Adiabatic dynamics of instantons on $S ^4 $

Franchetti, Guido; Schroers, Bernd J.

doi:10.1007/s00220-016-2769-6

Adiabatic dynamics of instantons on $S ^4$

Guido Franchetti
(
- Heriot-Watt U. and
- Maxwell Inst. Math. Sci., Edinburgh
)
,
Bernd J. Schroers
(
- Heriot-Watt U. and
- Maxwell Inst. Math. Sci., Edinburgh
)

Aug 26, 2015

44 pages

Published in:

Commun.Math.Phys. 353 (2017) 1, 185-228

Published: Oct 15, 2016

e-Print:

1508.06566 [hep-th]

DOI:

10.1007/s00220-016-2769-6

View in:

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Abstract: (Springer)

We define and compute the L

^{2}

metric on the framed moduli space of circle invariant 1-instantons on the 4-sphere. This moduli space is four dimensional and our metric is

{SO(3) \times U(1)}

symmetric. We study the behaviour of generic geodesics and show that the metric is geodesically incomplete. Circle-invariant instantons on the 4-sphere can also be viewed as hyperbolic monopoles, and we interpret our results from this viewpoint. We relate our results to work by Habermann on unframed instantons on the 4-sphere and, in the limit where the radius of the 4-sphere tends to infinity, to results on instantons on Euclidean 4-space.

Note:

49 pages, 11 figures. Significant improvements in the discussion of framing in v2

space: Euclidean
instanton
sphere
moduli space
adiabatic
monopole
SO(3)
U(1)

References(23)

Figures(11)

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