G. Papadopoulos

Compactification of D = 11 supergravity on spaces of exceptional holonomy

Abstract We investigate the compactification of D = 11 supergravity to D = 5,4,3, on compact manifolds of holonomy SU (3) (Calabi-Yau), G 2 , and Spin (7), respectively, making use of examples of the latter two cases found recently by Joyce. In each case the lower dimensional theory is a Maxwell/Einstein supergravity theory. We find evidence for an equivalence, in certain cases, with heterotic string compactifications from D = 10 to D = 5,4,3, on compact manifolds of holonomy SU (2) ( K 3 × S 1 ), SU (3), and G 2 , respectively. Calabi-Yau manifolds with Hodge numbers h 1,1 = h 1,2 = 19 play a significant role in the proposed equivalences.

Complex geometry of conifolds and a 5-brane wrapped on a 2-sphere

We investigate solutions of type II supergravity which have the product R 1,3 ×M 6 structure with non-compact M 6 factor and which preserve at least four supersymmetries. In particular, we consider various conifolds and the N = 1 supersymmetric ‘NS5-brane wrapped on a 2-sphere’ solution recently discussed in hep-th/0008001. In all of these cases, we explicitly construct the complex structures, and the K¨ ahler and parallel (3, 0)-forms of the corresponding M 6 . In addition, we verify that the above solutions preserve, respectively, eight and four supersymmetries of the underlying type II theory. We also demonstrate that the ordinary and fractional D3-brane (5-brane wrapped on a 2-cycle) solutions on singular, resolved and deformed conifolds, and the (S-dual of) NS5-brane wrapped on 2-sphere can be obtained as special cases from a universal ansatz for the supergravity fields, i.e. from a single one-dimensional action governing their radial evolution. We show that like the 3-branes on conifolds, the NS5brane on a 2-sphere background can be found as a solution of a first-order system following from a superpotential.

Vanishing theorems and string backgrounds

We show various vanishing theorems for the cohomology groups of compact Hermitian manifolds for which the Bismut connection has a (restricted) holonomy contained in SU(n) and classify all such manifolds of dimension four. In this way we provide necessary conditions for the existence of such structures on compact Hermitian manifolds with vanishing first Chern class of non-Kahler type. Then we apply our results to solutions of the string equations and show that such solutions admit various cohomological restrictions such as, for example, that under certain natural assumptions the plurigenera vanish. We also find that under some assumptions the string equations are equivalent to the condition that a certain vector is parallel with respect to the Bismut connection.

New supergravities with central charges and Killing spinors in 2+1 dimensions

Abstract We construct a new class of ( p , q )-extended Poincare supergravity theories in 2+1 dimensions as Chern-Simons theories of supersymmetry algebras with both central and automorphism charges. The new theories have the advantage that they are limits of corresponding ( p , q ) adS supergravity theories and, for not too large a value of N = p + q , that they have a natural formulation in terms of off-shell superfields, in which context the distinction between theories having the same value of N but different ( p , q ) arises because of inequivalent conformal compensator superfields. We also show that, unlike previously constructed N -extended Poincare supergravity theories, the new (2,0) theory admits conical spacetimes with Killing spinors. Many of our results on (2,0) Poincare supergravity continue to apply in the presence of coupling to N = 2 supersymmetric sigma-model matter.

Ultra-violet behaviour of two-dimensional supersymmetric non-linear σ-models

Abstract The conditions for a non-linear σ-model in two dimensions to have (p, q) supersymmetry are briefly reviewed. It is shown how to construct off-shell (p, q) superfields for a wide class of models. General ultra-violet power counting rules are given. These imply that (4, q) models for 0 ⩽ q ⩽ 4 are ultra-violet finite.

A no-go theorem for string warped compactifications

Abstract We give necessary conditions for the existence of perturbative heterotic and common sector type II string warped compactifications preserving four and eight supersymmetries to four spacetime dimensions, respectively. In particular, we find that the only compactifications of heterotic string with the spin connection embedded in the gauge connection and type II strings are those on Calabi–Yau manifolds with constant dilaton. We obtain similar results for compactifications to six and to two dimensions.

The geometry of the one-dimensional supersymmetric non-linear sigma models

A new class of one-dimensional non-linear sigma models with N supersymmetries is constructed by generalising the action and the supersymmetry transformations of these theories. The study of the geometry of the associated sigma model manifolds reveals new structures which are different from those found in the two-dimensional theories. In particular, certain N=2 models are defined on manifolds with foliations and the existence of an N=3 multiplet is demonstrated. Conventional off-shell non-linear constrained multiplets with actions are given for all these theories.

The spinorial geometry of supersymmetric IIB backgrounds

We solve the Killing spinor equations of supersymmetric IIB backgrounds which admit one supersymmetry and the Killing spinor has stability subgroup G2 in Spin(9, 1) × U(1). We find that such backgrounds admit a timelike Killing vector field and the geometric structure of the spacetime reduces from Spin(9, 1) × U(1) to G2. We determine the type of G2 structure that the spacetime admits by computing the covariant derivatives of the spacetime forms associated with the Killing spinor bilinears. We also solve the Killing spinor equations of backgrounds with two supersymmetries and -invariant spinors, and four supersymmetries with - and with G2-invariant spinors. We show that the Killing spinor equations factorize in two sets, one involving the geometry and the 5-form flux, and the other the 3-form flux and the scalars. In the and cases, the spacetime admits a parallel null vector field and so the spacetime metric can be locally described in terms of Penrose coordinates adapted to the associated rotation free, null, geodesic congruence. The transverse space of the congruence is a Spin(7) and a SU(4) holonomy manifold, respectively. In the G2 case, all the fluxes vanish and the spacetime is the product of a three-dimensional Minkowski space with a holonomy G2 manifold.

Calibrations and Intersecting Branes

Abstract:We investigate the solutions of Nambu–Goto-type actions associated with calibrations. We determine the supersymmetry preserved by these solutions using the contact set of the calibration and examine their bulk interpretation as intersecting branes. We show that the supersymmetry preserved by such solutions is closely related to the spinor singlets of the subgroup G of Spin (9,1) or Spin (10,1) that rotates the tangent spaces of the brane. We find that the supersymmetry projections of the worldvolume solutions are precisely those of the associated bulk configurations. We also investigate the supersymmetric solutions of a Born–Infeld action. We show that in some cases this problem again reduces to counting spinor singlets of a subgroup of Spin (9,1) acting on the associated spinor representations. We also find new worldvolume solutions which preserve 1/8 of the supersymmetry of the bulk and give their bulk interpretation.

Further remarks on the geometry of two-dimensional non-linear σ-models

A class of extended supersymmetric two-dimensional non-linear sigma -models can be formulated in terms of constrained extended superfields. The conditions for these constraints to be linearisable are examined. These conditions involve generalised Nijenhuis tensors and curvature tensors constructed from the complex structures on the target manifold. Off-shell constrained extended superfields are constructed for the Yang-Mills sector of the (2, 0) and (4, 0) models. These superfields will exist provided that certain conditions are satisfied; these conditions are most conveniently expressed in terms of the geometry of fibre bundles. The existence of (4, 0) superfields implies that the general (4, 0) sigma -model with Yang-Mills sector is ultraviolet finite.