Free Fermions and Extended Conformal Algebras

A class of algebras is constructed using free fermions and the invariant antisymmetric tensors associated with irreducible holonomy groups. (This version contains minor typographical corrections and some additional references. )Comment: 7 pages, KCL-Th-94-1

Finiteness and anomalies in (4,0) supersymmetric sigma models

Power-counting arguments based on extended superfields have been used to argue that two-dimensional supersymmetric sigma models with (4,0) supersymmetry are finite. This result is confirmed up to three loop order in pertubation theory by an explicit calculation using (1,0) superfields. In particular, it is shown that the finite counterterms which must be introduced into the theory in order to maintain (4,0) supersymmetry are precisely the terms that are required to establish ultra-violet finiteness.Comment: 19 page

Holonomy groups and W-symmetries

Irreducible sigma models, i.e. those for which the partition function does not factorise, are defined on Riemannian spaces with irreducible holonomy groups. These special geometries are characterised by the existence of covariantly constant forms which in turn give rise to symmetries of the supersymmetric sigma model actions. The Poisson bracket algebra of the corresponding currents is a W-algebra. Extended supersymmetries arise as special cases.Comment: pages 2

Massive IIA supergravities

We perform a systematic search for all possible massive deformations of IIA supergravity in ten dimensions. We show that there exist exactly two possibilities: Romans supergravity and Howe-Lambert-West supergravity. Along the way we give the full details of the ten-dimensional superspace formulation of the latter. The scalar superfield at canonical mass dimension zero (whose lowest component is the dilaton), present in both Romans and massless IIA supergravities, is not introduced from the outset but its existence follows from a certain integrability condition implied by the Bianchi identities. This fact leads to the possibility for a certain topological modification of massless IIA, reflecting an analogous situation in eleven dimensions.Comment: 35 pages; v2: typos corrected, added eq. (A4

Heterotic-type IIA duality with fluxes

In this paper we study a possible non-perturbative dual of the heterotic string compactified on K3 x T^2 in the presence of background fluxes. We show that type IIA string theory compactified on manifolds with SU(3) structure can account for a subset of the possible heterotic fluxes. This extends our previous analysis to a case of a non-perturbative duality with fluxes.Comment: 26 pages, minor corrections; version to appear in JHE

Twistor spaces for HKT manifolds

We construct the twistor space associated with an HKT manifold, that is, a hyper-K\"ahler manifold with torsion, a type of geometry that arises as the target space geometry in two-dimensional sigma models with (4,0) supersymmetry. We show that this twistor space has a natural complex structure and is a holomorphic fibre bundle over the complex projective line with fibre the associated HKT manifold. We also show how the metric and torsion of the HKT manifold can be determined from data on the twistor space by a reconstruction theorem. We give a geometric description of the sigma model (4,0) superfields as holomorphic maps (suitably understood) from a twistorial extension of (4,0) superspace (harmonic superspace) into the twistor space of the sigma model target manifold and write an action for the sigma model in terms of these (4,0) superfields.Comment: 15 pages, Phyzz

Twisting K3 x T^2 Orbifolds

We construct a class of geometric twists of Calabi-Yau manifolds of Voisin-Borcea type (K3 x T^2)/Z_2 and study the superpotential in a type IIA orientifold based on this geometry. The twists modify the direct product by fibering the K3 over T^2 while preserving the Z_2 involution. As an important application, the Voisin-Borcea class contains T^6/(Z_2 x Z_2), the usual setting for intersecting D6 brane model building. Past work in this context considered only those twists inherited from T^6, but our work extends these twists to a subset of the blow-up modes. Our work naturally generalizes to arbitrary K3 fibered Calabi-Yau manifolds and to nongeometric constructions.Comment: 57 pages, 4 figures; uses harvmac.tex, amssym.tex; v3: minor corrections, references adde

Intersection rules, dynamics and symmetries

We consider theories containing gravity, at most one dilaton and form field strengths. We show that the existence of particular BPS solutions of intersecting extremal closed branes select the theories, which upon dimensional reduction to three dimensions possess a simple simply laced Lie group symmetry G. Furthermore these theories can be fully reconstructed from the dynamics of such branes and of their openings. Amongst such theories are the effective actions of the bosonic sector of M-theory and of the bosonic string. The BPS intersecting brane solutions form representations of a subgroup of the group of Weyl reflections and outer automorphisms of the triple Kac-Moody extension G+++ of the G algebra, which cannot be embedded in the overextended Kac-Moody subalgebra G++ characterising the cosmological Kasner solutions.Comment: Latex 30 pages, 3 figure

Scherk-Schwarz reduction of M-theory on G2-manifolds with fluxes

We analyse the 4-dimensional effective supergravity theories obtained from the Scherk--Schwarz reduction of M-theory on twisted 7-tori in the presence of 4-form fluxes. We implement the appropriate orbifold projection that preserves a G2-structure on the internal 7-manifold and truncates the effective field theory to an N=1, D=4 supergravity. We provide a detailed account of the effective supergravity with explicit expressions for the Kaehler potential and the superpotential in terms of the fluxes and of the geometrical data of the internal manifold. Subsequently, we explore the landscape of vacua of M-theory compactifications on twisted tori, where we emphasize the role of geometric fluxes and discuss the validity of the bottom-up approach. Finally, by reducing along isometries of the internal 7-manifold, we obtain superpotentials for the corresponding type IIA backgrounds.Comment: 43 pages, Latex; v3 typos corrected, one reference added, JHEP versio

Topological A-Type Models with Flux

We study deformations of the A-model in the presence of fluxes, by which we mean rank-three tensors with antisymmetrized upper/lower indices, using the AKSZ construction. Generically these are topological membrane models, and we show that the fluxes are related to deformations of the Courant bracket which generalize the twist by a closed 3-from $H$, in the sense that satisfying the AKSZ master equation implies the integrability conditions for an almost generalized complex structure with respect to the deformed Courant bracket. In addition, the master equation imposes conditions on the fluxes that generalize $dH=0$. The membrane model can be defined on a large class of $U(m)$- and $U(m) \times U(m)$-structure manifolds, including geometries inspired by $(1,1)$ supersymmetric $\sigma$-models with additional supersymmetries due to almost complex (but not necessarily complex) structures in the target space. Furthermore, we show that the model can be defined on three particular half-flat manifolds related to the Iwasawa manifold. When only $H$-flux is turned on it is possible to obtain a topological string model, which we do for the case of a Calabi-Yau with a closed 3-form turned on. The simplest deformation from the A-model is due to the $(2,0)+ (0,2)$ component of a non-trivial $b$-field. The model is generically no longer evaluated on holomorphic maps and defines new topological invariants. Deformations due to $H$-flux can be more radical, completely preventing auxiliary fields from being integrated out.Comment: 30 pages. v2: Improved Version. References added. v3: Minor changes, published in JHE