498 research outputs found
Simple de Sitter Solutions
We present a framework for de Sitter model building in type IIA string
theory, illustrated with specific examples. We find metastable dS minima of the
potential for moduli obtained from a compactification on a product of two Nil
three-manifolds (which have negative scalar curvature) combined with
orientifolds, branes, fractional Chern-Simons forms, and fluxes. As a discrete
quantum number is taken large, the curvature, field strengths, inverse volume,
and four dimensional string coupling become parametrically small, and the de
Sitter Hubble scale can be tuned parametrically smaller than the scales of the
moduli, KK, and winding mode masses. A subtle point in the construction is that
although the curvature remains consistently weak, the circle fibers of the
nilmanifolds become very small in this limit (though this is avoided in
illustrative solutions at modest values of the parameters). In the simplest
version of the construction, the heaviest moduli masses are parametrically of
the same order as the lightest KK and winding masses. However, we provide a
method for separating these marginally overlapping scales, and more generally
the underlying supersymmetry of the model protects against large corrections to
the low-energy moduli potential.Comment: 37 pages, harvmac big, 4 figures. v3: small correction
Link Homologies and the Refined Topological Vertex
We establish a direct map between refined topological vertex and sl(N)
homological invariants of the of Hopf link, which include Khovanov-Rozansky
homology as a special case. This relation provides an exact answer for
homological invariants of the of Hopf link, whose components are colored by
arbitrary representations of sl(N). At present, the mathematical formulation of
such homological invariants is available only for the fundamental
representation (the Khovanov-Rozansky theory) and the relation with the refined
topological vertex should be useful for categorifying quantum group invariants
associated with other representations (R_1, R_2). Our result is a first direct
verification of a series of conjectures which identifies link homologies with
the Hilbert space of BPS states in the presence of branes, where the physical
interpretation of gradings is in terms of charges of the branes ending on
Lagrangian branes.Comment: 38 pages, 5 figure
On effective action of string theory flux compactifications
We discuss four dimensional effective actions of string theory flux
compactifications. These effective actions describe four dimensional gravity
coupled to overall Kahler modulus of the compactification manifold. We
demonstrate the agreement between ten dimensional equations of motion of
supergravity with localized branes, and equations of motion derived from the
effective action. The agreement is lost however if one evaluates the full
effective action on the equations of motion for a subset of the supergravity
modes, provided these modes depend on-shell on the Kahler modulus.Comment: 25 pages; v2: refs adde
A Note on Flux Induced Superpotentials in String Theory
Non-vanishing fluxes in M-theory and string theory compactifications induce a
superpotential in the lower dimensional theory. Gukov has conjectured the
explicit form of this superpotential. We check this conjecture for the
heterotic string compactified on a Calabi-Yau three-fold as well as for warped
M-theory compactifications on Spin(7) holonomy manifolds, by performing a
Kaluza-Klein reduction.Comment: 19 pages, no figure
Type IIB Theory on Half-flat Manifolds
In this note we derive the low-energy effective action of type IIB theory
compactified on half-flat manifolds and we show that this precisely coincides
with the low-energy effective action of type IIA theory compactified on a
Calabi-Yau manifold in the presence of NS three-form fluxes. We provide in this
way a further check of the recently formulated conjecture that half-flat
manifolds appear as mirror partners of Calabi-Yau manifolds when NS fluxes are
turned on.Comment: 15 pages, no figure
Geometric Engineering of N=2 CFT_{4}s based on Indefinite Singularities: Hyperbolic Case
Using Katz, Klemm and Vafa geometric engineering method of
supersymmetric QFTs and results on the classification of generalized
Cartan matrices of Kac-Moody (KM) algebras, we study the un-explored class of
CFTs based on \textit{indefinite} singularities. We show
that the vanishing condition for the general expression of holomorphic beta
function of quiver gauge QFTs coincides exactly with the
fundamental classification theorem of KM algebras. Explicit solutions are
derived for mirror geometries of CY threefolds with \textit{% hyperbolic}
singularities.Comment: 23 pages, 4 figures, minor change
Refined, Motivic, and Quantum
It is well known that in string compactifications on toric Calabi-Yau
manifolds one can introduce refined BPS invariants that carry information not
only about the charge of the BPS state but also about the spin content. In this
paper we study how these invariants behave under wall crossing. In particular,
by applying a refined wall crossing formula, we obtain the refined BPS
degeneracies for the conifold in different chambers. The result can be
interpreted in terms of a new statistical model that counts `refined' pyramid
partitions; the model provides a combinatorial realization of wall crossing and
clarifies the relation between refined pyramid partitions and the refined
topological vertex. We also compare the wall crossing behavior of the refined
BPS invariants with that of the motivic Donaldson-Thomas invariants introduced
by Kontsevich-Soibelman. In particular, we argue that, in the context of BPS
state counting, the three adjectives in the title of this paper are essentially
synonymous.Comment: 31 pages, 12 figures, harvma
Effective Actions for Massive Kaluza-Klein States on AdS_3 x S^3 x S^3
We construct the effective supergravity actions for the lowest massive
Kaluza-Klein states on the supersymmetric background AdS_3 x S^3 x S^3. In
particular, we describe the coupling of the supergravity multiplet to the
lowest massive spin-3/2 multiplet which contains 256 physical degrees of
freedom and includes the moduli of the theory. The effective theory is realized
as the broken phase of a particular gauging of the maximal three-dimensional
supergravity with gauge group SO(4) x SO(4). Its ground state breaks half of
the supersymmetries leading to 8 massive gravitinos acquiring mass in a super
Higgs effect. The holographic boundary theory realizes the large N=(4,4)
superconformal symmetry.Comment: 31 pages, v2: minor change
Special colored Superpolynomials and their representation-dependence
We introduce the notion of "special superpolynomials" by putting q=1 in the
formulas for reduced superpolynomials. In this way we obtain a generalization
of special HOMFLY polynomials depending on one extra parameter t. Special
HOMFLY are known to depend on representation R in especially simple way: as
|R|-th power of the fundamental ones. We show that the same dependence persists
for our special superpolynomials in the case of symmetric representations, at
least for the 2-strand torus and figure-eight knots. For antisymmetric
representations the same is true, but for t=1 and arbitrary q. It would be
interesting to find an interpolation between these two relations for arbitrary
representations, but no superpolynomails are yet available in this case.Comment: 5 page
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