11,483 research outputs found
New gravitational solutions via a Riemann-Hilbert approach
We consider the Riemann-Hilbert factorization approach to solving the field
equations of dimensionally reduced gravity theories. First we prove that
functions belonging to a certain class possess a canonical factorization due to
properties of the underlying spectral curve. Then we use this result, together
with appropriate matricial decompositions, to study the canonical factorization
of non-meromorphic monodromy matrices that describe deformations of seed
monodromy matrices associated with known solutions. This results in new
solutions, with unusual features, to the field equations.Comment: 29 pages, 2 figures; v2: reference added, matches published versio
BPS Action and Superpotential for Heterotic String Compactifications with Fluxes
We consider N =1 compactifications to four dimensions of heterotic string
theory in the presence of fluxes. We show that up to order O(\alpha'^2) the
associated action can be written as a sum of squares of BPS-like quantities. In
this way we prove that the equations of motion are solved by backgrounds which
fulfill the supersymmetry conditions and the Bianchi identities. We also argue
for the expression of the related superpotential and discuss the radial modulus
stabilization for a class of examples.Comment: LaTeX, 28 pages. Minor changes, one more reference added. Final
version to appear on JHE
On Quantum Special Kaehler Geometry
We compute the effective black hole potential V of the most general N=2, d=4
(local) special Kaehler geometry with quantum perturbative corrections,
consistent with axion-shift Peccei-Quinn symmetry and with cubic leading order
behavior. We determine the charge configurations supporting axion-free
attractors, and explain the differences among various configurations in
relations to the presence of ``flat'' directions of V at its critical points.
Furthermore, we elucidate the role of the sectional curvature at the
non-supersymmetric critical points of V, and compute the Riemann tensor (and
related quantities), as well as the so-called E-tensor. The latter expresses
the non-symmetricity of the considered quantum perturbative special Kaehler
geometry.Comment: 1+43 pages; v2: typo corrected in the curvature of Jordan symmetric
sequence at page 2
Heterotic String Theory on non-Kaehler Manifolds with H-Flux and Gaugino Condensate
We discuss compactifications of heterotic string theory to four dimensions in
the presence of H-fluxes, which deform the geometry of the internal manifold,
and a gaugino condensate which breaks supersymmetry. We focus on the
compensation of the two effects in order to obtain vacua with zero cosmological
constant and we comment on the effective superpotential describing these vacua.Comment: 6 page
Deformations of special geometry: in search of the topological string
The topological string captures certain superstring amplitudes which are also
encoded in the underlying string effective action. However, unlike the
topological string free energy, the effective action that comprises
higher-order derivative couplings is not defined in terms of duality covariant
variables. This puzzle is resolved in the context of real special geometry by
introducing the so-called Hesse potential, which is defined in terms of duality
covariant variables and is related by a Legendre transformation to the function
that encodes the effective action. It is demonstrated that the Hesse potential
contains a unique subsector that possesses all the characteristic properties of
a topological string free energy. Genus contributions are constructed
explicitly for a general class of effective actions associated with a
special-K\"ahler target space and are shown to satisfy the holomorphic anomaly
equation of perturbative type-II topological string theory. This identification
of a topological string free energy from an effective action is primarily based
on conceptual arguments and does not involve any of its more specific
properties. It is fully consistent with known results. A general theorem is
presented that captures some characteristic features of the equivalence, which
demonstrates at the same time that non-holomorphic deformations of special
geometry can be dealt with consistently.Comment: 44 pages, LaTex; v2, v3: minor text improvement
How Does a Fundamental String Stretch its Horizon?
It has recently been shown that if we take into account a class of higher
derivative corrections to the effective action of heterotic string theory, the
entropy of the black hole solution representing elementary string states
correctly reproduces the statistical entropy computed from the degeneracy of
elementary string states. So far the form of the solution has been analyzed at
distance scales large and small compared to the string scale. We analyze the
solution that interpolates between these two limits and point out a subtlety in
constructing such a solution due to the presence of higher derivative terms in
the effective action. We also study the T-duality transformation rules to
relate the moduli fields of the effective field theory to the physical
compactification radius in the presence of higher derivative corrections and
use these results to find the physical radius of compactification near the
horizon of the black hole. The radius approaches a finite value even though the
corresponding modulus field vanishes. Finally we discuss the non-leading
contribution to the black hole entropy due to space-time quantum corrections to
the effective action and the ambiguity involved in comparing this result to the
statistical entropy.Comment: LaTeX file, 38 pages; v2: minor changes and added reference
Effective action for the field equations of charged black holes
In this article, we consistently reduce the equations of motion for the
bosonic N = 2 supergravity action, using a multi-centered black hole ansatz for
the metric. This reduction is done in a general, non-supersymmetric setup, in
which we extend concepts of BPS black hole technology. First of all we obtain a
more general form of the black hole potential, as part of an effective action
for both the scalars and the vectors in the supergravity theory. Furthermore,
we show that there are extra constraints specifying the solution, which we
calculate explicitly. In the literature, these constraints have already been
studied in the one-center case. We also show that the effective action we
obtain for non-static metrics, can be linked to the "entropy function" for the
spherically symmetric case, as defined by Sen and Cardoso et al.Comment: 18 pages, (v2: small corrections, version to be published in CQG
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