Hypermultiplet Moduli Space Research Articles

Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds

We compute the contribution of Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds to the metric on the hypermultiplet moduli space in the large volume, weak coupling limit. Our results are in perfect agreement with the predictions based on S-duality, mirror symmetry and supersymmetry.

D-instantons in Type IIA string theory on Calabi-Yau threefolds

Type IIA string theory compactified on a Calabi-Yau threefold has a hypermultiplet moduli space whose metric is known to receive non-perturbative corrections from Euclidean D2-branes wrapped on 3-cycles. These corrections have been computed earlier by making use of mirror symmetry, S-duality and twistorial description of quaternionic geometries. In this paper we compute the leading corrections in each homology class using a direct world-sheet approach without relying on any duality symmetry or supersymmetry. Our results are in perfect agreement with the earlier predictions.

Hypermultiplet gaugings and supersymmetric solutions from 11D and massive IIA supergravity on hbox {H}^{(p,q)} spaces

Supersymmetric text {AdS}_{4}, text {AdS}_{2} times Sigma _{2} and asymptotically hbox {AdS}_{4} black hole solutions are studied in the context of non-minimal mathcal {N}=2 supergravity models involving three vector multiplets (STU-model) and Abelian gaugings of the universal hypermultiplet moduli space. Such models correspond to consistent subsectors of the text {SO}(p,q) and text {ISO}(p,q) gauged maximal supergravities that arise from the reduction of 11D and massive IIA supergravity on text {H}^{(p,q)} spaces down to four dimensions. A unified description of all the models is provided in terms of a square-root prepotential and the gauging of a duality-hidden symmetry pair of the universal hypermultiplet. Some aspects of M-theory and massive IIA holography are mentioned in passing.

Partial SUSY breaking for asymmetric Gepner models and non-geometric flux vacua

Using the method of simple current extensions, asymmetric Gepner models of Type IIB with mathcal{N} = 1 space-time supersymmetry are constructed. The combinatorics of the massless vector fields suggests that these classical Minkowski string vacua provide fully backreacted solutions corresponding to mathcal{N} = 1 minima of mathcal{N} = 2 gauged supergravity. The latter contain abelian gaugings along the axionic isometries in the hypermultiplet moduli space, and can be considered as Type IIB flux compactifications on Calabi-Yau manifolds equipped with (non-)geometric fluxes. For a particular class of asymmetric Gepner models, we are able to explicitly specify the underlying CICYs and to check necessary conditions for a GSUGRA interpretation. If this conjecture is correct, there exists a large class of exactly solvable non-geometric flux compactifications on CY threefolds.

Non-perturbative scalar potential inspired by type IIA strings on rigid CY

Motivated by a class of flux compactifications of type IIA strings on rigid Calabi-Yau manifolds, preserving N=2 local supersymmetry in four dimensions, we derive a non-perturbative potential of all scalar fields from the exact D-instanton corrected metric on the hypermultiplet moduli space. Applying this potential to moduli stabilization, we find a discrete set of exact vacua for axions. At these critical points, the stability problem is decoupled into two subspaces spanned by the axions and the other fields (dilaton and Kahler moduli), respectively. Whereas the stability of the axions is easily achieved, numerical analysis shows instabilities in the second subspace.

N = 2 heterotic-type II duality and bundle moduli

Heterotic string compactifications on a $K3$ surface $\mathfrak{S}$ depend on a choice of hyperk\"ahler metric, anti-self-dual gauge connection and Kalb-Ramond flux, parametrized by hypermultiplet scalars. The metric on hypermultiplet moduli space is in principle computable within the $(0,2)$ superconformal field theory on the heterotic string worldsheet, although little is known about it in practice. Using duality with type II strings compactified on a Calabi-Yau threefold, we predict the form of the quaternion-K\"ahler metric on hypermultiplet moduli space when $\mathfrak{S}$ is elliptically fibered, in the limit of a large fiber and even larger base. The result is in general agreement with expectations from Kaluza-Klein reduction, in particular the metric has a two-stage fibration structure, where the $B$-field moduli are fibered over bundle and metric moduli, while bundle moduli are themselves fibered over metric moduli. A more precise match must await a detailed analysis of $R^2$-corrected ten-dimensional supergravity.

Moduli spaces in AdS 4 supergravity

We study the structure of the supersymmetric moduli spaces of ${\cal N}=1$ and ${\cal N}=2$ supergravity theories in $AdS_4$ backgrounds. In the ${\cal N}=1$ case, the moduli space cannot be a complex submanifold of the K\"ahler field space, but is instead real with respect to the inherited complex structure. In ${\cal N}=2$ supergravity the same result holds for the vector multiplet moduli space, while the hypermultiplet moduli space is a K\"ahler submanifold of the quaternionic-K\"ahler field space. These findings are in agreement with AdS/CFT considerations.

Heterotic-type II duality in twistor space

Abstract Heterotic string theory compactified on a K3 surface times T 2 is believed to beequivalent to type II string theory on a suitable Calabi-Yau threefold. In particular, it must share the same hypermultiplet moduli space. Building on the known twistorial description on the type II side, and on recent progress on the map between type II and heterotic moduli in the limit where both the type II and heterotic strings become classical, we provide a new twistorial construction of the hypermultiplet moduli space in this limit which is adapted to the symmetries of the heterotic string. We also take steps towards understanding the twistorial description for heterotic worldsheet instanton corrections away from the classical limit. As a spin-off, we obtain a twistorial description of a class of automorphic forms of SO(4, n, $\mathbb{Z}$ ) obtained by Borcherds’ lift.

S-duality in twistor space

Abstract In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space $ {\mathcal{M}_H} $ must carry an isometric action of the modular group SL(2, $ \mathbb{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 $ {\mathcal{M}_H} $ , and construct a general class of SL(2, $ \mathbb{Z} $ )-invariant quaternion-Kähler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. This family should include $ {\mathcal{M}_H} $ corrected by D3-D1-D(-1)-instantons (with five-brane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional $ \mathcal{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.

String Vacua in Exceptional Generalized Geometry

In this note we outline the main results of a forthcoming publication [M. Grana, F. Orsi, to appear], in collaboration with M. Grana. We analyze Minkowski vacua in the language of exceptional generalized geometry (EGG). Once we identify a twisted derivative operator that contains all NS and RR fluxes and transforms covariantly under the E 7 ( 7 ) U-duality group, we find the differential equations on the structures which parameterize the vector and hypermultiplet moduli spaces of N = 2 supergravity, and interpret them in terms of integrability of such structures. We pursue this analysis for both N = 1 and N = 2 vacua.

Self-dual Einstein spaces, heavenly metrics, and twistors

Four-dimensional quaternion-Kähler metrics, or equivalently self-dual Einstein spaces M, are known to be encoded locally into one real function h subject to Przanowski’s heavenly equation. We elucidate the relation between this description and the usual twistor description for quaternion-Kähler spaces. In particular, we show that the same space M can be described by infinitely many different solutions h, associated with different complex (local) submanifolds on the twistor space, and therefore to different (local) integrable complex structures on M. We also study quaternion-Kähler deformations of M and, in the special case where M has a Killing vector field, show that the corresponding variations in h are related to eigenmodes of the conformal Laplacian on M. We exemplify our findings on the four-sphere S4, the hyperbolic plane H4, and on the “universal hypermultiplet,” i.e., the hypermultiplet moduli space in type IIA string compactified on a rigid Calabi–Yau threefold.

Towards the quantum corrected hypermultiplet moduli space

We review recent progress in understanding the hypermultiplet moduli space arising from compactifications of type II strings on Calabi-Yau threefolds.

Moduli Potentials in Type IIA Compactifications with RR and NS Flux

We describe a simple class of type-IIA string compactifications on Calabi-Yau manifolds where background fluxes generate a potential for the complex structure moduli, the dilaton, and the Kähler moduli. This class of models corresponds to gauged = 2 supergravities, and the potential is completely determined by a choice of gauging and by data of the = 2 Calabi-Yau model — the prepotential for vector multiplets and the quaternionic metric on the hypermultiplet moduli space. Using mirror symmetry, one can determine many (though not all) of the quantum corrections which are relevant in these models.

SUPERPOTENTIAL OF THE M-THEORY CONIFOLD AND TYPE IIA STRING THEORY

The membrane instanton superpotential for M-theory on the G2 holonomy manifold given by the cone on S3×S3 is given by the dilogarithm and has Heisenberg monodromy group in the quantum moduli space. We compare this to a Heisenberg group action on the type IIA hypermultiplet moduli space for the universal hypermultiplet, to metric corrections from membrane instantons related to a twisted dilogarithm for the deformed conifold and to a flat bundle related to a conifold period, the Heisenberg group and the dilogarithm appearing in five-dimensional Seiberg/Witten theory.

Hypermultiplet moduli space and three dimensional gauge theories

We establish a relation, conjectured recently by E. Witten, between the hypermultiplet moduli space in compactifications of the heterotic string on an A-D-E singularities, and the moduli spaces of three dimensional pure gauge theories with the corresponding A-D-E gauge groups. It is possible to add a bounded number of heterotic fivebranes sitting in the singularity, while (in leading order in $\alpha'$) keeping the heterotic string perturbative. The corresponding hypermultiplet moduli space is given by the moduli space of a three dimensional gauge theory with matter.