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Finkelstein-Rubinstein constraints from ADHM data and rational maps

Josh Cork, Derek Harland

Abstract

We establish simple formulae for computing Finkelstein-Rubinstein signs for Skyrme fields generated in two ways: from instanton ADHM data, and from rational maps. This may be used to compute homotopy classes of general loops in the configuration spaces of skyrmions, and as a result provide a useful tool for a quantum treatment beyond rigid-body quantisation of skyrmions.

Finkelstein-Rubinstein constraints from ADHM data and rational maps

Abstract

We establish simple formulae for computing Finkelstein-Rubinstein signs for Skyrme fields generated in two ways: from instanton ADHM data, and from rational maps. This may be used to compute homotopy classes of general loops in the configuration spaces of skyrmions, and as a result provide a useful tool for a quantum treatment beyond rigid-body quantisation of skyrmions.
Paper Structure (5 sections, 2 theorems, 31 equations, 1 figure)

This paper contains 5 sections, 2 theorems, 31 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Instantons and ADHM data
  3. Rational maps
  4. Examples
  5. Conclusion and outlook

Key Result

Theorem 1

Let $(L^t,M^t)\in I_N$ be a loop of ADHM matrices satisfying loop-cgt as above, and let $U^t$ be the corresponding loop in the space of Skyrme fields. The Finkelstein--Rubinstein sign of this loop is given by

Figures (1)

  • Figure 1: The path in the $N=3$ configuration space generated by the data \ref{['D2d-data']}.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof