SU(2) calorons and magnetic monopoles

Kimyeong Lee; Changhai Lu

doi:10.1103/PhysRevD.58.025011

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SU(2) calorons and magnetic monopoles

Kimyeong Lee^* and Changhai Lu^†

Physics Department, Columbia University, New York, New York 10027

^*Electronic address: klee@phya.snu.ac.kr
^†Electronic address: chlu@cuphy3.phys.columbia.edu

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Phys. Rev. D 58, 025011 – Published 22 June, 1998

DOI: https://doi.org/10.1103/PhysRevD.58.025011

Abstract

We investigate the self-dual Yang-Mills gauge configurations on $R^{3} \times S^{1}$ when the gauge symmetry SU(2) is broken to U(1) by the Wilson loop. We construct the explicit field configuration for a single instanton by the Nahm method and show that an instanton is composed of two self-dual monopoles of opposite magnetic charge. We normalize the moduli space metric of an instanton and study various limits of the field configuration and its moduli space metric.

References (17)

K. Lee and P. Yi, Phys. Rev. D 56, 3711 (1997).
K. Lee, Phys. Lett. B 426, 323 (1998).
W. Nahm, in Group Theoretical Methods in Physics, Proceedings of the International Colloquium, Trieste, Italy, 1983, edited by D. Denardo (Springer, Berlin, 1984); H. Garland and M. Murray, Commun. Math. Phys. 120, 335 (1988).
E.J. Weinberg, Nucl. Phys. B167, 500 (1980).
B.J. Harrington and H.K. Shepard, Phys. Rev. D 17, 2122 (1978).
P. Rossi, Nucl. Phys. B149, 170 (1979).
D. Gross, R. Pisarski, and L.G. Yaffe, Rev. Mod. Phys. 53, 43 (1981).
K. Lee, E.J. Weinberg, and P. Yi, Phys. Rev. D 54, 1633 (1996).
K. Lee, E.J. Weinberg, and P. Yi, Phys. Lett. B 376, 97 (1996); J.P. Gauntlett and D.A. Lowe, Nucl. Phys. B472, 194 (1996); S.A. Connell (unpublished).
W. Nahm, Phys. Lett. 90B, 413 (1980); N.J. Hitchin, Commun. Math. Phys. 89, 145 (1983); E. Corrigan and P. Goddard, Ann. Phys. (N.Y.) 154, 253 (1984); H. Nakajima, in Einstein Metrics and Yang-Mills Connections, edited by T. Mabuch (Marcel Dekker, New York, 1993).
M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld, and Tu.I. Mannin, Phys. Lett. 65A, 185 (1978).
K. Lee, E.J. Weinberg, and P. Yi, Phys. Rev. D 54, 6351 (1996).
A.A. Belavin, A.M. Polyakov, A.S. Shvarts, and Yu.S. Tyupkin, Phys. Lett. 59B, 85 (1975).
J.P. Gauntlett, Nucl. Phys. B411, 433 (1994).
R. Jackiw, C. Nohl, and C. Rebbi, Phys. Rev. D 15, 1642 (1977); ibid.N.H. Christ, E.J. Weinberg, and N.K. Stanton, 18, 2013 (1978).
G. ’t Hooft, Nucl. Phys. B190, 455 (1981).
T.C. Kraan and P. van Baal, Phys. Lett. B 428, 268 (1998).

[c1] K. Lee and P. Yi, Phys. Rev. D 56, 3711 (1997).

[c2] K. Lee, Phys. Lett. B 426, 323 (1998).

[c3] W. Nahm, in Group Theoretical Methods in Physics, Proceedings of the International Colloquium, Trieste, Italy, 1983, edited by D. Denardo (Springer, Berlin, 1984); H. Garland and M. Murray, Commun. Math. Phys. 120, 335 (1988).

[c4] E.J. Weinberg, Nucl. Phys. B167, 500 (1980).

[c5] B.J. Harrington and H.K. Shepard, Phys. Rev. D 17, 2122 (1978).

[c6] P. Rossi, Nucl. Phys. B149, 170 (1979).

[c7] D. Gross, R. Pisarski, and L.G. Yaffe, Rev. Mod. Phys. 53, 43 (1981).

[c8] K. Lee, E.J. Weinberg, and P. Yi, Phys. Rev. D 54, 1633 (1996).

[c9] K. Lee, E.J. Weinberg, and P. Yi, Phys. Lett. B 376, 97 (1996); J.P. Gauntlett and D.A. Lowe, Nucl. Phys. B472, 194 (1996); S.A. Connell (unpublished).

[c10] W. Nahm, Phys. Lett. 90B, 413 (1980); N.J. Hitchin, Commun. Math. Phys. 89, 145 (1983); E. Corrigan and P. Goddard, Ann. Phys. (N.Y.) 154, 253 (1984); H. Nakajima, in Einstein Metrics and Yang-Mills Connections, edited by T. Mabuch (Marcel Dekker, New York, 1993).

[c11] M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld, and Tu.I. Mannin, Phys. Lett. 65A, 185 (1978).

[c12] K. Lee, E.J. Weinberg, and P. Yi, Phys. Rev. D 54, 6351 (1996).

[c13] A.A. Belavin, A.M. Polyakov, A.S. Shvarts, and Yu.S. Tyupkin, Phys. Lett. 59B, 85 (1975).

[c14] J.P. Gauntlett, Nucl. Phys. B411, 433 (1994).

[c15] R. Jackiw, C. Nohl, and C. Rebbi, Phys. Rev. D 15, 1642 (1977); ibid.N.H. Christ, E.J. Weinberg, and N.K. Stanton, 18, 2013 (1978).

[c16] G. ’t Hooft, Nucl. Phys. B190, 455 (1981).

[c17] T.C. Kraan and P. van Baal, Phys. Lett. B 428, 268 (1998).

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SU(2) calorons and magnetic monopoles

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