Extended supersymmetry and gravitational instantons

Methods of extended supersymmetry are used to construct explicitly an instanton solution of the Euclidian Einstein equations in empty space.Translated fromIzvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 18–21, June, 1989.     

Spontaneous supersymmetry breaking induced by vacuum condensates

We propose a novel mechanism of spontaneous supersymmetry breaking which relies upon a ubiquitous feature of Quantum Field Theory, vacuum condensates. Such condensates play a crucial role in many phenomena. Examples include Unruh effect, superconductors, particle mixing, and quantum dissipative systems. We argue that in all these phenomena supersymmetry, when present, is spontaneously broken. Evidence for our conjecture is given for the Wess–Zumino model, that can be considered as an approximation to the supersymmetric extensions of the above mentioned systems. The magnitude of the effect is estimated for a recently proposed experimental setup based on an optical lattice.     

Spontaneous breaking of anti-de sitter supersymmetry

We compute the one-loop effective potential of the Wess-Zumino model in Anti-de Sitter space. The effect of the background geometry is determined exactly. After the renormalization of the kinetic action and the insertion of a linear counterterm in the superpotential, we solve the quantum-corrected equations of motion, obtaining the vacuum solutions in the semiclassical approximation. The vacuum expectation values of theA andB fields are shifted by finite terms which depend upon the boundary conditions for the field propagators. Despite this result, we show with complete generality that supersymmetry is preserved to the one-loop order at each classically supersymmetric extremum of the effective potential.     

Spontaneous supersymmetry breaking by large-N matrices

Motivated by supersymmetry breaking in matrix model formulations of superstrings, we present some concrete models, in which the supersymmetry is preserved for any finite N, but gets broken at infinite N, where N is the rank of matrix variables. The models are defined as supersymmetric field theories coupled to some matrix models, and in the induced action obtained after integrating out the matrices, supersymmetry is spontaneously broken only when N is infinity. In our models, the large value of N gives a natural explanation for the origin of small parameters appearing in the field theories which trigger the supersymmetry breaking.     

Spontaneous supersymmetry breaking in string theory

We present a construction of string theories, with spontaneously broken supersymmetry and chiral fermion families, obtained by a suitable choice of boundary conditions in toroidal compactifications of ten-dimensional (1,1) or heterotic models. The crystallographic groups in four-dimensions determine the possible values of the supersymmetry-breaking parameters, which therefore are discrete.     

Spontaneous breaking of supersymmetry through dimensional reduction

A general technique for deriving consistent theories with spontaneously broken supersymmetry and massive gravitinos is illustrated by exploiting the chiral invariance of N = 1 supergravity in four dimensions to construct a theory with broken N = 2 supersymmetry in three dimensions.     

Spontaneous supersymmetry breaking in supersymmetric string theories

A generalization of the dimensional reduction of supersymmetric string theories is introduced which leads to spontaneous breaking of supersymmetry. This supersymmetry breaking has non-trivial consequences for the quantization and dynamics of the theory. The lowest quantum correction to the cosmological constant is calculated and found to be unacceptably large.     

Quantizing gravitational instantons

Gravitational instantons are complete non-singular positive definite metrics satisfying the Einstein equations with or without cosmological constant. We treat quantum fluctuations about such solutions and introduce a useful decomposition of the space of gravitational degrees of freedom in terms of which the one-loop corrections take an especially simple form. We treat in detail the question of zero modes, and the fluctuations about de Sitter space.     

Spontaneous breaking of supersymmetry and gauge invariance in supergravity

Using the new minimal auxiliary fields of N = 1 supergravity it is found possible to construct a model of local supersymmetry which spontaneously breaks both supersymmetry and gauge invariance. The status of the cosmological constant resulting from this breaking is discussed.     

Gravitational instantons and Euclidean supersymmetry

Supersymmetric instanton solutions in four-dimensional Euclidean ungauged Einstein–Maxwell theory are analysed and classified according to the fraction of supersymmetry they preserve, using spinorial geometry techniques.     

Spontaneous supersymmetry breaking and superconductivity in a non-relativistic model

The conjecture that supersymmetry breaking implies superconductivity is supported by the analysis of a class of supersymmetric non-relativistic models involving only fermions. Here the investigation is extened to a non-relativistic model involving both fermions and bosons, which in a sense is the non-relativistic version of the Wess-Zumino model. A sufficient condition is established for the validity of the conjecture. This condition can be possibly violated at most in a two-dimensional subspace of the three-dimensional space of the coupling constants.     

Symmetry breaking by instantons in supergravity

The non-zero modes of different spin operators on the background of a self-dual gravitational instanton are all related by global supersymmetry transformations and completely cancel in the one-loop term, which is determined entirely by the zero modes. We derive the number of zero modes of each spin. In an asymptotically locally Euclidean self-dual instanton there are 2τ $\text{spin}\text{-}\text{3}\text{2}$ zero modes and 3τ spin-2 zero modes, where τ is the Hirzebruch signature. Up to 3 of the spin-2 zero modes (depending on boundary conditions) may correspond to global rotations. The $\text{spin}\text{-}\text{3}\text{2}$ zero modes break the U(1) chiral symmetry and give rise to helicity-changing amplitudes. Together with the spin-2 zero modes they determine the trace anomaly or scaling behaviour. We can compare our results with the perturbation theory predictions for the axial vector current and trace anomalies in K3, the unique compact self-dual gravitational instanton, because in this case there are no boundary terms. We obtain agreement.     

One-sided type-D gravitational instantons

It is shown that for every one-sided type-D gravitational instanton, Einstein's vacuum equations can be reduced locally to a single second-order, nonlinear differential equation of second degree of one real function.     

Electroweak breaking and supersymmetry breaking

We discuss the clash between the absence of fine tuning in the Higgs potential and a sufficient suppression of flavour changing neutral current transitions in supersymmetric extensions of the standard model. It is pointed out that horizontalU(1) symmetry combined with theD-term supersymmetry breaking provides a realistic framework for solving both problems.     

Twistor spinors and gravitational instantons

We construct a complete Riemannian metric on the four-dimensional vector space ⁴ which carries a two-dimensional space of twistor spinor with common zero point. This metric is half-conformally flat but not conformally flat. The construction uses a conformal completion at infinity of theEguchi-Hanson metric on the exterior of a closed ball in ⁴.     

Black holes on gravitational instantons

In this paper, we classify and construct five-dimensional black holes on gravitational instantons in vacuum Einstein gravity, with R×U(1)×U(1)$\mathbb{R}\times U(1)\times U(1)$ isometry. These black holes have spatial backgrounds which are Ricci-flat gravitational instantons with U(1)×U(1)$U(1)\times U(1)$ isometry, and are completely regular space–times outside the event horizon. Most of the known exact five-dimensional vacuum black-hole solutions can be classified within this scheme. Amongst the new space–times presented are static black holes on the Euclidean Kerr and Taub-bolt instantons. We also present a rotating black hole on the Eguchi–Hanson instanton.