We show here that from the metric of the manifold M20, i.e., the reduced moduli of SU(2) 2-monopoles in Yang-Mills-Higgs theory, one can recover the respective moduli of spectral curves using the method Gauss-Manin connection in disguise. This work is a step toward creating an inverse process of finding the metric of any Mk0, from spectral curves. This is a thirty year old problem that we hope to shed some light on.

1.
N. J.
Hitchin
,
Commun. Math. Phys.
83
,
579
(
1982
).
2.
J. A. C.
Morales
,
H.
Movasati
,
Y.
Nikdelan
,
R.
Roychowdhury
, and
M. A. C.
Torres
,
SIGMA
14
,
003
(
2018
); e-print arXiv:1709.09682 [math.DG].
3.
J.
Hurtubise
,
Commun. Math. Phys.
92
,
195
(
1983
).
4.
M.
Alim
,
H.
Movasati
,
E.
Scheidegger
, and
S.-T.
Yau
,
Commun. Math. Phys.
344
,
889
(
2016
).
5.
H.
Movasati
,
Multiple Integrals and Modular Differential Equations
, Volume 28 of Brazilian Mathematics Colloquium (
Instituto de Matemática Pura e Aplicada, IMPA
,
2011
).
6.
H.
Movasati
,
Ann. Math. Blaise Pascal
19
,
307
(
2012
).
7.
M. F.
Atiyah
and
R. S.
Ward
,
Commun. Math. Phys.
55
,
117
(
1977
).
8.
M. F.
Atiyah
and
N.
Hitchin
,
The Geometry and Dynamics of Magnetic Monopoles
(
Princeton University Press
,
2014
).
9.
R. S.
Ward
and
R. O.
Wells
,
Twistor Geometry and Field Theory
(
Cambridge University Press
,
Cambridge
,
1990
), Vol. 4.
10.
E.
Bogomol’nyi
,
Sov. J. Nucl. Phys.
24
,
4
(
1976
) (in English).
11.
N. J.
Hitchin
,
Commun. Math. Phys.
89
,
145
(
1983
).
12.
N.
Ercolani
and
A.
Sinha
,
Commun. Math. Phys.
125
,
385
(
1989
).
13.
R. S.
Ward
,
Commun. Math. Phys.
79
,
317
(
1981
).
14.
P. M.
Sutcliffe
,
Int. J. Mod. Phys.
A12
,
4663
(
1997
); e-print arXiv:hep-th/9707009 [hep-th].
15.
16.
H.
Movasati
,
Manuscripta Math.
139
,
495
(
2012
).
17.
P. A.
Griffiths
,
Am. J. Math.
90
,
568
(
1968
).
18.
P. A.
Griffiths
,
Am. J. Math.
90
,
805
(
1968
).
19.
H.
Movasati
,
Asian J. Math.
21
,
463
482
(
2017
).
20.
H.
Movasati
,
Surveys of Modern Mathematics
(
IP
,
Boston
,
2015
), Vol. 170. Available online at http://w3.impa.br/hossein/myarticles/GMCD-MQCY3.pdf.
21.
H.
Movasati
and
Y.
Nikdelan
, preprint arXiv:1603.09411 (
2016
).
22.
S.
Ramanujan
,
Trans. Cambridge Philos. Soc.
22
,
159
(
1916
).
23.
L.
Bianchi
,
Gen. Relativ. Gravitation
33
,
2171
(
2001
).
24.
Y.
Manin
and
M.
Marcolli
, preprint arXiv:1504.04005 (
2015
).
25.
G. W.
Gibbons
and
C. N.
Pope
,
Commun. Math. Phys.
66
,
267
(
1979
).
26.
M.
Prasad
and
C. M.
Sommerfield
,
Phys. Rev. Lett.
35
,
760
(
1975
).
You do not currently have access to this content.