We consider intersecting brane solutions of the type IIB matrix model. It is shown that fermionic zero-modes arise on such backgrounds, localized at the brane intersections. They lead to chiral fermions in four dimensions under certain conditions. Such configurations reproduce many of the welcome features in similar string-theoretic constructions. Therefore they can be used to construct semi-realistic particle physics models in the framework of Yang-Mills matrix models. In particular, we present a brane configuration which realizes the correct chiral spectrum of the standard model in the matrix model. Furthermore, the stability of intersecting branes is discussed by analyzing the 1-loop effective action. It is shown that intersecting branes may form a bound state for certain flux configurations. The four-dimensional geometry of the branes is generic, and determined by the (emergent) gravity sector of the matrix model.Comment: 35 pages. V2: discussion on SUSY added V3: improved discussion of the Higgs secto

Abstract:We compare the gauging of the Bargmann algebra, for the case of arbitrary torsion, with the result that one obtains from a null-reduction of General Relativity. Whereas the two procedures lead to the same result for Newton-Cartan geometry with arbitrary torsion, the null-reduction of the Einstein equations necessarily leads to Newton-Cartan gravity with zero torsion. We show, for three space-time dimensions, how Newton-Cartan gravity with arbitrary torsion can be obtained by starting from a Schrödinger field theory with dynamical exponent z = 2 for a complex compensating scalar and next coupling this field theory to a z = 2 Schrödinger geometry with arbitrary torsion. The latter theory can be obtained from either a gauging of the Schrödinger algebra, for arbitrary torsion, or from a null-reduction of conformal gravity.

An interesting consequence of string dualities is that they reveal situations where the geometry of a string background appears to be globally ill-defined, a phenomenon usually referred to as non-geometry. On the other hand, string theory contains extended objects with non-trivial monodromy around them, often dubbed defect or exotic branes in co-dimension two. We determine and examine the worldvolume actions and the couplings of certain such branes. In particular, based on specific chains of T and S-dualities, we derive the DBI and WZ actions, which describe the dynamics of type IIB fivebranes as well as their couplings to the appropriate gauge potentials associated to mixed symmetry tensors. Based on these actions we discuss how these branes act as sources of non-geometric fluxes. In one case this flux is what is usually termed Q flux, associated to a T-fold compactification, while in the S-dual case a type of non-geometry related to the Ramond-Ramond sector is encountered.

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. 1 a.chatzistavrakidis@gmail.com 2 larisa@irb.hr 3 Fech.Scen.Khoo@irb.hr 4 R.J.Szabo@hw.ac.uk 29)19 In this subsection we simplify the notation for the components of the map ρ + by denoting (ρ + ) I J as ρ I J .