73 research outputs found
Tensor supermultiplets and toric quaternion-Kahler geometry
We review the relation between 4n-dimensional quaternion-Kahler metrics with
n+1 abelian isometries and superconformal theories of n+1 tensor
supermultiplets. As an application we construct the class of eight-dimensional
quaternion-Kahler metrics with three abelian isometries in terms of a single
function obeying a set of linear second-order partial differential equations.Comment: 8 pages, Contribution to the proceedings of the RTN ForcesUniverse
Network Workshop, Napoli, October 9th - 13th, 200
Orientifolding in N=2 Superspace
We discuss orientifold projections on superspace effective actions for
hypermultiplets. We present a simple and new mechanism that allows one to find
the Kahler potential and complex structure for the N=1 theory directly in terms
of the parent N=2 theory. As an application, we demonstrate our method for
Calabi-Yau orientifold compactifications of type IIB superstrings.Comment: 7 page
Twistor Approach to String Compactifications: a Review
We review a progress in obtaining the complete non-perturbative effective
action of type II string theory compactified on a Calabi-Yau manifold. This
problem is equivalent to understanding quantum corrections to the metric on the
hypermultiplet moduli space. We show how all these corrections, which include
D-brane and NS5-brane instantons, are incorporated in the framework of the
twistor approach, which provides a powerful mathematical description of
hyperkahler and quaternion-Kahler manifolds. We also present new insights on
S-duality, quantum mirror symmetry, connections to integrable models and
topological strings.Comment: 99 pages; minor corrections; journal versio
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
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
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
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
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