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.     

Algebraic instantons

In previous papers we have considered an algebraic gauge theory in terms of extensions of Lie algebras. In this letter we show that algebraic instantonic solutions can be constructed in such a framework.     

Platonic instantons

The construction of Yang-Mills instantons with the symmetries of the platonic solids is described within the ADHM construction. As an example, the ADHM data is presented for an icosahedrally symmetric charge seventeen instanton with the structure of the truncated icosahedron. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

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.     

On constrained instantons

A simple method is presented for doing systematic constrained instanton calculations in models such as φ⁴ or Higgs theories where the presence of a mass term prevents the existence of a classical solution. As an application, instanton estimates of the large-order behavior of the perturbation series in massive φ₄⁴ theory are derived. (These estimates agree with those of Frishman and Yankielowicz.)     

Dual instantons

A completely positive master equation describing quantum dissipation for a Brownian particle is derived starting from microphysical collisions, exploiting a recently introduced approach to subdynamics of a macrosystem. The obtained equation can be cast into Lindblad form with a single generator for each Cartesian direction. Temperature dependent friction and diffusion coefficients for both position and momentum are expressed in terms of the collision cross section.     

Construction of instantons

A complete construction, involving only linear algebra, is given for all self-dual euclidean Yang-Mills fields.     

Supersymmetry and instantons

We show that the eigenvalue equations for the fluctuation of scalars, fermions and gluon around any classical self-dual solution of the Yang-Mills theory have the same spectrum of non-zero eigenvalues. In the case of a supersymmetric Yang- Mills theory this implies that the one loop correction around any self-dual instanton is just given by a counting of the zero modes of the gluon, fermion and ghost.     

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.     

Light quarks and instantons

Instantons and anti-instantons can profoundly influence the structure of a non-Abelian gauge theory involving N flavors of massless quarks. Interactions of the quarks with these pseudoparticles can spontaneously generate a quark mass, break the theory's SU(N) × SU(N) chiral symmetry and bind quark-antiquark pairs to form N² ? 1 Goldstone bosons. If the spontaneously generated quark mass is small, multipseudoparticle configurations can be treated in a dilute gas approximation.     

Why instantons are monopoles

It is shown that instantons are hyperbolic monopoles for the loop group with non-maximal symmetry breaking at infinity.Research supported in part by NSF grant DMS-8506130     

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.