96 research outputs found
Nearly K\"ahler heterotic compactifications with fermion condensates
We revisit AdS_4 heterotic compactifications on nearly K\"ahler manifolds in
the presence of H-flux and certain fermion condensates. Unlike previous
studies, we do not assume the vanishing of the supersymmetry variations.
Instead we determine the full equations of motion originating from the
ten-dimensional action, and subsequently we provide explicit solutions to them
on nearly K\"ahler manifolds at first order in alpha'. The Bianchi identity is
also taken into account in order to guarantee the absence of all anomalies. In
the presence of H-flux, which is identified with the torsion of the internal
space, as well as of fermion condensates in the gaugino and dilatino sectors,
new solutions are determined. These solutions provide a full classification of
consistent backgrounds of heterotic supergravity under our assumptions. All the
new solutions are non-supersymmetric, while previously known supersymmetric
ones are recovered too. Our results indicate that fully consistent
(supersymmetric or not) heterotic vacua on nearly K\"ahler manifolds are
scarce, even on AdS_4, and they can be completely classified.Comment: 1+17 pages, 1 figure; v2: remark and two references added, published
versio
Bundles over Nearly-Kahler Homogeneous Spaces in Heterotic String Theory
We construct heterotic vacua based on six-dimensional nearly-Kahler
homogeneous manifolds and non-trivial vector bundles thereon. Our examples are
based on three specific group coset spaces. It is shown how to construct line
bundles over these spaces, compute their properties and build up vector bundles
consistent with supersymmetry and anomaly cancelation. It turns out that the
most interesting coset is . This space supports a large number of
vector bundles which lead to consistent heterotic vacua, some of them with
three chiral families.Comment: 32 pages, reference adde
On Lie-algebraic solutions of the type IIB matrix model
A systematic search for Lie algebra solutions of the type IIB matrix model is
performed. Our survey is based on the classification of all Lie algebras for
dimensions up to five and of all nilpotent Lie algebras of dimension six. It is
shown that Lie-type solutions of the equations of motion of the type IIB matrix
model exist and they correspond to certain nilpotent and solvable Lie algebras.
Their representation in terms of Hermitian matrices is discussed in detail.
These algebras give rise to certain non-commutative spaces for which the
corresponding star-products are provided. Finally the issue of constructing
quantized compact nilmanifolds and solvmanifolds based on the above algebras is
addressed.Comment: 22 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
Yang-Mills instantons and dyons on homogeneous G_2-manifolds
We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is
a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R
x G/H carries a G_2-structure. After imposing a general G-invariance condition,
Yang-Mills theory with torsion on R x G/H is reduced to Newtonian mechanics of
a particle moving in R^6, R^4 or R^2 under the influence of an inverted
double-well-type potential for the cases G/H = SU(3)/U(1)xU(1),
Sp(2)/Sp(1)xU(1) or G_2/SU(3), respectively. We analyze all critical points and
present analytical and numerical kink- and bounce-type solutions, which yield
G-invariant instanton configurations on those cosets. Periodic solutions on S^1
x G/H and dyons on iR x G/H are also given.Comment: 1+26 pages, 14 figures, 6 miniplot
Gravity and compactified branes in matrix models
A mechanism for emergent gravity on brane solutions in Yang-Mills matrix
models is exhibited. Newtonian gravity and a partial relation between the
Einstein tensor and the energy-momentum tensor can arise from the basic matrix
model action, without invoking an Einstein-Hilbert-type term. The key
requirements are compactified extra dimensions with extrinsic curvature M^4 x K
\subset R^D and split noncommutativity, with a Poisson tensor \theta^{ab}
linking the compact with the noncompact directions. The moduli of the
compactification provide the dominant degrees of freedom for gravity, which are
transmitted to the 4 noncompact directions via the Poisson tensor. The
effective Newton constant is determined by the scale of noncommutativity and
the compactification. This gravity theory is well suited for quantization, and
argued to be perturbatively finite for the IKKT model. Since no
compactification of the target space is needed, it might provide a way to avoid
the landscape problem in string theory.Comment: 35 pages. V2: substantially revised and improved, conclusion
weakened. V3: some clarifications, published version. V4: minor correctio
Heterotic domain wall solutions and SU(3) structure manifolds
We examine compactifications of heterotic string theory on manifolds with
SU(3) structure. In particular, we study N = 1/2 domain wall solutions which
correspond to the perturbative vacua of the 4D, N =1 supersymmetric theories
associated to these compactifications. We extend work which has appeared
previously in the literature in two important regards. Firstly, we include two
additional fluxes which have been, heretofore, omitted in the general analysis
of this situation. This allows for solutions with more general torsion classes
than have previously been found. Secondly, we provide explicit solutions for
the fluxes as a function of the torsion classes. These solutions are
particularly useful in deciding whether equations such as the Bianchi
identities can be solved, in addition to the Killing spinor equations
themselves. Our work can be used to straightforwardly decide whether any given
SU(3) structure on a six-dimensional manifold is associated with a solution to
heterotic string theory. To illustrate how to use these results, we discuss a
number of examples taken from the literature.Comment: 34 pages, minor corrections in second versio
Gauge-Higgs Unification In Spontaneously Created Fuzzy Extra Dimensions
We propose gauge-Higgs unification in fuzzy extra dimensions as a possible
solution to the Higgs naturalness problem. In our approach, the fuzzy extra
dimensions are created spontaneously as a vacuum solution of certain
four-dimensional gauge theory. As an example, we construct a model which has a
fuzzy torus as its vacuum. The Higgs field in our model is associated with the
Wilson loop wrapped on the fuzzy torus. We show that the quadratic divergence
in the mass of the Higgs field in the one-loop effective potential is absent.
We then argue based on symmetries that the quantum corrections to the Higgs
mass is suppressed including all loop contributions. We also consider a
realization on the worldvolume theory of D3-branes probing orbifold with discrete torsion.Comment: 1+38 pages, 4 figures v2: refs adde
Coset Space Dimensional Reduction and Wilson Flux Breaking of Ten-Dimensional N=1, E(8) Gauge Theory
We consider a N=1 supersymmetric E(8) gauge theory, defined in ten dimensions
and we determine all four-dimensional gauge theories resulting from the
generalized dimensional reduction a la Forgacs-Manton over coset spaces,
followed by a subsequent application of the Wilson flux spontaneous symmetry
breaking mechanism. Our investigation is constrained only by the requirements
that (i) the dimensional reduction leads to the potentially phenomenologically
interesting, anomaly free, four-dimensional E(6), SO(10) and SU(5) GUTs and
(ii) the Wilson flux mechanism makes use only of the freely acting discrete
symmetries of all possible six-dimensional coset spaces.Comment: 45 pages, 2 figures, 10 tables, uses xy.sty, longtable.sty,
ltxtable.sty, (a shorter version will be published in Eur. Phys. J. C
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