Flux String Research Articles

Searching for axions and ALPs from string theory

We review searches for closed string axions and axion–like particles (ALPs) in IIB string flux compactifications. For natural values of the background fluxes and TeV scale gravitino mass, the moduli stabilisation mechanism of the LARGE Volume Scenario predicts the existence of a QCD axion candidate with intermediate scale decay constant, fa ~ 109÷12 GeV, associated with the small cycles wrapped by the branes hosting the visible sector, plus a nearly massless and nearly decoupled ALP associated with the LARGE cycle. In setups where the visible sector branes are wrapping more than the minimum number of two intersecting cycles, there are more ALPs which have approximately the same decay constant and coupling to the photon as the QCD axion candidate, but which are exponentially lighter. There are exciting phenomenological opportunities to search for these axions and ALPs in the near future. For fa ~ 1011÷12 GeV, the QCD axion can be the dominant part of dark matter and be detected in haloscopes exploiting microwave cavities. For fa ~ 109÷10 GeV, the additional ALPs could explain astrophysical anomalies and be searched for in the upcoming generation of helioscopes and light–shining–through–a–wall experiments.

The string origin of SUSY flavor violation

We argue that in large classes of string compactifications with a MSSM-like structure substantial flavor violating SUSY-breaking soft terms are generically induced. We specify to the case of flavor dependent soft-terms in type IIB/F-theory SU(5) unified models, although our results can be easily extended to other settings. The Standard Model (SM) degrees of freedom reside in a local system of 7-branes wrapping a 4-fold S in the extra dimensions. It is known that in the presence of closed string 3-form fluxes SUSY-breaking terms are typically generated. We explore the generation dependence of these soft terms and find that non-universalities arise whenever the flux varies over the 4-fold S. These non-universalities are parametrically suppressed by (M GUT /M Pl)1/3. They also arise in the case of varying open string fluxes, in this case parametrically suppressed by $ \alpha_{\mathrm{GUT}}^{{{1 \left/ {2} \right.}}} $ . For a standard unification scheme with M GUT ≃ 1016 GeV and α GUT ≃ 1/24 these suppressions are very mild. Although limits from the kaon mass difference Δm K are easily obeyed for squark masses above the present LHC limits, constraints from the CP-violation parameter ϵ K imply squark masses in the multi-TeV region. The constraints from BR(μ → eγ) turn out to be the strongest ones, with slepton masses of order ~ 10 TeV or heavier required to obey the experimental limits. These sfermion masses are consistent with the observed large value m H ≃ 126 GeV of the Higgs mass. We discuss under what conditions such strong limits may be relaxed allowing for SUSY particle production at LHC.

Propagation of magnetic charge monopoles and Dirac flux strings in an artificial spin-ice lattice

We systematically investigate magnetic reversal of permalloy islands in a square spin-ice geometry with in situ Lorentz microscopy. Differential phase imaging reveals the presence of a flux channel similar to a Dirac string between the magnetic charge monopoles during the reversal. Analysis of the phase images shows that positively and negatively charged monopoles always move together with the flux channel. Statistical analysis of monopole populations and system correlations shows the emergence of a highly frustrated state for low magnetizations. This state is explained by a strong influence of charge ordering, which limits monopole densities.

Modulated reheating and large non-gaussianity in string cosmology

A generic feature of the known string inflationary models is that the same physics that makes the inflaton lighter than the Hubble scale during inflation often also makes other scalars this light. These scalars can acquire isocurvature fluctuations during inflation, and given that their VEVs determine the mass spectrum and the coupling constants of the effective low-energy field theory, these fluctuations give rise to couplings and masses that are modulated from one Hubble patch to another. These seem just what is required to obtain primordial adiabatic fluctuations through conversion into density perturbations through the `modulation mechanism', wherein reheating takes place with different efficiency in different regions of our Universe. Fluctuations generated in this way can generically produce non-gaussianity larger than obtained in single-field slow-roll inflation; potentially observable in the near future. We provide here the first explicit example of the modulation mechanism at work in string cosmology, within the framework of LARGE Volume Type-IIB string flux compactifications. The inflationary dynamics involves two light Kähler moduli: a fibre divisor plays the rôle of the inflaton whose decay rate to visible sector degrees of freedom is modulated by the primordial fluctuations of a blow-up mode (which is made light by the use of poly-instanton corrections). We find the challenges of embedding the mechanism into a concrete UV completion constrains the properties of the non-gaussianity that is found, since for generic values of the underlying parameters, the model predicts a local bi-spectrum with fNL of order `a few'. However, a moderate tuning of the parameters gives also rise to explicit examples with fNL ∼ \U0001d4aa(20) potentially observable by the Planck satellite.

Asymmetric orbifolds, non-geometric fluxes and non-commutativity in closed string theory

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 {\alpha}'. Finally, we relate these asymmetric orbifold spaces to inherently stringy Scherk-Schwarz backgrounds and non-geometric fluxes.

Physical vacua in IIB compactifications with a single Kähler modulus

We search for phenomenologically viable vacua of IIB string flux compactifications on Calabi-Yau orientifolds with a single Kaehler modulus. We perform both analytic studies and numerical searches in order to find models with de Sitter vacua and TeV-scale SUSY particle phenomenology.

Flux and instanton effects in local F-theory models and hierarchical fermion masses

We study the deformation induced by fluxes and instanton effects on Yukawa couplings involving 7-brane intersections in local F-theory constructions. In the absence of non-perturbative effects, holomorphic Yukawa couplings do not depend on open string fluxes. On the other hand instanton effects (or gaugino condensation on distant 7-branes) do induce corrections to the Yukawas. The leading order effect may also be captured by the presence of closed string (1,2) IASD fluxes, which give rise to a non-commutative structure. We check that even in the presence of these non-perturbative effects the holomorphic Yukawas remain independent of magnetic fluxes. Although fermion mass hierarchies may be obtained from these non-perturbative effects, they would give identical Yukawa couplings for D-quark and Lepton masses in SU(5) F-theory GUT's, in contradiction with experiment. We point out that this problem may be solved by appropriately normalizing the wavefunctions. We show in a simple toy model how the presence of hypercharge flux may then be responsible for the difference between D-quarks and Lepton masses in local SU(5) GUT's.

U-dual fluxes and Generalized Geometry

We perform a systematic analysis of generic string flux compactifications, making use of Exceptional Generalized Geometry (EGG) as an organizing principle. In particular, we establish the precise map between fluxes, gaugings of maximal 4d supergravity and EGG, identifying the complete set of gaugings that admit an uplift to 10d heterotic or type IIB supegravity backgrounds. Our results reveal a rich structure, involving new deformations of 10d supergravity backgrounds, such as the RR counterparts of the β-deformation. These new deformations are expected to provide the natural extension of the β-deformation to full-fledged F-theory backgrounds. Our analysis also provides some clues on the 10d origin of some of the particularly less well understood gaugings of 4d supergravity. Finally, we derive the explicit expression for the effective superpotential in arbitrary $ \mathcal{N} = 1 $ heterotic or type IIB orientifold compactifications, for all the allowed fluxes.

Non-standard primordial fluctuations and nongaussianity in string inflation

Inflationary scenarios in string theory often involve a large number of light scalar fields, whose presence can enrich the post-inflationary evolution of primordial fluctuations generated during the inflationary epoch. We provide a simple example of such post-inflationary processing within an explicit string-inflationary construction, using a Kahler modulus as the inflaton within the framework of LARGE Volume Type-IIB string flux compactifications. We argue that inflationary models within this broad category often have a selection of scalars that are light enough to be cosmologically relevant, whose contributions to the primordial fluctuation spectrum can compete with those generated in the standard way by the inflaton. These models consequently often predict nongaussianity at a level, f_NL ~ O(10), potentially observable by the Planck satellite, with a bi-spectrum maximized by triangles with squeezed shape in a string realisation of the curvaton scenario. We argue that the observation of such a signal would robustly prefer string cosmologies such as these that predict a multi-field dynamics during the very early universe.

Induced vacuum current and magnetic field in the background of a cosmic string

Vacuum polarization effects in the cosmic string background are considered. We find that a current is induced in the vacuum of the quantized massive scalar field and that the current circulates around the string which is generalized to a (d − 2)-brane in locally flat (d + 1)-dimensional spacetime. As a consequence of the Maxwell equation, a magnetic field strength is also induced in the vacuum and is directed along the cosmic string. The dependence of the current and the field strength on the string flux and tension is comprehensively analysed. Both the current and the field strength are holomorphic functions of the space dimension, decreasing exponentially with the distance from the string. In the case of d = 3 we show that, due to the vacuum polarization, the cosmic string is enclosed in a tube of the magnetic flux lines if the mass of the quantized field is less than the inverse of the transverse size of the string core.

Monopoles and flux strings from SU(2) adjoint scalars

We construct, in an SU(2) gauge theory with two adjoint scalars, flux strings with monopoles attached at the ends. One scalar breaks SU(2) → U(1) and produces monopoles, the other then breaks the U(1) and produces strings. Dualizing, we write the theory in terms of effective string variables and show that the flux in the string is exactly saturated by the monopoles at the ends.

Confinement and nonperturbative tachyons in brane-antibrane systems

We present a worldvolume effective action suitable for the study of the confined phase of a (Dp,Dp) system at weak coupling. We identify the mechanism by which the fundamental string arises from this action as a confined electric flux string when the Dp and the Dp annihilate. We construct an explicit dual action, more suitable for the study of the strong coupling regime, and show that it realizes a generalized Higgs-Stueckelberg phase for the (relative) (p-2)-form field dual to the (overall) Born-Infeld vector. This is the mechanism put forward by Yi and collaborators based on duality arguments in order to explain the breaking of the overall U(1) gauge group at strong coupling. Indeed, in our dual description the Goldstone boson is a (p-3) form magnetically charged with respect to the overall Born-Infeld vector field. This indicates that the condensing tachyonic objects originate from open D(p-2)-branes stretched between the brane and the antibrane. Our results provide an explicit realization of the breaking of the overall U(1) gauge group perturbatively, in a way consistent with the duality symmetries of string theory.

Creating semiclassical black holes in collider experiments and keeping them on a string

We argue that a simple modification of the TeV scale quantum gravity scenario allows production of semiclassical black holes in particle collisions at the LHC. The key idea is that in models with large extra dimensions the strength of gravity in the bulk can be higher than on the brane where we live. A well-known example of this situation is the case of warped extra dimensions. Even if the energy of the collision is not sufficient to create a black hole on the brane, it may be enough to produce a particle which accelerates into the bulk up to trans-Planckian energy and creates a large black hole there. In a concrete model we consider, the black hole is formed in a collision of the particle with its own image at an orbifold plane. When the particle in question carries some Standard Model gauge charges the created black hole gets attached to our brane by a string of the gauge flux. For a 4-dimensional observer such system looks as a long-lived charged state with the mass continuously decreasing due to Hawking evaporation of the black hole. This provides a distinctive signature of black hole formation in our scenario.

Non-perturbative and flux superpotentials for type I strings on the [formula omitted] orbifold

Non-perturbative effects are studied for type I strings on the Z 3 orbifold with Chan–Paton symmetry broken by Wilson lines. Generalizing previous analyses that have focussed on (bi)fundamentals, it is argued that (anti)symmetric representations of the resulting gauge group play a decisive role in generating an ADS-like superpotential in this and related cases. Non-perturbative corrections in the closed string moduli are only allowed if properly dressed with open string fields charged under the anomalous U ( 1 ) of the orbifold. A general discussion of instanton effects in SYM and string theories is given. Non-perturbative superpotentials induced by both ED5's and ED1's are analyzed. The superpotential generated by closed string fluxes, viz. Scherk–Schwarz shifts (torsion), R–R 3-form flux as well as non-geometric fluxes is derived. Some preliminary comments on the compatibility of the two kinds of superpotentials and the issue of moduli stabilization are presented.

Consistent de Sitter string vacua from Kähler stabilization and D‐term uplifting

AbstractIn this note, we review our construction of de Sitter vacua in type IIB flux compactifications, in which moduli stabilization and D‐term uplifting can be combined consistently with the supergravity constraints. Here, the closed string fluxes fix the dilaton and the complex structure moduli while perturbative quantum corrections to the Kähler potential stabilize the volume Kähler modulus in an AdS4‐vacuum. Then, magnetized D7‐branes provide consistent supersymmetric D‐term uplifting towards dS4. Based on hep‐th/0602253.

De Sitter string vacua from Kähler uplifting

We present a new way to construct de Sitter vacua in type IIB flux compactifications, in which the interplay of the leading perturbative and non-perturbative effects stabilize all moduli in dS vacua at parametrically large volume. Here, the closed string fluxes fix the dilaton and the complex structure moduli while the universal leading perturbative quantum correction to the Kahler potential together with non-perturbative effects stabilize the volume Kahler modulus in a dS_4-vacuum. Since the quantum correction is known exactly and can be kept parametrically small, this construction leads to calculable and explicitly realized de Sitter vacua of string theory with spontaneously broken supersymmetry.

De Sitter string vacua from perturbative Kähler corrections and consistent D-terms

We present a new way to construct de Sitter vacua in type IIB flux compactifications, in which moduli stabilization and D-term uplifting can be combined in a manner consistent with the supergravity constraints. Here, the closed string fluxes fix the dilaton and the complex structure moduli while perturbative quantum corrections to the Kahler potential stabilize the volume Kahler modulus in an AdS4-vacuum. Then, the presence of magnetized D7-branes in this setup provide supersymmetric D-terms in a fully consistent way which uplift the AdS4-vacuum to a metastable dS-minimum.

Flux compactifications and generalized geometries**This is an abridged version of Physics Reports, M Graña, ‘Flux compactifications in string theory: A comprehensive review’ 423 91–158, Copyright (2006), reprinted with permission from Elsevier.

Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi–Yau and Calabi–Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.

Low-energy supersymmetry breaking from string flux compactifications: Benchmark scenarios

Soft supersymmetry breaking terms were recently derived for type IIB string flux compactifications with all moduli stabilised. Depending on the choice of the discrete input parameters of the compactification such as fluxes and ranks of hidden gauge groups, the string scale was found to have any value between the TeV and GUT scales. We study the phenomenological implications of these compactifications at low energy. Three realistic scenarios can be identified depending on whether the Standard Model lies on D3 or D7 branes and on the value of the string scale. For the MSSM on D7 branes and the string scale between 10^12 GeV and 10^17 GeV we find that the LSP is a neutralino, while for lower scales it is the stop. At the GUT scale the results of the fluxed MSSM are reproduced, but now with all moduli stabilised. For the MSSM on D3 branes we identify two realistic scenarios. The first one corresponds to an intermediate string scale version of split supersymmetry. The second is a stringy mSUGRA scenario. This requires tuning of the flux parameters to obtain the GUT scale. Phenomenological constraints from dark matter, (g-2)_mu and BR(b->s gamma) are considered for the three scenarios. We provide benchmark points with the MSSM spectrum, making the models suitable for a detailed phenomenological analysis.

Brane world effective actions for D-branes with fluxes

We develop systematic string techniques to study brane world effective actions for models with magnetized (or equivalently intersecting) D-branes. In particular, we derive the dependence on all NS–NS moduli of the kinetic terms of the chiral matter in a generic non-supersymmetric brane configurations with non-commuting open string fluxes. Near a N = 1 supersymmetric point the effective action is consistent with a Fayet–Iliopoulos supersymmetry breaking and the normalization of the scalar kinetic terms is nothing else than the Kähler metric. We also discuss, from a stringy perspective, D and F term breaking mechanisms, and how, in this generic set up, the Kähler metric enters in the physical Yukawa couplings.