63 research outputs found
Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions
Theories defined in higher than four dimensions have been used in various
frameworks and have a long and interesting history. Here we review certain
attempts, developed over the last years, towards the construction of unified
particle physics models in the context of higher-dimensional gauge theories
with non-commutative extra dimensions. These ideas have been developed in two
complementary ways, namely (i) starting with a higher-dimensional gauge theory
and dimensionally reducing it to four dimensions over fuzzy internal spaces and
(ii) starting with a four-dimensional, renormalizable gauge theory and
dynamically generating fuzzy extra dimensions. We describe the above approaches
and moreover we discuss the inclusion of fermions and the construction of
realistic chiral theories in this context
Topological Field Theories induced by twisted R-Poisson structure in any dimension
We construct a class of topological field theories with Wess-Zumino term in
spacetime dimensions whose target space has a geometrical structure
that suitably generalizes Poisson or twisted Poisson manifolds. Assuming a
field content comprising a set of scalar fields accompanied by gauge fields of
degree we determine a generic Wess-Zumino topological field theory
in dimensions with background data consisting of a Poisson 2-vector, a
-vector and a -form satisfying a specific geometrical
condition that defines a -twisted -Poisson structure of order . For
this class of theories we demonstrate how a target space covariant formulation
can be found by means of an auxiliary connection without torsion. Furthermore,
we study admissible deformations of the generic class in special spacetime
dimensions and find that they exist in dimensions 2, 3 and 4. The
two-dimensional deformed field theory includes the twisted Poisson sigma model,
whereas in three dimensions we find a more general structure that we call
bi-twisted -Poisson. This extends the twisted -Poisson structure of order
3 by a non-closed 3-form and gives rise to a topological field theory whose
covariant formulation requires a connection with torsion and includes a twisted
Poisson sigma model in three dimensions as a special case. The relation of the
corresponding structures to differential graded Q-manifolds based on the degree
shifted cotangent bundle is discussed, as well as the
obstruction to them being QP-manifolds due to the Wess-Zumino term.Comment: 40 page
Orbifolds, fuzzy spheres and chiral fermions
Starting with a N=4 supersymmetric Yang-Mills theory in four dimensions with
gauge group SU(3N) we perform an orbifold projection leading to a N=1
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)xSU(2)xSU(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)xU(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.Comment: 24 pages, minor changes, references added, matching with the
published versio
Dirac structures on nilmanifolds and coexistence of fluxes
We study some aspects of the generalized geometry of nilmanifolds and examine
to which extent different types of fluxes can coexist on them. Nilmanifolds
constitute a class of homogeneous spaces which are interesting in string
compactifications with fluxes since they carry geometric flux by construction.
They are generalized Calabi-Yau spaces and therefore simple examples of
generalized geometry at work. We identify and classify Dirac structures on
nilmanifolds, which are maximally isotropic subbundles closed under the Courant
bracket. In the presence of non-vanishing fluxes, these structures are twisted
and closed under appropriate extensions of the Courant bracket. Twisted Dirac
structures on a nilmanifold may carry multiple coexistent fluxes of any type.
We also show how dual Dirac structures combine to Courant algebroids and work
out an explicit example where all types of generalized fluxes coexist. These
results may be useful in the context of general flux compactifications in
string theory.Comment: 1+25 pages; v2: clarifying comments and 6 references added, published
versio
T-duality without isometry via extended gauge symmetries of 2D sigma models
Target space duality is one of the most profound properties of string theory.
However it customarily requires that the background fields satisfy certain
invariance conditions in order to perform it consistently; for instance the
vector fields along the directions that T-duality is performed have to generate
isometries. In the present paper we examine in detail the possibility to
perform T-duality along non-isometric directions. In particular, based on a
recent work of Kotov and Strobl, we study gauged 2D sigma models where gauge
invariance for an extended set of gauge transformations imposes weaker
constraints than in the standard case, notably the corresponding vector fields
are not Killing. This formulation enables us to follow a procedure analogous to
the derivation of the Buscher rules and obtain two dual models, by integrating
out once the Lagrange multipliers and once the gauge fields. We show that this
construction indeed works in non-trivial cases by examining an explicit class
of examples based on step 2 nilmanifolds.Comment: 1+18 pages; version 2: corrections and improvements, more complete
version than the published on
Sigma models for genuinely non-geometric backgrounds
The existence of genuinely non-geometric backgrounds, i.e. ones without
geometric dual, is an important question in string theory. In this paper we
examine this question from a sigma model perspective. First we construct a
particular class of Courant algebroids as protobialgebroids with all types of
geometric and non-geometric fluxes. For such structures we apply the
mathematical result that any Courant algebroid gives rise to a 3D topological
sigma model of the AKSZ type and we discuss the corresponding 2D field
theories. It is found that these models are always geometric, even when both
2-form and 2-vector fields are neither vanishing nor inverse of one another.
Taking a further step, we suggest an extended class of 3D sigma models, whose
world volume is embedded in phase space, which allow for genuinely
non-geometric backgrounds. Adopting the doubled formalism such models can be
related to double field theory, albeit from a world sheet perspective.Comment: 1+34 pages, v2. added references and additional comments; published
versio
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