49 research outputs found
Covariant N=2 heterotic string in four dimensions
We construct a covariant formulation of the heterotic superstring on K3 times
T^2 with manifest N=2 supersymmetry. We show how projective superspace appears
naturally in the hybrid formulation giving a (partially) geometric
interpretation of the harmonic parameter. The low-energy effective action for
this theory is given by a non-standard form of N=2 supergravity which is
intimately related to the N=1 old-minimal formulation. This formalism can be
used to derive new descriptions of interacting projective superspace field
theories using Berkovits' open string field theory and the the heterotic
Berkovits-Okawa-Zwiebach construction.Comment: 11+3 page
S-duality in Twistor Space
In type IIB string compactifications on a Calabi-Yau threefold, the
hypermultiplet moduli space must carry an isometric action of the modular
group SL(2,Z), inherited from the S-duality symmetry of type IIB string theory
in ten dimensions. We investigate how this modular symmetry is realized at the
level of the twistor space of , and construct a general class of
SL(2,Z)-invariant quaternion-Kahler metrics with two commuting isometries,
parametrized by a suitably covariant family of holomorphic transition
functions. This family should include corrected by D3-D1-D(-1)-instantons
(with fivebrane corrections ignored) and, after taking a suitable rigid limit,
the Coulomb branch of five-dimensional N=2 gauge theories compactified on a
torus, including monopole string instantons. These results allow us to
considerably simplify the derivation of the mirror map between type IIA and IIB
fields in the sector where only D1-D(-1)-instantons are retained.Comment: 29 pages, 1 figur
Hypermultiplets and Topological Strings
The c-map relates classical hypermultiplet moduli spaces in compactifications
of type II strings on a Calabi-Yau threefold to vector multiplet moduli spaces
via a further compactification on a circle. We give an off-shell description of
the c-map in N=2 superspace. The superspace Lagrangian for the hypermultiplets
is a single function directly related to the prepotential of special geometry,
and can therefore be computed using topological string theory. Similarly, a
class of higher derivative terms for hypermultiplets can be computed from the
higher genus topological string amplitudes. Our results provide a framework for
studying quantum corrections to the hypermultiplet moduli space, as well as for
understanding the black hole wave-function as a function of the hypermultiplet
moduli.Comment: 21 pages, references adde
TBA for non-perturbative moduli spaces
Recently, an exact description of instanton corrections to the moduli spaces
of 4d N=2 supersymmetric gauge theories compactified on a circle and Calabi-Yau
compactifications of Type II superstring theories was found. The equations
determining the instanton contributions turn out to have the form of
Thermodynamic Bethe Ansatz. We explore further this relation and, in
particular, we identify the contact potential of quaternionic string moduli
space with the free energy of the integrable system and the Kahler potential of
the gauge theory moduli space with the Yang-Yang functional. We also show that
the corresponding S-matrix satisfies all usual constraints of 2d integrable
models, including crossing and bootstrap, and derive the associated Y-system.
Surprisingly, in the simplest case the Y-system is described by the MacMahon
function relevant for crystal melting and topological strings.Comment: 25 pages, 1 figur
Off-shell N=2 tensor supermultiplets
A multiplet calculus is presented for an arbitrary number n of N=2 tensor
supermultiplets. For rigid supersymmetry the known couplings are reproduced. In
the superconformal case the target spaces parametrized by the scalar fields are
cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant
potentials, subject to certain constraints. The coupling to conformal
supergravity enables the derivation of a large class of supergravity
Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing
the tensor fields into scalars leads to hypermultiplets with hyperkahler or
quaternion-Kahler target spaces with at least n abelian isometries. It is
demonstrated how to use the calculus for the construction of Lagrangians
containing higher-derivative couplings of tensor multiplets. For the
application of the c-map between vector and tensor supermultiplets to
Lagrangians with higher-order derivatives, an off-shell version of this map is
proposed. Various other implications of the results are discussed. As an
example an elegant derivation of the classification of 4-dimensional
quaternion-Kahler manifolds with two commuting isometries is given.Comment: 36 page
Completeness in supergravity constructions
We prove that the supergravity r- and c-maps preserve completeness. As a
consequence, any component H of a hypersurface {h=1} defined by a homogeneous
cubic polynomial such that -d^2 h is a complete Riemannian metric on H defines
a complete projective special Kahler manifold and any complete projective
special Kahler manifold defines a complete quaternionic Kahler manifold of
negative scalar curvature. We classify all complete quaternionic Kahler
manifolds of dimension less or equal to 12 which are obtained in this way and
describe some complete examples in 16 dimensions.Comment: 29 page
Supergravity description of spacetime instantons
We present and discuss BPS instanton solutions that appear in type II string
theory compactifications on Calabi-Yau threefolds. From an effective action
point of view these arise as finite action solutions of the Euclidean equations
of motion in four-dimensional N=2 supergravity coupled to tensor multiplets. As
a solution generating technique we make use of the c-map, which produces
instanton solutions from either Euclidean black holes or from Taub-NUT like
geometries.Comment: 35 pages, some clarifications adde
D-instantons and twistors: some exact results
We present some results on instanton corrections to the hypermultiplet moduli
space in Calabi-Yau compactifications of Type II string theories. Previously,
using twistor methods, only a class of D-instantons (D2-instantons wrapping
A-cycles) was incorporated exactly and the rest was treated only linearly. We
go beyond the linear approximation and give a set of holomorphic functions
which, through a known procedure, capture the effect of D-instantons at all
orders. Moreover, we show that for a sector where all instanton charges have
vanishing symplectic invariant scalar product, the hypermultiplet metric can be
computed explicitly.Comment: 32 pages, 3 figures, uses JHEP3.cls; some changes in section 3.3.3;
corrected formula for the contact potentia
Heterotic-Type II duality in the hypermultiplet sector
We revisit the duality between heterotic string theory compactified on K3 x
T^2 and type IIA compactified on a Calabi-Yau threefold X in the hypermultiplet
sector. We derive an explicit map between the field variables of the respective
moduli spaces at the level of the classical effective actions. We determine the
parametrization of the K3 moduli space consistent with the Ferrara-Sabharwal
form. From the expression of the holomorphic prepotential we are led to
conjecture that both X and its mirror must be K3 fibrations in order for the
type IIA theory to have an heterotic dual. We then focus on the region of the
moduli space where the metric is expressed in terms of a prepotential on both
sides of the duality. Applying the duality we derive the heterotic
hypermultiplet metric for a gauge bundle which is reduced to 24 point-like
instantons. This result is confirmed by using the duality between the heterotic
theory on T^3 and M-theory on K3. We finally study the hyper-Kaehler metric on
the moduli space of an SU(2) bundle on K3.Comment: 27 pages; references added, typos correcte
D3-instantons, Mock Theta Series and Twistors
The D-instanton corrected hypermultiplet moduli space of type II string
theory compactified on a Calabi-Yau threefold is known in the type IIA picture
to be determined in terms of the generalized Donaldson-Thomas invariants,
through a twistorial construction. At the same time, in the mirror type IIB
picture, and in the limit where only D3-D1-D(-1)-instanton corrections are
retained, it should carry an isometric action of the S-duality group SL(2,Z).
We prove that this is the case in the one-instanton approximation, by
constructing a holomorphic action of SL(2,Z) on the linearized twistor space.
Using the modular invariance of the D4-D2-D0 black hole partition function, we
show that the standard Darboux coordinates in twistor space have modular
anomalies controlled by period integrals of a Siegel-Narain theta series, which
can be canceled by a contact transformation generated by a holomorphic mock
theta series.Comment: 42 pages; discussion of isometries is amended; misprints correcte