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Register a new userK3 x T^2/Z_2 orientifolds with fluxes, open string moduli and critical points
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We extend the four-dimensional gauged supergravity analysis of type IIB vacua on $K3times T^2/Z_2$ to the case where also D3 and D7 moduli, belonging to N=2 vector multiplets, are turned on. In this case, the overall special geometry does not correspond to a symmetric space, unless D3 or D7 moduli are switched off. In the presence of non--vanishing fluxes, we discuss supersymmetric critical points which correspond to Minkowski vacua, finding agreement with previous analysis. Finally, we point out that care is needed in the choice of the symplectic holomorphic sections of special geometry which enter the computation of the scalar potential.
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We study Fayet-Iliopoulos (FI) terms of six-dimensional supersymmetric Abelian gauge theory compactified on a $T^2/Z_2$ orbifold. Such orbifold compactifications can lead to localized FI-terms and instability of bulk zero modes. We study 1-loop correction to FI-terms in more general geometry than the previous works. We find induced FI-terms depend on the complex structure of the compact space. We also find the complex structure of the torus can be stabilized at a specific value corresponding to a self-consistent supersymmetric minimum of the potential by such 1-loop corrections, which is applicable to the modulus stabilization.
A recently constructed limit of K3 has a long neck consisting of segments, each of which is a nilfold fibred over a line, that are joined together with Kaluza-Klein monopoles. The neck is capped at either end by a Tian-Yau space, which is non-compact, hyperkahler and asymptotic to a nilfold fibred over a line. We show that the type IIA string on this degeneration of K3 is dual to the type I$$ string, with the Kaluza-Klein monopoles dual to the D8-branes and the Tian-Yau spaces providing a geometric dual to the O8 orientifold planes. At strong coupling, each O8-plane can emit a D8-brane to give an O8$^*$ plane, so that there can be up to 18 D8-branes in the type I$$ string. In the IIA dual, this phenomenon occurs at weak coupling and there can be up to 18 Kaluza-Klein monopoles in the dual geometry. We consider further duals in which the Kaluza-Klein monopoles are dualised to NS5-branes or exotic branes. A 3-torus with $H$-flux can be realised in string theory as an NS5-brane wrapped on $T^3$, with the 3-torus fibred over a line. T-dualising gives a 4-dimensional hyperkahler manifold which is a nilfold fibred over a line, which can be viewed as a Kaluza-Klein monopole wrapped on $T^2$. Further T-dualities then give non-geometric spaces fibred over a line and can be regarded as wrapped exotic branes. These are all domain wall configurations, dual to the D8-brane. Type I$$ string theory is the natural home for D8-branes, and we dualise this to find string theory homes for each of these branes. The Kaluza-Klein monopoles arise in the IIA string on the degenerate K3. T-duals of this give exotic branes on non-geometric spaces.
We discuss general properties of moduli stablization in KKLT scenarios in type IIB orientifold compactifications. In particular, we find conditions for the Kaehler potential to allow a KKLT scenario for a manifold X_6 without complex structure moduli, i.e. h_(2,1)(X_6)=0. This way, a whole class of type IIB orientifolds with h_(2,1)(X_6)=0 is ruled out. This excludes in particular all Z_N- and Z_N x Z_M-orientifolds X_6 with h_(2,1)(X_6)=0 for a KKLT scenario. This concerns Z_3, Z_7, Z_3 x Z_3, Z_4 x Z_4, Z_6 x Z_6 and Z_2 x Z_6 -both at the orbifold point and away from it. Furthermore, we propose a mechanism to stabilize the Kaehler moduli accociated to the odd cohomology H^(1,1)_-(X_6). In the second part of this work we discuss the moduli stabilization of resolved type IIB Z_N- or Z_N x Z_M - orbifold/orientifold compactifications. As examples for the resolved Z_6 and Z_2 x Z_4 orbifolds we fix all moduli through a combination of fluxes and racetrack superpotential.
We discuss flux quantization and moduli stabilization in toroidal type IIB Z_N - or Z_N x Z_M -orientifolds, focusing mainly on their orbifold limits. After presenting a detailed discussion of their moduli spaces and effective actions, we study the supersymmetric vacuum structure of these models and derive criteria for the existence of stable minima. Furthermore, we briefly investigate the models away from their orbifold points and comment on the microscopic origin of their non-perturbative superpotentials.
We consider classes of T_6 orientifolds, where the orientifold projection contains an inversion I_{9-p} on 9-p coordinates, transverse to a Dp-brane. In absence of fluxes, the massless sector of these models corresponds to diverse forms of N=4 supergravity, with six bulk vector multiplets coupled to N=4 Yang--Mills theory on the branes. They all differ in the choice of the duality symmetry corresponding to different embeddings of SU(1,1)times SO(6,6+n) in Sp(24+2n,R), the latter being the full group of duality rotations. Hence, these Lagrangians are not related by local field redefinitions. When fluxes are turned on one can construct new gaugings of N=4 supergravity, where the twelve bulk vectors gauge some nilpotent algebra which, in turn, depends on the choice of fluxes.
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