Small deformations of the Prasad-Sommerfield solution

Journal Article · Tue May 15 04:00:00 EDT 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.19.2997· OSTI ID:5987513

Adler, S L

I study solutions of the static Euclidean anti-self-dual SU(2) Yang-Mills equations which differ by a small perturbation from the Prasad-Sommerfield solution. I find explicit expressions for two series of perturbation mode functions of angular momentum l and even and odd parity, and classify the modes according to several criteria. There are seven nondilatational modes which have singularities removable by gauge transformation: 3 translations (l = 1), 1 gauge mode (l = 0), and a family of 3 odd-parity gauge modes (l = 1). The translations and l = 0 gauge modes have nonvanishing, and normalizable, projections into the background gauge, while the odd-parity l = 1 modes have vanishing projection into the background gauge. Among the singular modes, there are an infinite number of modes, irregular at r = 0, which nonetheless satisfy the boundary conditions for finite-energy solutions on the sphere at infinity. I show, by discussing the analogous problem of the axially symmetric solutions of the stationary Einstein equations, that non-normalizable modes are relevant in determining whether a spherically symmetric solution of a nonlinear system has axially symmetric extensions. The analysis of perturbations around the Prasad-Sommerfield solution implies that if an axially symmetric extension exists, it cannot be reached by integration out along a tangent vector defined by a nonvanishing, nonsingular small-perturbation mode of the class explicitly constructed.

• Research Organization: The Institute for Advanced Study, Princeton, New Jersey 08540
• OSTI ID: 5987513
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 19:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
BAG MODEL
BOUNDARY CONDITIONS
COMPOSITE MODELS
EUCLIDEAN SPACE
EXTENDED PARTICLE MODEL
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
PARITY
PARTICLE MODELS
PARTICLE PROPERTIES
PERTURBATION THEORY
QUARK MODEL
RIEMANN SPACE
SPACE
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
YANG-MILLS THEORY