D = 5, N = 2 Geometric Higher Curvature Supergravity in the Second-Order Canonical Theory

The supersymmetric extension of the five-dimensional Chern–Simons gravity is studied from the Hamiltonian point of view. This model containing the Gauss–Bonnet term quadratic in the Riemann curvature is the gauge theory of the supergroup SU(2,2/1). In the first order, the theory has a polynomial structure, but the second-order leads to a nonpolynomial structure for both the Hamiltonian and the supersymmetry transformation rules of the fields. The second-order theory has the advantage that the apparent gauge degrees of freedom are unambiguously removed leaving only the physical ones. This important feature is analyzed by constructing the second-order Hamiltonian theory. The gauge invariances of the model and the generator of time evolution are found.     

The imaginary Starobinsky model and higher curvature corrections

We elaborate on the predictions of the imaginary Starobinsky model of inflation coupled to matter, where the inflaton is identified with the imaginary part of the inflaton multiplet suggested by the Supergravity embedding of a pure gravity. In particular, we study the impact of higher‐order curvature terms and show that, depending on the parameter range, one may find either a quadratic model of chaotic inflation or monomial models of chaotic inflation with fractional powers between 1 and 2.     

FRW minisuperspace with local N=4 supersymmetry and self‐interacting scalar field

A supersymmetric FRW model with a scalar supermultiplet and generic superpotential is analysed from a quantum cosmological perspective. The corresponding Lorentz and supersymmetry constraints allow to establish a system of first order partial differential equations from which solutions can be obtained. We show that this is possible when the superpotential is expanded in powers of a parameter λ?1. At order λ⁰ we find the general class of solutions, which include in particular quantum states reported in the current literature. New solutions are partially obtained at order λ¹, where the dependence on the superpotential is manifest. These classes of solutions can be employed to find states for higher orders in λ. Our analysis further points to the following: (i) supersymmetric wave functions can only be found when the superpotential has either an exponential behaviour, an effective cosmological constant form or is zero; (ii) If the superpotential behaves differently during other periods, the wave function is trivial ( = 0, i.e., no supersymmetric states). We conclude this paper discussing how our FRW minisuperspace (with N = 4 supersymmetry and invariance under time‐reparametrization) can be relevant concerning the issue of supersymmetry breaking.     

Universal Bose-Fermi mass-relations in Kaluza-Klein supergravity and harmonic analysis on coset manifolds with Killing spinors

Universal mass-relations between Bose and Fermi modes are obtained via general relations existing among the spectra of invariant operators on coset manifolds with Killing spinors. In particular zero-modes for pseudoscalars, spinors, and Lichnerowitz scalars are always related to the isometry and cohomology properties of the manifold. The structure of the four-dimensional supersymmetry rules on physical modes is given. Furthermore, the harmonies of the possible massless multiplets, namely, the gravitational multiplet, the Killing gauge multiplet, and the Betti gauge multiplet, are exhibited for general manifolds. Comments on matter and quasi-massless multiplets conclude the paper.     

The effective action of D‐branes in Calabi‐Yau orientifold compactifications

In this review article we study type IIB superstring compactifications in the presence of space‐time filling D‐branes while preserving 𝒩=1 supersymmetry in the effective four‐dimensional theory. This amount of unbroken supersymmetry and the requirement to fulfill the consistency conditions imposed by the space‐time filling D‐branes lead to Calabi‐Yau orientifold compactifications. For a generic Calabi‐Yau orientifold theory with space‐time filling D3‐ or D7‐branes we derive the low‐energy spectrum. In a second step we compute the effective 𝒩=1 supergravity action which describes in the low‐energy regime the massless open and closed string modes of the underlying type IIB Calabi‐Yau orientifold string theory. These 𝒩=1 supergravity theories are analyzed and in particular spontaneous supersymmetry breaking induced by non‐trivial background fluxes is studied. For D3‐brane scenarios we compute soft‐supersymmetry breaking terms resulting from bulk background fluxes whereas for D7‐brane systems we investigate the structure of D‐ and F‐terms originating from worldvolume D7‐brane background fluxes. Finally we relate the geometric structure of D7‐brane Calabi‐Yau orientifold compactifications to 𝒩=1 special geometry.     

On renormalizability of non-anticommutativeN=(1, 0) theories with singlet deformation

We study the quantum properties of two theories with a non-anticommutative chiral singlet deformation ofN=(1, 1) supersymmetry: the Abelian model of a vector gauge multiplet and the model of a gauge multiplet interacting with a neutral hypermultiplet. Both these models are proved to be not only renormalizable but also finite.     

New nonlinear σ-model with N=4 extended supersymmetry

A new nonlinear -model with N=4 supersymmetry in d=2 is constructed in terms of a N=2 tensor multiplet in d=4. Four equivalent formulations of the theory in superspace are obtained. The component structure of the model is considered by means of the Legendre transformation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 70–74, September, 1987.     

Algebraic properties of extended supergravity theories

Chirality transformations and generalized duality transformations are used to show that the extended O(2) and O(3) supergravity theories in fact have a U(2) and a U(3) invariance respectively. The coupling of these supergravity theories to matter multiplets having global extended supersymmetry is considered. In one case where the matter multiplet has a non-vanishing central charge, one finds a minimal coupling of the vector field of the supergravity multiplet.     

Some invariant Lagrangians for local supersymmetry

The recently analyzed commutator algebra of local supersymmetry is supplemented by the transformation laws for a chiral multiplet. Several separately invariant (up to a divergence) Lagrangians are constructed and their relation to previously found models is investigated.     

Gauged supergravities in various spacetime dimensions

In this review article we study the gaugings of extended supergravity theories in various space‐time dimensions. These theories describe the low‐energy limit of non‐trivial string compactifications. For each theory under consideration we review all possible gaugings that are compatible with supersymmetry. They are parameterized by the so‐called embedding tensor which is a group theoretical object that has to satisfy certain representation constraints. This embedding tensor determines all couplings in the gauged theory that are necessary to preserve gauge invariance and supersymmetry. The concept of the embedding tensor and the general structure of the gauged supergravities are explained in detail. The methods are then applied to the half‐maximal (N = 4) supergravities in d = 4 and d = 5 and to the maximal supergravities in d = 2 and d = 7. Examples of particular gaugings are given. Whenever possible, the higher‐dimensional origin of these theories is identified and it is shown how the compactification parameters like fluxes and torsion are contained in the embedding tensor.     

A heterotic N=2 string with space–time supersymmetry

We reconsider the issue of embedding space–time fermions into the four-dimensional N=2 worldsheet supersymmetric string. A new heterotic theory is constructed, taking the right-movers from the N=4 topological extension of the conventional N=2 string but a c=0 conformal field theory supporting target-space supersymmetry for the left-moving sector. The global bosonic symmetry of the full formalism proves to be U(1,1), just as in the usual N=2 string. Quantization reveals a spectrum of only two physical states, one boson and one fermion, which fall in a multiplet of (1,0) supersymmetry.     

The supersymmetric Higgs mechanism—Quartet decoupling and nondoubled Goldstone bosons

A complete quantum field theoretic analysis of the supersymmetric Higgs mechanism is presented, in the general case where the Goldstone bosons may be either doubled or nondoubled. If gauge fields are coupled to nondoubled Goldstone bosons, it is found that supersymmetry is spontaneously broken not just by the masses but also by the spins of the physical particles. The spectrum reveals no supersymmetry multiplet structure. The decoupling of unphysical degrees of freedom is carefully discussed, and the quartet decoupling mechanism for gauged Goldstone bosons is extended to supersymmetry theories. The results are illustrated with an SU(2) × U(1) model.     

Massless spectrum and critical dimension of the supermembrane

We show the existence of massless particles in the supermembrane. These occur in the sector of a completely collapsed membrane and receive zero vacuum energy thanks to supersymmetry. Only in the 11-dimensional supermembrane the massless states include a graviton. Thus, in the critical dimension d = 11 the massless particles correspond to the supergravity multiplet. We also find that higher extended objects beyond the supermembrane have no critical dimension in which the supergravity multiplet emerges.     

Super-higgs effect in supergravity with general scalar interactions

Using the recently established tensor calculus for supergravity, we construct the most general action for the scalar multiplet coupling. We discuss under which conditions supersymmetry is broken spontaneously and show explicitly that the gravitino acquires a mass by absorbing the Goldstone fermion. Parity violation as well as a cosmological constant can be avoided.     

SUPERSYMMETRIC

In this paper we investigate some properties of the "linear" superfields, and givethe variation of this "linear" multiplet under an infinitesimal supersymmetry trans-formation.     

Gauge Fields and Singletons of AdS2p+1

We show that p-forms on AdS2p+1 describe both singletons and massless particles. On the 2p-dimensional boundary the singleton p-form Lagrangian reduces to the conformally invariant functional F2. All the representations, singletons as well as massless, are zero center modules and involve a vacuum mode. Two- and three-form singleton fields are required by supersymmetry in AdS5 and AdS7 supergravity, respectively.     

Supersymmetry among free fermions and superstrings

A complete classification is given of all supersymmetric theories of free massless two-dimensional fermions. This, in particular, implies a classification of all free-fermion representations of super Kac-Moody algebras. It is shown that these cannot be used to construct new string theories with unbroken supersymmetry in Minkowski space-time, other than the torus-compactifications of the known ten-dimensional superstrings. Assuming anti-de-Sitter space-time could restore conformal invariance, it is shown how one could construct a string theory whose low-lying excitations form a multiplet of gauged N = 8 supergravity.     

New model of the higher spin particle

We elaborate on a new model of the higher spin (HS) particle which makes manifest the classical equivalence of the HS particle of the unfolded formulation and the HS particle model with a bosonic counterpart of supersymmetry. Both these models emerge as two different gauges of the new master system. Physical states of the master model are massless HS multiplets described by complex HS fields which carry an extra U(1) charge q. The latter fully characterizes the given multiplet by fixing the minimal helicity at q/2. We construct the twistorial formulation of the master model and discuss symmetries of the new HS multiplets within its framework. The text was submitted by the authors in English.     

Symmetry structures of superstring field theories

A new extended formulation of free supersymmetric string field theories is presented. The hidden symmetries are exhibited and their quantization is given. The rigid space-time supersymmetry of the free theory is discussed.