We discuss the origin of the choice of global structure for six dimensional $(2,0)$ theories and their compactifications in terms of their realization from IIB string theory on ALE spaces. We find that the ambiguity in the choice of global structure on the field theory side can be traced back to a subtle effect that needs to be taken into account when specifying boundary conditions at infinity in the IIB orbifold, namely the known non-commutativity of RR fluxes in spaces with torsion. As an example, we show how the classification of $\mathcal{N}=4$ theories by Aharony, Seiberg and Tachikawa can be understood in terms of choices of boundary conditions for RR fields in IIB. Along the way we encounter a formula for the fractional instanton number of $\mathcal{N}=4$ ADE theories in terms of the torsional linking pairing for rational homology spheres. We also consider six-dimensional $(1,0)$ theories, clarifying the rules for determining commutators of flux operators for discrete 2-form symmetries. Finally, we analyze the issue of global structure for four dimensional theories in the presence of duality defects.
In this paper we consider a class of exactly solvable closed string flux backgrounds that exhibit non-commutativity in the closed string coordinates. They are realized in terms of freely-acting asymmetric Z_N-orbifolds, which are themselves close relatives of twisted torus fibrations with elliptic Z_N-monodromy (elliptic T-folds). We explicitly construct the modular invariant partition function of the models and derive the non-commutative algebra in the string coordinates, which is exact to all orders in α'. Finally, we relate these asymmetric orbifold spaces to inherently stringy Scherk-Schwa…
In this note I demonstrate that certain findings on IIB flux compactifications in the large complex structure limit, when combined with recent statistical bounds on the large $h^{2,1}$ limit, are compatible with the Tadpole Conjecture, contrary to previous claims.
We explore several consequences of the recently discovered intrinsic non-commutativity of the zero-mode sector of closed string theory. In particular, we illuminate the relation between T-duality and this intrinsic non-commutativity and also note that there is a simple closed string product, equivalent to the splitting-joining interaction of the pants diagram, that respects this non-commutativity and is covariant with respect to T-duality. We emphasize the central role played by the symplectic form $ω$ on the space of zero modes. Furthermore, we begin an exploration of new non-commutative stri…
Using a recently proposed group-theoretical approach, we explore novel gaugings of maximal supergravity in four dimensions with gauge group embeddings that can be generated by fluxes of IIB string theory. The corresponding potentials are positive without stationary points. Some allow domain wall solutions which can be elevated to ten dimensions. Appropriate truncations describe type-IIB flux compactifications on T^6 orientifolds leading to non-maximal, four-dimensional, supergravities.
We quantize the type IIB GS string action on AdS3 X S3 with pure NSNS background and we show that it is equivalent to Liouville with periodic boundary condition plus free spacetime fermions.
Various approaches to T-duality with NSNS three-form flux are reconciled. Non-commutative torus fibrations are shown to be the open-string version of T-folds. The non-geometric T-dual of a three-torus with uniform flux is embedded into a generalized complex six-torus, and the non-geometry is probed by D0-branes regarded as generalized complex submanifolds. The non-commutativity scale, which is present in these compactifications, is given by a holomorphic Poisson bivector that also encodes the variation of the dimension of the world-volume of D-branes under monodromy. This bivector is shown to …
We study in detail some aspects of duality between type IIB and M-theory. We focus on the duality between type IIB string theory on K3 x T^2/Z_2 orientifold and M-theory on K3 x K3, in the F-theory limit. We give the explicit map between the fields and in particular between the moduli of compactification, studying their behavior under the F-theory limit. Turning on fluxes generates a potential for the moduli both in type IIB and in M-theory. We verify that the type IIB analysis gives the same results of the F-theory analysis. In particular, we check that the two potentials match.
We study type IIB string compactifications in the presence of RR and NSNS fluxes using worldsheet techniques. Vertex operators corresponding to internal RR and NSNS fluxes are constructed in the hybrid formalism with manifest target space supersymmetry. In a simple class of examples, we compute various known physical phenomena such as warping and the generation of a superpotential for complex structure moduli. The results are in precise agreement with the supergravity literature.
We propose a general spinor Ansatz to find supersymmetric configurations preserving 4-dimensional Poincare' invariance in the context of type IIB supergravity in the presence of general fluxes. We show how this removes the imaginary-selfduality (ISD) constraint on the 3-form flux and present a simple example with nonvanishing (0,3) flux. To characterize the geometrical properties of such configurations we will use the tool of SU(2) structures on the internal space, which are naturally linked to the form of the Ansatz we propose.
We generalize the recently proposed mechanism by Demirtas, Kim, McAllister and Moritz arXiv:1912.10047 for the explicit construction of type IIB flux vacua with $|W_0|\ll 1$ to the region close to the conifold locus in the complex structure moduli space. For that purpose tools are developed to determine the periods and the resulting prepotential close to such a codimension one locus with all the remaining moduli still in the large complex structure regime. As a proof of principle we present a working example for the Calabi-Yau manifold $\mathbb{P}_{1,1,2,8,12}[24]$.
We study a class of orientifold compactifications of type IIB supergravity with fluxes down to 4D in connection with truncations of half-maximal gauged supergravities yielding isotropic STU-models with minimal supersymmetry. In this context, we make use of a group-theoretical approach in order to derive flux-induced superpotentials for different IIB backgrounds. We first review the toroidal case yielding GKP-like superpotentials characterised by their \emph{no-scale} behaviour. We then turn to $S^{3} \times S^{3}$ and $S^{3} \times \mathbb{T}^{3}$, which, surprisingly, give rise to effective d…
We revisit flux compactifications of type IIB string theory on `spaces' dual to rigid Calabi-Yau manifolds. This rather unexplored part of the string landscapes harbors many interesting four-dimensional solutions, namely supersymmetric $\mathcal{N}=1$ Minkowski vacua without flat direction and infinite families of AdS vacua, some potentially with unrestricted rank for the gauge group. We also comment on the existence of metastable dS solutions in this setup. We discuss how these solutions fit into the web of swampland conjectures.
We consider Type IIB orientifold models on Calabi-Yau spaces with three-form G-flux turned on. These fluxes freeze some of the complex structure moduli and the complex dilaton via an F-term scalar potential. By introducing pairs of D9-anti-D9 branes with abelian magnetic fluxes it is possible to freeze also some of the Kaehler moduli via a D-term potential. Moreover, such magnetic fluxes in general lead to chiral fermions, which make them interesting for string model-building. These issues are demonstrated in a simple toy model based on a Z_2 x Z_2' orbifold.
We derive the 3D N=1 superpotential for the closed string sector of type IIB supergravity on toroidal O5 orientifolds with co-calibrated G2 structure and RR background flux. We find that such compactifications can provide full closed string moduli stabilization on supersymmetric AdS$_3$ vacua, and once we include brane-supersymmetry-breaking we also find indication for the existence of classical 3D de Sitter solutions. The latter however are rather difficult to reconcile with the shape moduli stabilization and flux quantization. We also discuss the possibility of achieving scale separation in …
We classify under some assumptions the IIB black hole horizons with 5-form flux preserving more than 2 supersymmetries. We find that the spatial horizon sections with non-vanishing flux preserving 4 supersymmetries are locally isometric either to S^1 * S^3 * T^4 or to S^1 * S^3 * K_3 and the associated near horizon geometries are locally isometric to AdS_3 * S^3 * T^4 and AdS_3 * S^3 * K_3$, respectively. The near horizon geometries preserving more than 4 supersymmetries are locally isometric to R^{1,1} * T^8.
We discuss supersymmetry breaking via 3-form fluxes in chiral supersymmetric type IIB orientifold vacua with D3- and D7-branes. After a general discussion of possible choices of fluxes allowing for stabilizing of a part of the moduli, we determine the resulting effective action including all soft supersymmetry breaking terms. We also extend the computation of our previous work concerning the matter field metrics arising from various open string sectors, in particular focusing on the 1/2 BPS D3/D7-brane configuration. Afterwards, the F-theory lift of our constructions is investigated.
We identify the low-energy Kähler potential of warped F-theory/IIB flux compactifications whose light spectrum includes universal, Kähler, axionic and mobile D3-brane moduli. The derivation is based on four-dimensional local superconformal symmetry and holomorphy of brane instanton contributions and it reproduces and generalises previous partial results. We compute the resulting kinetic terms, which show their explicit dependence on the warping. The Kähler potential satisfies the no-scale condition and produces, at leading order in the large volume expansion, a specific correction to the unwar…
We revisit the two-stage procedure for moduli stabilization in Type IIB orientifolds at light Kähler-modulus limit. In view of the necessity to keep the Kähler geometry structure of the moduli space during the stabilization, we define a holomorphic quantity called effective superpotential. The KKLT superpotential as well as the superpotential proposed by Villadoro and Zwirner are then examined with respect to this holomorphic effective superpotential. The mechanism is also illustrated with a simple toy model of one complex structure modulus.
We consider flux vacua for type IIB orientifold compactifications and study their interplay with the tadpole-cancellation condition. As a concrete example we focus on $\mathbb T^6/\mathbb Z_2\times \mathbb Z_2$, for which we find that solutions to the F-term equations at weak coupling, large complex structure and large volume require large flux contributions. Such contributions are however strongly disfavored by the tadpole-cancellation condition. We furthermore find that solutions which stabilize moduli in this perturbatively-controlled regime are only a very small fraction of all solutions, …
We construct non-perturbatively exact four-dimensional Minkowski vacua of type IIB string theory with non-trivial fluxes. These solutions are found by gluing together, consistently with U-duality, local solutions of type IIB supergravity on $T^4 \times \mathbb{C}$ with the metric, dilaton and flux potentials varying along $\mathbb{C}$ and the flux potentials oriented along $T^4$. We focus on solutions locally related via U-duality to non-compact Ricci-flat geometries. More general solutions and a complete analysis of the supersymmetry equations are presented in the companion paper [1]. We buil…
In this note we study the mass spectrum of type IIB flux compactifications. We first give a general discussion of the mass matrix for F-term vacua in four-dimensional N=1 supergravity theories and then specialize to type IIB Calabi-Yau orientifold compactifications in the presence of geometric and non-geometric fluxes. F-term vacua in this setting are in general AdS$_4$ vacua for which we compute the conformal dimensions of operators dual to the scalar fields. For the mirror-dual of the DGKT construction we find that one-loop corrections to the complex-structure moduli space lead to real-value…
We continue the study of supersymmetric type IIB pp wave solutions by Maldacena and Maoz (hep-th/0207284), who showed Ramond-Ramond five-forms can induce potential terms in the light cone string actions which are nonlinear sigma models with special holonomy target spaces. We show nonvanishing Ramond-Ramond three-forms provide extra potential terms involving Killing vectors in the string action and identify the supersymmetry requirements. In particular, in solutions with (1,1) worldsheet supersymmetry, the Killing vectors are required to be self-dual in Spin(7).
We consider flux compactifications of type IIB string theory and F-theory in which the respective superpotentials at large complex structure are dominated by cubic or quartic terms in the complex structure moduli. In this limit, the low-energy effective theory for the complex structure and axio-dilaton sector exhibits universal properties that are insensitive to the details of the compactification manifold or the flux configuration. We show that there are no vacua in this region and the spectrum of the Hessian matrix is highly peaked and consists only of three distinct eigenvalues ($0$, $2m_{3…
In the present paper, we reexamine the moduli stabilization problem of the Type IIB orientifolds with one complex structure modulus in a modified two-step procedure. The full superpotential including both the 3-form fluxes and the non-perturbative corrections is used to yield a F-term potential. This potential is simplified by using one optimization condition to integrate the dilaton field out. It is shown that having a locally stable supersymmetric Anti-deSitter vacuum is not inevitable for these orientifolds, which depend strongly upon the details of the flux parameters. For those orientifol…
A scenario for stabilization of axionic moduli fields in the context of type IIB Calabi-Yau flux compactifications is discussed in detail. We consider the case of a Calabi-Yau orientifold with h^{1,1}_- \neq 0 which allows for the presence of B_2 and C_2-moduli. In an attempt to generalize the KKLT and the Large Volume Scenario, we show that these axions can also be stabilized - some already at tree level, and others when we include perturbative α'-corrections to the Kaehler potential K and nonperturbative D3-instanton contributions to the superpotential W. At last, we comment on the possible …
On the Type IIB toroidal T^6 orientifolds with generic flux compactifications, we conjecture that in generic supsersymmetric Minkowski vacua, at least one of the flux contributions to the seven-brane and D3-brane tadpoles is positive if the moduli are stabilized properly, and then the tadpole cancellation conditions can not be relaxed. To study the supsersymmetric Minkowski flux vacua, we simplify the fluxes reasonably and discuss the corresponding superpotential. We show that we can not have simultaneously the positive real parts of all the moduli and the negative/zero flux contributions to a…
We report on the construction of four dimensional gauged supergravity models that can be interpreted as type IIB orientifold compactification in presence of 3-form fluxes and D3--branes. We mainly address our attention to the symplectic embedding of the U-duality group of the theory and the consequent choice of the gauge group, whose four dimensional killing vectors are the remnant of the ten dimensional fluxes. We briefly discuss the structure of the scalar potential arising from the gauging and the properties of the killing vectors in order to preserve some amount of supersymmetry.
This article represents the author's PhD thesis which is focused on moduli stabilisation in type IIB Calabi-Yau flux compactifications and its applications to cosmology. I derive the topological conditions on an arbitrary Calabi-Yau to give rise to the very promising LARGE Volume Scenario. After a systematic study of the behaviour of string loop corrections for general type IIB compactifications, I show how they play a crucial role to achieve full moduli stabilisation. I then apply these results to cosmology showing how, in the case of K3-fibrations, string loop corrections give rise naturally…
We find analytic solutions of type IIB supergravity on geometries that locally take the form $\text{Mink}\times M_4\times \mathbb{C}$ with $M_4$ a generalised complex manifold. The solutions involve the metric, the dilaton, NSNS and RR flux potentials (oriented along the $M_4$) parametrised by functions varying only over $\mathbb{C}$. Under this assumption, the supersymmetry equations are solved using the formalism of pure spinors in terms of a finite number of holomorphic functions. Alternatively, the solutions can be viewed as vacua of maximally supersymmetric supergravity in six dimensions …
We analyze the tree-level potential of type IIB flux compactifications in warped Calabi-Yau orientifolds, in regions of weak coupling and moderately large complex structure. In this regime, one may approximate the flux-induced superpotential $W$ by a polynomial on the axio-dilaton and complex structure fields, and a significant fraction of vacua corresponds to a quadratic $W$. In this quadratic case, we argue that vacua fall into three classes, for which one can push the analytic description of their features. In particular, we provide analytic expressions for the vacuum expectation values and…
A supersymmetric vacuum has to obey a set of constraints on fluxes as well as first order differential equations defined by the G-structures of the internal manifold. We solve these equations for type IIB supergravity with SU(3) structures. The 6-dimensional internal manifold has to be complex, the axion/dilaton is in general non-holomorphic and a cosmological constant is only possible if the SU(3) structures are broken to SU(2) structures. The general solution is expressed in terms of one function which is holomorphic in the three complex coordinates and if this holomorphic function is consta…
We report on a new class of flux vacua generically present in Calabi-Yau compactifications of type-IIB string theory. At these vacua, the mass spectrum of the complete axio-dilaton/complex structure sector is given, to leading order in $α'$ and $g_s$, by a simple analytic formula independent of the choice of Calabi-Yau. We provide a method to find these vacua, and construct an ensemble of $17,054$ solutions for the Calabi-Yau hypersurface $\mathbb{WP}_{[1,1,1,6,9]}^4$, where the masses of the axio-dilaton and the $272$ complex structure fields can be explicitly computed.
We study moduli stabilization in Calabi-Yau orientifold compactifications of type IIB string theory with O3- and O7-planes. We consider a Calabi-Yau three-fold with Hodge number $h^{2,1}=50$ and stabilize all axio-dilaton and complex-structure moduli by three-form fluxes. This is a challenging task, especially for large moduli-space dimensions. To address this question we develop an algorithm to generate $10^5$ flux vacua with small flux number $N_{\rm flux}$. Based on recent results by Crinò et al. we estimate the bound imposed by the tadpole-cancellation condition as $N_{\rm flux}\leq \mathc…
In a setup of type IIB superstring compactification on an orientifold of a ${\mathbb T}^6/{\mathbb Z}_4$ sixfold, the presence of geometric flux ($ω$) and non-geometric fluxes ($Q, R$) is implemented along with the standard NS-NS and RR three-form fluxes ($H, F$). After computing the F/D-term contributions to the ${\cal N}=1$ four dimensional effective scalar potential, we rearrange the same into `suitable' pieces by using a set of new generalized flux orbits. Subsequently, we dimensionally oxidize the various pieces of the total four dimensional scalar potential to guess their ten-dimensional…
We derive and carry out a detailed analysis of the equations of motion of the type IIB D branes in generic supergravity backgrounds with fluxes making account of the worldvolume Born-Infeld gauge field and putting a special emphasis on the structure of the Dirac equation for Dp brane fermionic modes. We present an explicit form of the worldvolume field equations for each of the Dp branes (p=1,3,5,7,9) in the cases in which the Neveu-Schwarz flux and the Ramond-Ramond p-form flux along the Dp-brane worldvolume are zero and the supergravity backgrounds do not necessarily induce the worldvolume B…
We consider the most general AdS$_3$ solutions of type IIB supergravity admitting a dynamical SU$(3)$ structure and preserving $\mathcal{N}=(0,2)$ supersymmetry. The analysis is broken into three distinct classes depending on whether the dynamical SU$(3)$ structure degenerates to a strict SU$(3)$ structure. The first class we consider allows for a holomorphically varying axio-dilaton consistent with the presence of $(p,q)$ 7-branes in addition to D3-branes and $(p,q)$ 5-branes. In the remaining two classes the axio-dilaton may vary but does not do so holomorphically. The second class of soluti…
In this paper we argue that the mechanism of unwinding inflation is naturally present in warped compactifications of type IIB string theory with local throats. The unwinding of flux is caused by its annihilation against branes. The resulting inflaton potential is linear with periodic modulations. We initiate an analysis of the inflationary dynamics and cosmological observables, which are highly constrained by moduli stabilization. For the simplified model of single-Kähler Calabi-Yau spaces we find that many, though not all of the consistency constraints can be satisfied. Particularly, in this …
We study the scalar potential in supersymmetric (orientifolded) Calabi Yau compactifications of Type IIB theory. We present a new mechanism to stabilize all closed string moduli at leading order in α^{'} by introducing consistently fluxes. As usual we consider the dilaton and the complex structure moduli stabilized by turning on three-form fluxes that couple to the F-part of the scalar potential. Kahler moduli get fixed by the combined action of the flux-induced scalar masses with magnetic fields of the open string sector, and Fayet-Illiopoulos terms. For supersymmetric three-form fluxes the m…
We study models of stabilization near large complex structure in type IIB O3/O7 flux compactifications. We consider a special family of examples with a single nonvanishing Yukawa coupling in the large complex structure limit, which allows us to study all possible stable vacua of the tree-level no-scale potential very explicitly. We find that, by tuning fluxes, both supersymmetric and nonsupersymmetric vacua can be realized at almost any point in the large complex structure moduli space of one-, two-, and three-parameter models. We also consider the effects of stringy corrections on tree-level …
We systematically investigate possibilities of realizing the spontaneous CP violation in Type IIB flux compactifications on toroidal orientifolds. Our detailed analysis leads to the presence of flat directions at degenerate CP-breaking and -conserving vacua for a generic choice of three-form fluxes, indicating that flux compactifications are not sufficient to realize the spontaneous CP violation. Furthermore, the four-dimensional CP can be embedded into the duality symmetries, namely modular symmetries for a particular choice of fluxes.
Utilizing a setup of type IIB superstring theory compactified on an orientifold of T^6/(Z2xZ2), we propose a modular invariant dimensional oxidation of the four-dimensional scalar potential. In the oxidized ten-dimensional supergravity action, the standard NS-NS and RR three form fluxes (H-, F-) as well as the non-geometric fluxes (Q-, P-) are found to nicely rearrange themselves to form generalized flux-combinations. As an application towards moduli stabilization, using the same S-duality invariant scalar potential, we examine the recently proposed No-Go theorem (in arXiv:1409.7075) about cre…
Flux vacua in type IIB compactifications on orbifolds: their finiteness and minimal string coupling
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；High Energy Physics Research Unit, Faculty of Science, Chulalongkorn University（朱拉隆功大学理学院高能物理研究单元）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文学系）；INFN, Sezione di Bologna（意大利国家核物理研究所博洛尼区分部）
We study $\mathcal{N}=1$ supersymmetric AdS$_3 \times M_7$ backgrounds of Type IIB supergravity, with non-vanishing axio-dilaton, three-form and five-form fluxes, and a "strict" $SU(3)$-structure on $M_7$. We derive the necessary and sufficient conditions for supersymmetry as a set of constraints on the torsion classes of the $SU(3)$-structure. Given an Ansatz for the three-form fluxes, the problem of also solving the equations of motion involves a "master equation", which generalizes ones that have previously appeared in the literature.
We investigate the near horizon geometry of IIB supergravity black holes with non-vanishing 5-form flux preserving at least two supersymmetries. We demonstrate that there are three classes of solutions distinguished by the choice of Killing spinors. We find that the spatial horizon sections of the class of solutions with an SU(4) invariant pure Killing spinor are hermitian manifolds and admit a hidden Kahler with torsion (KT) geometry compatible with the SU(4) structure. Moreover the Bianchi identity of the 5-form, which also implies the field equations, can be expressed in terms of the torsio…
Supersymmetric Minkowski vacua in IIB orientifold compactifications based on orbifolds with background fluxes and non-perturbative superpotentials are investigated. Especially, microscopic requirements and difficulties to obtain such vacua are discussed. We show that orbifold models with one and two complex structure moduli and supersymmetric 2-form flux can be successfully stabilized to such vacua. By taking additional gaugino condensation on fixed space-time filling D3-branes into account also models without complex structure can be consistently stabilized to Minkowski vacua.
We classify discrete modular symmetries in the effective action of Type IIB string on toroidal orientifolds with three-form fluxes, emphasizing on $T^6/\mathbb{Z}_2$ and $T^6/(\mathbb{Z}_2\times \mathbb{Z}_2^\prime)$ orientifold backgrounds. On the three-form flux background, the modular group is spontaneously broken down to its congruence subgroup whose pattern is severely constrained by a quantization of fluxes and tadpole cancellation conditions. We explicitly demonstrate that the congruence subgroups appearing in the effective action arise on magnetized D-branes wrapping certain cycles of …
We compute the spectra of the Hessian matrix, ${\cal H}$, and the matrix ${\cal M}$ that governs the critical point equation of the low-energy effective supergravity, as a function of the complex structure and axio-dilaton moduli space in type IIB flux compactifications at large complex structure. We find both spectra analytically in an $h^{1,2}_-+3$ real-dimensional subspace of the moduli space, and show that they exhibit a universal structure with highly degenerate eigenvalues, independently of the choice of flux, the details of the compactification geometry, and the number of complex struct…
A particular decoupling limit of non-extremal (D1, D3) brane bound state system of type IIB string theory is known to give the gravity dual of space-space non- commutative Yang-Mills (NCYM) theory at finite temperature. We use a string probe in this background to compute the jet quenching parameter in the strongly coupled plasma of hot non-commutative Yang-Mills theory in (3+1)-dimensions from gauge/gravity duality. We give the expressions for the jet quenching parameter for both small and large non-commutativity. For small non-commutativity, we find that the value of the jet quenching paramet…
We study the behaviour of the string loop corrections to the N=1 4D supergravity Kaehler potential that occur in flux compactifications of IIB string theory on general Calabi-Yau three-folds. We give a low energy interpretation for the conjecture of Berg, Haack and Pajer for the form of the loop corrections to the Kaehler potential. We check the consistency of this interpretation in several examples. We show that for arbitrary Calabi-Yaus, the leading contribution of these corrections to the scalar potential is always vanishing, giving an "extended no-scale structure". This result holds as lon…
We study the flux parameter spaces for semi-realistic supersymmetric Pati-Salam models in the AdS vacua on Type IIA orientifold and realistic supersymmetric Pati-Salam models in the Minkowski vacua on Type IIB orientifold. Because the fluxes can be very large, we show explicitly that there indeed exists a huge number of semi-realistic Type IIA and realistic Type IIB flux models. In the Type IIA flux models, in the very large flux limit, the theory can become weakly coupled and the AdS vacua can approach to the Minkowski vacua. In a series of realistic Type IIB flux models, at the string scale,…
We construct a U(1) bundle over N(1,1), usually considered as an SO(3) bundle over CP^2, and show that type IIB supergravity can be consistently compactified over it. With the five form flux turned on, there is a solution for which the metric becomes Einstein. We also turn on 3-form fluxes and show that there is a one parameter family of solutions. In particular, there is a limiting solution of large 3-form fluxes for which two U(1) fiber directions of the metric shrink to zero size. We also discuss compactifications over N(1,1) to AdS_3. All solutions turn out to be non-supersymmetric.
We describe a duality relation between configurations of M5-branes in M-theory and type IIB theory on Taub-NUT geometries with NSNS and RR 3-form field strength fluxes. The flux parameters are controlled by the angles between the M5-brane and the (T)duality directions. For one M5-brane, the duality leads to a family of supersymmetric flux configurations which interpolates between imaginary self-dual fluxes and fluxes similar to the Polchinski-Strassler kind. For multiple M5-branes, the IIB configurations are related to fluxes for twisted sector fields in orbifolds. The dual M5-brane picture al…
We study gauge threshold corrections for local GUT models in IIB/F-theory. Consistency with holomorphy requirements of supergravity and the Kaplunovsky-Louis formula implies that the unification scale is enhanced by the bulk radius R from the string scale to M_X =RM_S. We argue that the stringy interpretation of this is via a locally uncancelled tadpole sourced by the hypercharge flux. This sources closed string modes propagating into the bulk; equivalently open string gauge coupling running up to the winding scale M_X. The enhancement to R M_s is tied to GUT breaking by a globally trivial hyp…
With model building applications in mind, we collect and develop basic techniques to analyze the landscape of D7-branes in type IIB compact Calabi-Yau orientifolds, in three different pictures: F-theory, the D7 worldvolume theory and D9-anti-D9 tachyon condensation. A significant complication is that consistent D7-branes in the presence of O7^- planes are generically singular, with singularities locally modeled by the Whitney Umbrella. This invalidates the standard formulae for charges, moduli space and flux lattice dimensions. We infer the correct formulae by comparison to F-theory and derive…
We analyse the most general bosonic supersymmetric solutions of type IIB supergravity whose metrics are warped products of five-dimensional anti-de Sitter space (AdS$_5$) with a five-dimensional Riemannian manifold $M_{5}$, where the five-form flux vanishes, while all remaining fluxes are allowed to be non-vanishing consistent with SO(4,2) symmetry. This completes the program of classifying all supersymmetric solutions of ten and eleven-dimensional supergravity with an AdS$_5$ factor. We investigate the supersymmetry conditions in some special cases, and demonstrate how these are satisfied by …
We use a T-duality invariant action to investigate the behaviour of a string in non-geometric backgrounds, where there is a non-trivial global $O(D,D)$ patching or monodromy. This action leads to a set of Dirac brackets describing the dynamics of the doubled string, with these brackets determined only by the monodromy. This allows for a simple derivation of non-commutativity and non-associativity in backgrounds which are (even locally) non-geometric. We focus here on the example of the three-torus with H-flux, finding non-commutativity but not non-associativity, and also comment on the relatio…
