Stringy Instanton Effects in Models with Rigid Magnetised D-branes

We compute instantonic effects in globally consistent T^6/Z2xZ2 orientifold models with discrete torsion and magnetised D-branes. We consider fractional branes and instantons wrapping the same rigid cycles. We clarify and analyse in detail the low-energy effective action on D-branes in these models. We provide explicit examples where instantons induce linear terms in the charged fields, or non-perturbative mass terms are generated. We also find examples where the gauge theory on fractional branes has conformal symmetry at one-loop, broken by instantonic mass terms at a hierarchically small energy scale.Comment: 60 pages. Refs added. Typos corrected in some eqs. Modified comments in subsection 4.

Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds

We describe the quantization of 2-plectic manifolds as they arise in the context of the quantum geometry of M-branes and non-geometric flux compactifications of closed string theory. We review the groupoid approach to quantizing Poisson manifolds in detail, and then extend it to the loop spaces of 2-plectic manifolds, which are naturally symplectic manifolds. In particular, we discuss the groupoid quantization of the loop spaces of R^3, T^3 and S^3, and derive some interesting implications which match physical expectations from string theory and M-theory.Comment: 71 pages, v2: references adde

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.Comment: 30 page

Matrix theory origins of non-geometric fluxes

We explore the origins of non-geometric fluxes within the context of M theory described as a matrix model. Building upon compactifications of Matrix theory on non-commutative tori and twisted tori, we formulate the conditions which describe compactifications with non-geometric fluxes. These turn out to be related to certain deformations of tori with non-commutative and non-associative structures on their phase space. Quantization of flux appears as a natural consequence of the framework and leads to the resolution of non-associativity at the level of the unitary operators. The quantum-mechanical nature of the model bestows an important role on the phase space. In particular, the geometric and non-geometric fluxes exchange their properties when going from position space to momentum space thus providing a duality among the two. Moreover, the operations which connect solutions with different fluxes are described and their relation to T-duality is discussed. Finally, we provide some insights on the effective gauge theories obtained from these matrix compactifications.Comment: 1+31 pages, reference list update

Non-perturbative Vacuum Destabilization and D-brane Dynamics

We analyze the process of string vacuum destabilization due to instanton induced superpotential couplings which depend linearly on charged fields. These non-perturbative instabilities result in potentials for the D-brane moduli and lead to processes of D-brane recombination, motion and partial moduli stabilization at the non-perturbative vacuum. By using techniques of D-brane instanton calculus, we explicitly compute this scalar potential in toroidal orbifold compactifications with magnetized D-branes by summing over the possible discrete instanton configurations. We illustrate explicitly the resulting dynamics in globally consistent models. These instabilities can have phenomenological applications to breaking hidden sector gauge groups, open string moduli stabilization and supersymmetry breaking. Our results suggest that breaking supersymmetry by Polonyi-like models in string theory is more difficult than expected.Comment: 61 pages, 6 figures, 5 tables; Minor corrections, version published in JHE

Holomorphic variables in magnetized brane models with continuous Wilson lines

We analyze the action of the target-space modular group in toroidal type IIB orientifold compactifications with magnetized D-branes and continuous Wilson lines. The transformation of matter fields agree with that of twisted fields in heterotic compactifications, constituting a check of type I/heterotic duality. We identify the holomorphic N = 1 variables for these compactifications. Matter fields and closed string moduli are both redefined by open string moduli. The redefinition of matter fields can be read directly from the perturbative Yukawa couplings, whereas closed string moduli redefinitions are obtained from D-brane instanton superpotential couplings. The resulting expressions reproduce and generalize, in the presence of internal magnetic fields, previous results in the literature.Comment: 9 pages, no figures; v2: conventions for Wilson lines changed, major simplifications in expressions, discussions extended, typos corrected, some references adde

Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds

We develop quantization techniques for describing the nonassociative geometry probed by closed strings in flat non-geometric R-flux backgrounds M. Starting from a suitable Courant sigma-model on an open membrane with target space M, regarded as a topological sector of closed string dynamics in R-space, we derive a twisted Poisson sigma-model on the boundary of the membrane whose target space is the cotangent bundle T^*M and whose quasi-Poisson structure coincides with those previously proposed. We argue that from the membrane perspective the path integral over multivalued closed string fields in Q-space is equivalent to integrating over open strings in R-space. The corresponding boundary correlation functions reproduce Kontsevich's deformation quantization formula for the twisted Poisson manifolds. For constant R-flux, we derive closed formulas for the corresponding nonassociative star product and its associator, and compare them with previous proposals for a 3-product of fields on R-space. We develop various versions of the Seiberg-Witten map which relate our nonassociative star products to associative ones and add fluctuations to the R-flux background. We show that the Kontsevich formula coincides with the star product obtained by quantizing the dual of a Lie 2-algebra via convolution in an integrating Lie 2-group associated to the T-dual doubled geometry, and hence clarify the relation to the twisted convolution products for topological nonassociative torus bundles. We further demonstrate how our approach leads to a consistent quantization of Nambu-Poisson 3-brackets.Comment: 52 pages; v2: references adde

3-cocycles, non-associative star-products and the magnetic paradigm of R-flux string vacua

We consider the geometric and non-geometric faces of closed string vacua arising by T-duality from principal torus bundles with constant H-flux and pay attention to their double phase space description encompassing all toroidal coordinates, momenta and their dual on equal footing. We construct a star-product algebra on functions in phase space that is manifestly duality invariant and substitutes for canonical quantization. The 3-cocycles of the Abelian group of translations in double phase space are seen to account for non-associativity of the star-product. We also provide alternative cohomological descriptions of non-associativity and draw analogies with the quantization of point-particles in the field of a Dirac monopole or other distributions of magnetic charge. The magnetic field analogue of the R-flux string model is provided by a constant uniform distribution of magnetic charge in space and non-associativity manifests as breaking of angular symmetry. The Poincare vector comes to rescue angular symmetry as well as associativity and also allow for quantization in terms of operators and Hilbert space only in the case of charged particles moving in the field of a single magnetic monopole

Pre - Inflationary Clues from String Theory ?

"Brane supersymmetry breaking" occurs in String Theory when the only available combinations of D-branes and orientifolds are not mutually BPS and yet do not introduce tree-level tachyon instabilities. It is characterized by the emergence of a steep exponential potential, and thus by the absence of maximally symmetric vacua. The corresponding low-energy supergravity admits intriguing spatially-flat cosmological solutions where a scalar field is forced to climb up toward the steep potential after an initial singularity, and additional milder terms can inject an inflationary phase during the ensuing descent. We show that, in the resulting power spectra of scalar perturbations, an infrared suppression is typically followed by a pre-inflationary peak that reflects the end of the climbing phase and can lie well apart from the approximately scale invariant profile. A first look at WMAP9 raw data shows that, while the chi^2 fits for the low-l CMB angular power spectrum are clearly compatible with an almost scale invariant behavior, they display nonetheless an eye-catching preference for this type of setting within a perturbative string regime.Comment: 34 pages, LaTeX, 16 eps figures. Relative displacement in fig. 14 and some typos corrected, references and acknowledgments updated. To appear in JCA

Structure in 6D and 4D N=1 supergravity theories from F-theory

We explore some aspects of 4D supergravity theories and F-theory vacua that are parallel to structures in the space of 6D theories. The spectrum and topological terms in 4D supergravity theories correspond to topological data of F-theory geometry, just as in six dimensions. In particular, topological axion-curvature squared couplings appear in 4D theories; these couplings are characterized by vectors in the dual to the lattice of axion shift symmetries associated with string charges. These terms are analogous to the Green-Schwarz terms of 6D supergravity theories, though in 4D the terms are not generally linked with anomalies. We outline the correspondence between F-theory topology and data of the corresponding 4D supergravity theories. The correspondence of geometry with structure in the low-energy action illuminates topological aspects of heterotic-F-theory duality in 4D as well as in 6D. The existence of an F-theory realization also places geometrical constraints on the 4D supergravity theory in the large-volume limit.Comment: 63 page