Non-geometric Backgrounds Research Articles

Stabilization of a twisted modulus on a mirror of rigid Calabi-Yau manifold

We study the stabilization of a twisted modulus in Type IIB flux compactifications on a mirror of the rigid Calabi-Yau threefold. By analyzing the effective action of twisted and untwisted moduli, we find that three-form fluxes satisfying the tadpole cancellation conditions lead to supersymmetric AdS vacua. We also investigate swampland conjectures on this non-geometric background.

Back to heterotic strings on ALE spaces. Part II. Geometry of T-dual little strings

This work is the second of a series of papers devoted to revisiting the properties of Heterotic string compactifications on ALE spaces. In this project we study the geometric counterpart in F-theory of the T-dualities between Heterotic ALE instantonic Little String Theories (LSTs) extending and generalising previous results on the subject by Aspinwall and Morrison. Since the T-dualities arise from a circle reduction one can exploit the duality between F-theory and M-theory to explore a larger moduli space, where T-dualities are realised as inequivalent elliptic fibrations of the same geometry. As expected from the Heterotic/F-theory duality the elliptic F-theory Calabi-Yau we consider admit a nested elliptic K3 fibration structure. This is central for our construction: the K3 fibrations determine the flavor groups and their global forms, and are the key to identify various T-dualities. We remark that this method works also more generally for LSTs arising from non-geometric Heterotic backgrounds. We study a first example in detail: a particularly exotic class of LSTs which are built from extremal K3 surfaces that admit flavor groups with maximal rank 18. We find all models are related by a so-called T-hexality (i.e. a 6-fold family of T-dualities) which we predict from the inequivalent elliptic fibrations of the extremal K3.

Holographic evidence for nonsupersymmetric conformal manifolds

We provide the first holographic evidence for the existence of a nonsupersymmetric conformal manifold arising from exactly marginal but supersymmetry-breaking deformations of a superconformal three-dimensional field theory. In particular, we construct a 2-parameter nonsupersymmetric deformation of a supersymmetric AdS nongeometric background in type IIB string theory. We prove that the nonsupersymmetric backgrounds are perturbatively stable and also do not suffer from various nonperturbative instabilities. Finally, we argue that diffeomorphism symmetry protects our solutions against higher-derivative string corrections.

Born sigma-models for para-Hermitian manifolds and generalized T-duality

We give a covariant realization of the doubled sigma-model formulation of duality-symmetric string theory within the general framework of para-Hermitian geometry. We define a notion of generalized metric on a para-Hermitian manifold and discuss its relation to Born geometry. We show that a Born geometry uniquely defines a worldsheet sigma-model with a para-Hermitian target space, and we describe its Lie algebroid gauging as a means of recovering the conventional sigma-model description of a physical string background as the leaf space of a foliated para-Hermitian manifold. Applying the Kotov–Strobl gauging leads to a generalized notion of T-duality when combined with transformations that act on Born geometries. We obtain a geometric interpretation of the self-duality constraint that halves the degrees of freedom in doubled sigma-models, and we give geometric characterizations of non-geometric string backgrounds in this setting. We illustrate our formalism with detailed worldsheet descriptions of closed string phase spaces, of doubled groups where our notion of generalized T-duality includes non-abelian T-duality, and of doubled nilmanifolds.

Torus bundles, automorphisms and T-duality

We reconsider some older constructions of T-duality, based on automorphisms of the worldsheet operator algebra, in a modern context. It has been long known that at special points in the moduli space of torus compactifications, the target space gauge symmetry may be enhanced. Away from such points the symmetry is broken and T-duality may be understood as a residual discrete gauge symmetry that survives this breaking. Drawing on work on connections over the space of string backgrounds, we discuss how to generalise this framework for T-duality to geometric and non-geometric backgrounds that are not full solutions of string theory, but may play an important role in exact backgrounds. Along the way we find an interesting algebraic structure and discuss its relationship with doubled geometry. We comment on non-isometric T-duality in this context.

Moduli spaces of non-geometric type II/heterotic dual pairs

We study the moduli spaces of heterotic/type II dual pairs in four dimensions with mathcal{N} = 2 supersymmetry corresponding to non-geometric Calabi-Yau backgrounds on the type II side and to T-fold compactifications on the heterotic side. The vector multiplets moduli space receives perturbative corrections in the heterotic description only, and non- perturbative correction in both descriptions. We derive explicitely the perturbative corrections to the heterotic four-dimensional prepotential, using the knowledge of its singularity structure and of the heterotic perturbative duality group. We also derive the exact hypermultiplets moduli space, that receives corrections neither in the string coupling nor in α′.

Current algebras, generalised fluxes and non-geometry

A Hamiltonian formulation of the classical world-sheet theory in a generic, geometric or non-geometric, NSNS background is proposed. The essence of this formulation is a deformed current algebra, which is solely characterised by the generalised fluxes describing such a background. The construction extends to backgrounds for which there is no Lagrangian description—namely magnetically charged backgrounds or those violating the strong constraint of double field theory—at the cost of violating the Jacobi identity of the current algebra. The known non-commutative and non-associative interpretation of non-geometric flux backgrounds is reproduced by means of the deformed current algebra. Furthermore, the provided framework is used to suggest a generalisation of Poisson–Lie T-duality to generic models with constant generalised fluxes. As a side note, the relation between Lie and Courant algebroid structures of the string current algebra is clarified.

Open-string non-associativity in an R-flux background

We derive the commutation relations for open-string coordinates on D-branes in non-geometric background spaces. Starting from D0-branes on a three-dimensional torus with H -flux, we show that open strings with end points on D3-branes in a three-dimensional R-flux background exhibit a non-associative phase-space algebra, which is similar to the non-associative R-flux algebra of closed strings. Therefore, the effective open-string gauge theory on the D3-branes is expected to be a non-associative gauge theory. We also point out differences between the non-associative phase space structure of open and closed strings in non-geometric backgrounds, which are related to the different structure of the world-sheet commutators of open and closed strings.

Special holonomy manifolds, domain walls, intersecting branes and T-folds

We discuss the special holonomy metrics of Gibbons, Lu, Pope and Stelle, which were constructed as nilmanifold bundles over a line by uplifting supersymmetric domain wall solutions of supergravity to 11 dimensions. We show that these are dual to intersecting brane solutions, and considering these leads us to a more general class of special holonomy metrics. Further dualities relate these to non-geometric backgrounds involving intersections of branes and exotic branes. We discuss the possibility of resolving these spaces to give smooth special holonomy manifolds.

Exotic branes from del Pezzo surfaces

We revisit a correspondence between toroidal compactifications of M-theory and del Pezzo surfaces, in which rational curves on the del Pezzo are related to $\frac{1}{2}$-BPS branes of the corresponding compactification. We argue that curves of higher genus correspond to nongeometric backgrounds of the M-theory compactifications, which are related to exotic branes. In particular, the number of ``special directions'' of the exotic brane is equal to the genus of the corresponding curve. In addition to predicting three new nongeometric backgrounds, we discuss a relation between addition of curves in the del Pezzo and the brane polarization effect.

Noncommutative gauge theories on D-branes in non-geometric backgrounds

We investigate the noncommutative gauge theories arising on the worldvolumes of D-branes in non-geometric backgrounds obtained by T-duality from twisted tori. We revisit the low-energy effective description of D-branes on three-dimensional T-folds, examining both cases of parabolic and elliptic twists in detail. We give a detailed description of the decoupling limits and explore various physical consequences of the open string non-geometry. The T-duality monodromies of the non-geometric backgrounds lead to Morita duality monodromies of the noncommutative Yang-Mills theories induced on the D-branes. While the parabolic twists recover the well-known examples of noncommutative principal torus bundles from topological T-duality, the elliptic twists give new examples of noncommutative fibrations with non-geometric torus fibres. We extend these considerations to D-branes in backgrounds with R-flux, using the doubled geometry formulation, finding that both the non-geometric background and the D-brane gauge theory necessarily have explicit dependence on the dual coordinates, and so have no conventional formulation in spacetime.

Recurrence relations for symplectic realization of (quasi)-Poisson structures

It is known that any Poisson manifold can be embedded into a bigger space which admits a description in terms of a global symplectic structure. Such a procedure is known as a symplectic realization and has a number of important applications like the quantization of the original Poisson manifold. In the present paper we extend the above idea to the case of quasi-Poisson structures which should not necessarily satisfy the Jacobi identity. For any given quasi-Poisson structure we provide a closed recursive formula for local embedding functions and Darboux coordinates. Our construction is illustrated for the examples of the constant R-flux algebra, quasi-Poisson structure isomorphic to the commutator algebra of imaginary octonions and the non-geometric M-theory R-flux background. In all cases we derive explicit formulas for the symplectic realization and the corresponding expression for Darboux coordinates.

Geometry and 2-Hilbert space for nonassociative magnetic translations

We suggest a geometric approach to quantisation of the twisted Poisson structure underlying the dynamics of charged particles in fields of generic smooth distributions of magnetic charge, and dually of closed strings in locally non-geometric flux backgrounds, which naturally allows for representations of nonassociative magnetic translation operators. We show how one can use the 2-Hilbert space of sections of a bundle gerbe in a putative framework for canonical quantisation. We define a parallel transport on bundle gerbes on $\mathbb{R}^d$ and show that it naturally furnishes weak projective 2-representations of the translation group on this 2-Hilbert space. We obtain a notion of covariant derivative on a bundle gerbe and a novel perspective on the fake curvature condition.

Open-string T-duality and applications to non-geometric backgrounds

We revisit T-duality transformations for the open string via Buscher’s procedure and work-out technical details which have been missing so far in the literature. We take into account non-trivial topologies of the world-sheet, we consider T-duality along directions with Neumann as well as Dirichlet boundary conditions, and we include collective T-duality along multiple directions.We illustrate this formalism with the example of the three-torus with H-flux and its T-dual backgrounds, and we discuss global properties of open-string boundary conditions on such spaces.

Double field theory and membrane sigma-models

We investigate geometric aspects of double field theory (DFT) and its formulation as a doubled membrane sigma-model. Starting from the standard Courant algebroid over the phase space of an open membrane, we determine a splitting and a projection to a subbundle that sends the Courant algebroid operations to the corresponding operations in DFT. This describes precisely how the geometric structure of DFT lies in between two Courant algebroids and is reconciled with generalized geometry. We construct the membrane sigma-model that corresponds to DFT, and demonstrate how the standard T-duality orbit of geometric and non-geometric flux backgrounds is captured by its action functional in a unified way. This also clarifies the appearence of noncommutative and nonassociative deformations of geometry in non-geometric closed string theory. Gauge invariance of the DFT membrane sigma-model is compatible with the flux formulation of DFT and its strong constraint, whose geometric origin is explained. Our approach leads to a new generalization of a Courant algebroid, that we call a DFT algebroid and relate to other known generalizations, such as pre-Courant algebroids and symplectic nearly Lie 2-algebroids. We also describe the construction of a gauge-invariant doubled membrane sigma-model that does not require imposing the strong constraint.

Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T -duality

Based on the construction of Poisson-Lie T -dual σ-models from a common parent action we study a candidate for the non-abelian respectively Poisson-Lie T -duality group. This group generalises the well-known abelian T -duality group O(d, d) and we explore some of its subgroups, namely factorised dualities, B- and β-shifts. The corresponding duality transformed σ-models are constructed and interpreted as generalised (non-geometric) flux backgrounds.We also comment on generalisations of results and techniques known from abelian T -duality. This includes the Lie algebra cohomology interpretation of the corresponding non-geometric flux backgrounds, remarks on a double field theory based on non-abelian T -duality and an application to the investigation of Yang-Baxter deformations. This will show that homogeneously Yang-Baxter deformed σ-models are exactly the non-abelian T -duality β-shifts when applied to principal chiral models.

Magnetic monopoles and nonassociative deformations of quantum theory

We examine certain nonassociative deformations of quantum mechanics and gravity in three dimensions related to the dynamics of electrons in uniform distributions of magnetic charge. We describe a quantitative framework for nonassociative quantum mechanics in this setting, which exhibits new effects compared to ordinary quantum mechanics with sourceless magnetic fields, and the extent to which these theoretical consequences may be experimentally testable. We relate this theory to noncommutative Jordanian quantum mechanics, and show that its underlying algebra can be obtained as a contraction of the alternative algebra of octonions. The uncontracted octonion algebra conjecturally describes a nonassociative deformation of three-dimensional quantum gravity induced by magnetic monopoles, which we propose is realised by a non-geometric Kaluza-Klein monopole background in M-theory.

Locally non-geometric fluxes and missing momenta in M-theory

We use exceptional field theory to describe locally non-geometric spaces of M-theory of more than three dimensions. For these spaces, we find a new set of locally non-geometric fluxes which lie in the R-R sector in the weak-coupling limit and can typically be characterised by mixed symmetry tensors. These spaces thus provide new examples of non-geometric backgrounds which go beyond the NS-NS sector of string theory. Starting from twisted tori we construct duality chains that lead to these new non-geometric backgrounds and we show that, just as in the four-dimensional case, there are missing momenta associated to the mixed symmetry tensors.

Non-geometric Calabi-Yau backgrounds and K3 automorphisms

We consider compactifications of type IIA superstring theory on mirror-folds obtained as K3 fibrations over two-tori with non-geometric monodromies involving mirror symmetries. At special points in the moduli space these are asymmetric Gepner models. The compactifications are constructed from non-geometric automorphisms that arise from the diagonal action of an automorphism of the K3 surface and of an automorphism of the mirror surface. We identify the corresponding gaugings of mathcal{N} = 4 supergravity in four dimensions, and show that the minima of the potential describe the same four-dimensional low-energy physics as the worldsheet formulation in terms of asymmetric Gepner models. In this way, we obtain a class of Minkowski vacua of type II string theory which preserve mathcal{N} = 2 supersymmetry. The massless sector consists of mathcal{N} = 2 supergravity coupled to 3 vector multiplets, giving the STU model. In some cases there are additional massless hypermultiplets.

On Inflation and de Sitter in Non‐Geometric String Backgrounds

AbstractWe study the problem of obtaining de Sitter and inflationary vacua from dimensional reduction of double field theory (DFT) on nongeometric string backgrounds. In this context, we consider a new class of effective potentials that admit Minkowski and de Sitter minima. We then construct a simple model of chaotic inflation arising from T‐fold backgrounds and we discuss the possibility of trans‐Planckian field range from nongeometric monodromies as well as the conditions required to get slow roll.