107 research outputs found
Matrix theory compactifications on twisted tori
We study compactifications of Matrix theory on twisted tori and
non-commutative versions of them. As a first step, we review the construction
of multidimensional twisted tori realized as nilmanifolds based on certain
nilpotent Lie algebras. Subsequently, matrix compactifications on tori are
revisited and the previously known results are supplemented with a background
of a non-commutative torus with non-constant non-commutativity and an
underlying non-associative structure on its phase space. Next we turn our
attention to 3- and 6-dimensional twisted tori and we describe consistent
backgrounds of Matrix theory on them by stating and solving the conditions
which describe the corresponding compactification. Both commutative and
non-commutative solutions are found in all cases. Finally, we comment on the
correspondence among the obtained solutions and flux compactifications of
11-dimensional supergravity, as well as on relations among themselves, such as
Seiberg-Witten maps and T-duality.Comment: 1+31 pages, v2: some comments and clarifications added, accepted for
publication in Physical Review
Courant sigma model and -algebras
The Courant sigma model is a 3-dimensional topological sigma model of AKSZ
type which has been used for the systematic description of closed strings in
non-geometric flux backgrounds. In particular, the expression for the fluxes
and their Bianchi identities coincide with the local form of the axioms of a
Courant algebroid. On the other hand, the axioms of a Courant algebroid also
coincide with the conditions for gauge invariance of the Courant sigma model.
In this paper we embed this interplay between background fluxes of closed
strings, gauge (or more precisely BRST) symmetries of the Courant sigma model
and axioms of a Courant algebroid into an -algebra structure. We show
how the complete BV-BRST formulation of the Courant sigma model is described in
terms of -algebras. Moreover, the morphism between the
-algebra for a Courant algebroid and the one for the corresponding
sigma model is constructed.Comment: 34 pages. v2: typos corrected, published versio
Instantons and Chern-Simons flows in 6, 7 and 8 dimensions
The existence of K-instantons on a cylinder M^7 = R_tau x K/H over a
homogeneous nearly K"ahler 6-manifold K/H requires a conformally parallel or a
cocalibrated G_2-structure on M^7. The generalized anti-self-duality on M^7
implies a Chern-Simons flow on K/H which runs between instantons on the coset.
For K-equivariant connections, the torsionful Yang-Mills equation reduces to a
particular quartic dynamics for a Newtonian particle on C. When the torsion
corresponds to one of the G_2-structures, this dynamics follows from a gradient
or hamiltonian flow equation, respectively. We present the analytic (kink-type)
solutions and plot numerical non-BPS solutions for general torsion values
interpolating between the instantonic ones.Comment: 1+8 pages, 14 figures; talk presented at SQS-11 during 18-23 July,
2011, at JINR, Dubna, Russia; v2: missing * in eq.(1) adde
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
Heat kernel expansion and induced action for matrix models
In this proceeding note, I review some recent results concerning the quantum
effective action of certain matrix models, i.e. the supersymmetric IKKT model,
in the context of emergent gravity. The absence of pathological UV/IR mixing is
discussed, as well as dynamical SUSY breaking and some relations with string
theory and supergravity.Comment: 11 pages, 1 figure; talk given at the 7th International Conference on
Quantum Theory and Symmetries, August 7-13, 2011, Prague/Czech Republi
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
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