Athanasios Chatzistavrakidis

Intersecting branes and a standard model realization in matrix models

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.

Matrix theory origins of non-geometric fluxes

A bstractWe 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.

Effective actions of nongeometric five-branes

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.

Orbifolds, fuzzy spheres and chiral fermions

Starting with a

On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes

\mathcal{N} = 4

Dimensional reduction of the heterotic string over nearly-Kähler manifolds

supersymmetric Yang-Mills theory in four dimensions with gauge group SU(3N) we perform an orbifold projection leading to a

Nearly Kähler heterotic compactifications with fermion condensates

\mathcal{N} = 1

Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions ⋆

supersymmetric SU(N)3 Yang-Mills theory with matter supermultiplets in bifundamental representations of the gauge group, which is chiral and anomaly free. Subsequently, we search for vacua of the projected theory which can be interpreted as spontaneously generated twisted fuzzy spheres. We show that by adding the appropriate soft supersymmetry breaking terms we can indeed reveal such vacua. Three cases are studied, where the gauge group is spontaneously broken further to the low-energy gauge groups SU(4)×SU(2)×SU(2), SU(4)3 and SU(3)3. Such models behave in intermediate scales as higher-dimensional theories with a finite Kaluza-Klein tower, while their low-energy physics is governed by the corresponding zero-modes and exhibit chirality in the fermionic sector. The most interesting case from the phenomenological point of view turns out to be the SU(3)3 unified theory, which has several interesting features such as (i) it can be promoted to a finite theory, (ii) it breaks further spontaneously first to the MSSM and then to SU(3)×U(1)em due to its own scalar sector, i.e. without the need of additional superfields and (iii) the corresponding vacua lead to spontaneously generated fuzzy spheres.

On the consistency of coset space dimensional reduction

We consider certain vacua of four-dimensional SU(N) gauge theory with the same field content as the N = 4 supersymmetric Yang-Mills theory, resulting from potentials which break the N = 4 supersymmetry as well as its global SO(6) symmetry down to SO(3) × SO(3). We show that the theory behaves at intermediate scales as Yang-Mills theory on M 4 × S 2 × S 2 R , where the extra dimensions are fuzzy spheres with magnetic fluxes. We determine in particular the structure of the zero modes due to the fluxes, which leads to low-energy mirror models.

Sigma models for genuinely non-geometric backgrounds

Our aim is to derive the effective action in four dimensions resulting by reducing dimensionally the ten-dimensional = 1 heterotic supergravity coupled to = 1 super Yang-Mills over manifolds admitting a nearly-K?hler structure. Given the fact that all homogeneous six-dimensional nearly-K?hler manifolds are included in the class of the corresponding non-symmetric coset spaces plus a group manifold, our procedure amounts in applying the Coset Space Dimensional Reduction scheme using these coset spaces as internal manifolds. In our examination firstly the rules of the reduction of the theory over a general six-dimensional non-symmetric manifold are stated and subsequently a detailed case by case analysis is performed for all the three non-symmetric coset spaces. For each case the four-dimensional scalar potential is derived and the corresponding nearly-K?hler limit is obtained. Finally, we determine the corresponding supergravity description of the four-dimensional theory employing the heterotic Gukov-Vafa-Witten formula and results of the special K?hler geometry.