Self-duality Constraint Research Articles

Hamiltonian quantization of self-dual tensor fields and a bosonic Nielsen-Ninomiya theorem

The quantization of self-dual tensor fields is carried out following the procedure of Batalin and Fradkin. The (anti) self-duality constraints (either fermionic or bosonic) in the action leads to the gravitational anomaly. In the process of gauge fixing, the impossibility of the co-existence of a positive hamiltonian and covariant action is shown. A version of the Nielsen-Ninomiya theorem applies to self-dual tensor fields viz. the lattice version of the theory shows species doubling with zero net chirality.

Superspace versions of topological theories

The topological Yang-Mills theory and the topological sigma model are presented in a superspace formulation. This greatly simplifies the field content of the theories, and makes the Q-invariance more obvious. The Feynman rules for the topological Yang-Mills theory are derived. We calculate the one-loop β-functions of the topological sigma model in superspace. The lattice version of these theories is presented. Unfortunately, the self-duality constraints of both models lead to spectrum doubling.

Linear system and conservation laws for d = 10 super-yang-mills

Abstract A new twistor-like parametrization of the linear system for d = 10 super-Yang-Mills is proposed. It is more suitable for power series expansion of conservation laws. We also perform dimensional reduction to obtain a much stronger four-dimensional linear system which includes SU(4) self-duality constraint.

Conditions of existence for a class of self-dual solutions of the Einstein equations

We study the integrability of the Einstein equations for a class of empty homogeneous space-times (Bianchi class A), once the self-duality constraints are imposed on the space-time itself. This system is integrable in the case of Bianchi type I and is a subset of Bianchi types VI0 and VII0. Bianchi type II space-times do not admit self-dual solutions and for the case of Bianchi VIII and IX we were unable to find a general integrability condition.

The general Taub-NUT-De Sitter metric as a self-dual Yang-Mills solution of gravity

We show in a simple and systematical way the self-duality constraints of certain SU(2) gauge fields can be used to rediscover the Einstein metrics. Starting with a metric tensor with two unknown functions, the self-duality constraints of the SU(2) gauge field obtained from the spin connections are studied. The general Taub-NUT-De Sitter metric is found to emerge quite simply as a solution, though the riemannian tensor of the metric itself is not self-dual in the general case. Different interesting limiting cases, such as the Eguchi-Hanson metric, are also obtained directly from the constraint equations.

Renormalization group calculation for Z(2) gauge theory

A renormalization group block-spin scheme for Z(2) gauge theory is constructed using a hamiltonian formulation. The renormalization group equations enable us to calculate the critical coupling and critical exponents both in 2 + 1 and 3 + 1 dimensions. The results compare favorably with those of the Ising model in a transverse field in the 2 + 1 case. In 3 + 1 dimensions the results turn out to satisfy the self-duality constraint. The critical exponents obtained are in agreement with the Migdal conjecture.

Gauge field configurations in curved spacetimes. I

We study classical solutions of SU(2) Yang-Mills field equations, with or without coupled scalar fields, in curved spacetimes. We consider, essentially, only static, spherically symmetric background metrics, for both Lorentz and Euclidean signatures. Section I presents the motivation for searching such solutions. In Sec. II, the equations of motion for a class of Ansatze and several static solutions are given, namely a class of scalar fields compatible with a point monopole and particular solutions, for gauge fields alone, in background Schwarzschild and de Sitter metrics, respectively. Some interesting properties are discussed. In Sec. III a finite-action, Prasad-Sommerfield-type solution is constructed for the O(4,1) de Sitter metric. In Sec. IV it is shown how one single, simple de Sitter solution can lead to various well-known flat-space solutions, and to new ones, through a systematic exploitation of conformal equivalence. Self-duality constraints are formulated explicitly in Sec. V for a static spherically symmetric metric. Certain results for the Robinson-Bertotti metric are given in Sec. VI.