Superstrings and the auxiliary field structure of supergravity

We construct the complete superfield of vertex operators corresponding to the four-dimensional N = 1 supergravity multiplet associated with the heterotic superstring. The supergravity fields are shown to consist of a graviton, gravitino, and two auxiliary fields and to form a new minimal supermultiplet. The role of R-invariance in new minimal supergravity is discussed.     

Superspace geometry from D = 4, N = 1 heterotic superstrings

The presence of classical κ-supersymmetry invariance is shown to be consistent with an off-shell D = 4, N = 1 conformal supergravity background in the presence of a tensor multiplet. We derive a suitable set of constraints, via super Weyl rescaling, for a heterotic superstring in such a background. Starting from the geometry of 16-16 supergravity and gauging the R-symmetry with a composite connection, we derive a geometrical structure similar to that of new minimal supergravity.     

The vanishing volume of N = 1 superspace

We show that the supergeometry of the new minimal formulation of N = 1 supergravity is a limiting case of the non-minimal supergeometry for which the volume of superspace vanishes. The action for supergravity in this case is then no longer the superdeterminant of the vielbein but is analogous to a special form of the Fayet-Iliopoulos term allowed only for the new minimal supergeometry. We discuss the restrictions on matter couplings imposed by the new and non-minimal supergeometries.     

The improved tensor multiplet in N = 2 supergravity

We construct a scale-invariant action for the N = 2 tensor multiplet which can be coupled to conformal supergravity. In spite of its non-polynomial form the action describes a free massless hypermultiplet. When used as a compensating multiplet it leads to a new minimal formulation of N = 2 Poincaré or de Sitter supergravity. We discuss its consequences and present a comparison with previous off-shell formulations.     

Magnetic charge can locally stabilize Kaluza-Klein bubbles

We construct a new 2-parameter family of static topological solitons in 5D minimal supergravity which are endowed with magnetic charge and mass. The solitons are asymptotically R⁴×S¹, where the radius of the S¹ has a lower bound Rs?Rmin. Setting up initial data on a Cauchy slice at a moment of time symmetry, we demonstrate that if Rs>Rmin these solitons correspond to a perturbatively stable “small” static bubble as well as an unstable “large” static bubble, whereas if Rs<Rmin there are no static bubbles. The energetics and thermodynamics of the magnetic black string are then discussed and it is shown that the locally stable bubble is the end point of a phase transition for an appropriate range of black string parameters.     

A nontrivial vacuum state in D = 10, N = 1 supergravity

We find a ground state of D = 10, N = 1 supergravity of the form (AdS(3) × R¹) × S³ × T³ which preserves all supersymmetries and should provide a gauged D = 4, N = 4 supergravity coupled to supermatter after dimensional reduction.     

A dual formulation of supergravity-matter theories

Generating supersymmetric AdS solutions in non-minimal supergravity in four dimensions is notoriously difficult. Indeed, it is a longstanding lore that such solutions exist only for old minimal supergravity. In this paper, we construct a dual formulation for general N=1 supergravity-matter systems that avoids the problem. In the case of pure supergravity without a cosmological constant, it coincides with the usual non-minimal (n=−1) supergravity, but in the presence of matter (or a cosmological constant) our formulation differs considerably. We also elaborate upon the framework of conformal superspace and the compensator method as applied to our theory. In particular, we show that one can encode the details of the Kähler potential and superpotential entirely within the geometry of superspace so that the general sigma-model action is encoded in a single compact term: the supervolume. Finally, we discuss the issue of supercurrents and propose a general form for the supercurrent in AdS.     

Energy and supercharge in higher derivative gravity

Explicit energy expressions are derived, by supergravity embedding, for quadratic curvature actions with or without Einstein terms. Applications include existence of stability domains in R+R² models, vanishing of supercharge in conformal supergravity and indefiniteness of the energy in the generic case. The contradiction between the indefiniteness of the energy and its seemingly positive supersymmetric H=ΣQ_α² form is traced to the necessarily indefinite Hilbert space of the fermionic sector, which implies H is really a difference of squares.     

Manifestly supersymmetric extensions of (curvature)2-terms in six-dimensional N = 2 supergravity

A systematic and manifestly supersymmetric procedure for supersymmetrization of general (curvature)²-terms in N = 2 supergravity in six dimensions (D = 6) is presented in superspace. The general form of new terms for the supersymmetrization in supertranslation rules is given. As a by-product, the superspace structure of quaternionic Kähler manifolds is elucidated. Our method is the D = 6 application of our previously established formulation for the D = 10, N = 1 supergravity with the O(α′) superstring corrections.     

Structure of supergravity

It is shown how to construct actions and kinetic multiplets out of scalar multiplets of supergravity. The multiplets containing the scalar and the conformal tensor are obtained and yield the gauge actions of Einstein and Weyl supergravity. The complete supersymmetric R² and Bel-Robinson invariants are also obtained as well as general n-loop counterterms.     

Manifestly supersymmetric O(α′) superstring corrections in new D = 10, N = 1 supergravity Yang-Mills theory

A systematic procedure in superspace to derive the O(α′) tree-level superstring corrections to the new D = 10, N = 1 (dual) supergravity Yang-Mills system is established. All the tree-level O(α′) corrections in the closed supersymmetry transformation laws are presented explicitly. These O(α′) corrections are regarded as a generalization of “matter” couplings in D = 10, N = 1 supergravity. The advantage of the superspace approach, based on superspace Bianchi identities, in comparison with the component formulation is elucidated. This new method is applicable to all anomaly-free D ⩽ 10 non-maximal supergravity theories, which utilize the Green-Schwarz mechanism. It also provides a way of introducing general higher-order powers of curvature tensors in D ⩽ 10 supergravity theories.     

Matter coupling and non-linear σ-models in N = 2 supergravity

Starting from an off-shell formulation of N = 2 supergravity, we construct the matter multiplet in its complex form (the scalar hypermultiplet) and in its real form. We construct the matter action which describes the coupling to supergravity. The interpretation where the 32 + 32 field components of the minimal gravitational multiplet are independent dynamical variables is known to be inconsistent for pure supergravity. We find it to be consistent when coupled to at least one matter multiplet, and to give rise to supersymmetric σ-models when coupled to at least two matter multiplets.     

Supergravity with one auxiliary spinor

We present an “intermediate” off-shell version of N = 1 supergravity and its tensor calculus. The supergravity multiplet has 16 + 16 field components. The formulation can be constrained to either of the minimal ones with 12 + 12 components, or enlarge by matter couplings to several 20 + 20 component versions. Self-coupled to its own axial gauge submultiplet it leads to spontaneous supersymmetry breaking in the form first discussed by Freedman and to a propagating gauge field.     

Supersymmetric flavon-chromon models

Using the supersymmetry and R-breaking mechanism induced by N=1 supergravity, we develop the minimal flavon-chromon preonic model where $\text{spin}\text{-}\text{1}\text{2}$ and spin-0 components of four preonic chiral multiplets correspond to flavons and chromons, from which quarks and leptons are made as composites. The emergence of the concepts of flavour and colour, in this minimal model, is synonymous with R and supersymmetry breaking. This breaking also gives a heavy mass to the gaugino, which is necessary for the implementation of the model.     

Gravitational supervertices in n=1, 4D superstrings

The gravitational supermultiplet for target space-time supersymmetry of four-dimensional heterotic strings is obtained. By an explicit construction of supervertex operators it is shown that the underlying superspace geometry corresponds to the “new-minimal” formulation of N = 1, 4D supergravity. The relation between R-symmetry in target space and the U(1) symmetry of the world-sheet N = 2 superconformal algebra is outlined.     

Cosmological solutions with Calabi-Yau compactification

Assuming a Calabi-Yau compactification, cosmological solutions are presented in ten-dimensional, N=1 Yang-Mills supergravity theory with the curvature squared term (R²_μνϱσ −4R_μν² + R²). In a vacuum state, Kasner-type soluti ons exist as well as (four-dimensional Minkoswki space-time)×(a Calabi-Yau space). In the later stage of the universe the (four-dimensional Friedmann universe)×(a constant Calabi-Yau space) is realized asymptotically like an attractor. This solution is asymptotically stable against small perturbations.     

Coupling the gauge-invariant supersymmetric non-linear sigma model to supergravity

The gauge-invariant supersymmetric non-linear sigma model is coupled to N = 1 supergravity. The results are expressed in the language of Kahler geometry. They lead to a deeper understanding of the connections between supergravity, R-invariance and the Fayet-Iliopoulos D-term. They also provide a foundation for phenomenological studies of supergravity theories.     

B s →μ + μ − decay in the R-parity violating minimal supergravity

We study B _s →μ ⁺ μ ^? in the context of the R-parity violating minimal supergravity in the high-tan?β regime. We find that the lowest value of the branching ratio can go well below the present LHCb sensitivity and hence B _s →μ ⁺ μ ^? can even be invisible to the LHC. We also find that the present upper bound on Br?(B _s →μ ⁺ μ ^?) puts strong constraint on the minimal supergravity parameter space. The constraints become more severe if the upper bound is close to its standard model prediction.     

On the origin of supergravity boundary terms in the AdS /CFT correspondence

The standard formulation of the AdS/CFT correspondence is incomplete since it requires adding to a supergravity action some a priori unknown boundary terms. We suggest a modification of the correspondence principle based on the Hamiltonian formulation of the supergravity action, which does not require any boundary terms. Then all the boundary terms of the standard formulation naturally appear by passing from the Hamiltonian version to the Lagrangian one. As examples the graviton part of the supergravity action on the product of AdS_d+1 with a compact Einstein manifold ϵ and fermions on AdS_d+1, are considered. We also discuss conformal transformations of gravity fields on the boundary of AdS and show that they are induced by the isometrics of AdS.