannot be maintained when moving along the geometrical moduli space of the brane, s ..."
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Cited by 56 (3 self)
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Abstract: The effect of fluxes on open string moduli is studied by analyzing the constraints imposed by supersymmetry on Dbranes in type IIB flux backgrounds. We show that generically the conditions of supersymmetry cannot be maintained when moving along the geometrical moduli space of the brane, so that open string moduli are lifted. In specific examples, we find that there is a disconnected and discrete set of supersymmetric solutions to the open string equations of motion, which extends the familiar closed string landscape to the open string sector. Permanent addressContents
Nonperturbative superpotentials in Ftheory and string duality
, 2005
"... We use openclosed string duality between Ftheory on K3 × K3 and type II strings on CY manifolds without branes to study nonperturbative superpotentials in generalized flux compactifications. On the Ftheory side we obtain the full flux potential including D3instanton contributions and show that ..."
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Cited by 45 (2 self)
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We use openclosed string duality between Ftheory on K3 × K3 and type II strings on CY manifolds without branes to study nonperturbative superpotentials in generalized flux compactifications. On the Ftheory side we obtain the full flux potential including D3instanton contributions and show that it leads to an explicit and simple realization of the three ingredients of the KKLT model for stringy dS vacua. The D3instanton contribution is highly nontrivial, can be systematically computed including the determinant factors and demonstrates that a particular flux lifts very effectively zero modes on the instanton. On the closed string side, we describe a generalization of the GukovVafaWitten superpotential for type II strings on generalized CY manifolds, depending on all moduli multiplets.
Lifting DInstanton Zero Modes by Recombination and Background Fluxes
, 2007
"... We study the conditions under which Dbrane instantons in Type II orientifold compactifications generate a nonperturbative superpotential. If the instanton is noninvariant under the orientifold action, it carries four instead of the two Goldstone fermions required for superpotential contributions. ..."
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Cited by 40 (15 self)
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We study the conditions under which Dbrane instantons in Type II orientifold compactifications generate a nonperturbative superpotential. If the instanton is noninvariant under the orientifold action, it carries four instead of the two Goldstone fermions required for superpotential contributions. Unless these are lifted, the instanton can at best generate higher fermionic Fterms of BeasleyWitten type. We analyse two strategies to lift the additional zero modes. First we discuss the process of instantonic brane recombination in Type IIA orientifolds. We show that in some cases charge invariance of the measure enforces the presence of further zero modes which, unlike the Goldstinos, cannot be absorbed. In other cases, the instanton exhibits reparameterisation zero modes after recombination and a superpotential is generated if these are lifted by suitable closed or open string couplings. In the second part of the paper we address lifting the extra Goldstinos of D3brane instantons by supersymmetric threeform background fluxes in Type IIB orientifolds. This requires nontrivial gauge flux on the instanton. Only if the part of the fermionic action linear in the gauge flux survives the orientifold projection can the extra Goldstinos be lifted.
Warped strings: Selfdual flux and contemporary compactifications
"... String theory is a leading candidate for the quantum theory of gravitation and is the only serious unified theory of all the forces of physics. Additionally, string theory seems to be mathematically unique, and it is possible that all the parameters of physics could be determined by the dynamics of ..."
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Cited by 34 (3 self)
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String theory is a leading candidate for the quantum theory of gravitation and is the only serious unified theory of all the forces of physics. Additionally, string theory seems to be mathematically unique, and it is possible that all the parameters of physics could be determined by the dynamics of string theory. However, there are two intertwined problems. First is that string theory requires ten dimensions for mathematical consistency, so six must be compact or otherwise decoupled from the physics we observe. Also, there exist many different ground states of string theory, so it is difficult to make predictions that are generic to string theory. Therefore, it is crucial to gain a broad understanding of all the string theory vacua, particularly those compactified to four dimensions. In recent years, our understanding of string theory compactifications has expanded greatly to include many new classes of solutions. In this dissertation, I discuss type IIB string compactifications in which the threeform field strengths satisfy a selfduality condition on the internal manifold. I
Building MSSM Flux Vacua
, 2008
"... We construct N = 1 and N = 0 chiral fourdimensional vacua of flux compactification in Type IIB string theory. These vacua have the common features that they are free of tadpole instabilities (both NSNS and RR) even for models with N = 0 supersymmetry. In addition, the dilaton/complex structure mod ..."
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Cited by 30 (4 self)
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We construct N = 1 and N = 0 chiral fourdimensional vacua of flux compactification in Type IIB string theory. These vacua have the common features that they are free of tadpole instabilities (both NSNS and RR) even for models with N = 0 supersymmetry. In addition, the dilaton/complex structure moduli are stabilised and the supergravity background metric is warped. We present an example in which the low energy spectrum contains the MSSM spectrum with three generations of chiral matter. In the N = 0 models, the background fluxes which stabilise the moduli also induce soft supersymmetry breaking terms in the gauge and chiral sectors of the theory, while satisfying the equation of motion. We also discuss some phenomenological features of these three generation MSSM flux vacua. Our techniques apply to other closed string backgrounds as well and, in fact, also allow to find new N = 1 Dbrane models which were believed not to exist. Finally, we discuss in detail the consistency conditions of these flux compactifications. Cancellation of Ktheory charges puts additional constraints on the consistency of the models, which render some chiral Dbrane models in the literature inconsistent.