TY - JOUR

T1 - Non-Abelian monopoles in the Higgs phase

AU - Nitta, Muneto

AU - Vinci, Walter

N1 - Funding Information:
W.V. would like to thank M. Shifman and Kenichi Konishi for their valuable comments on the preliminary version of the paper. The work of M.N. is partially supported by a Grant-in-Aid for Scientific Research No. 20740141 from the Ministry of Education, Culture, Sports, Science and Technology , Japan. The work of W.V. is supported by the DOE grant DE-FG02-94ER40823 .

PY - 2011/7/1

Y1 - 2011/7/1

N2 - We use the moduli matrix approach to study the moduli space of 1/4 BPS kinks supported by vortices in the Higgs phase of N=2 supersymmetric U(N) gauge theories when non-zero masses for the matter hypermultiplets are introduced. We focus on the case of degenerate masses. In these special cases vortices acquire new orientational degrees of freedom, and become "non-Abelian". Kinks acquire new degrees of freedom too, and we will refer to them as "non-Abelian". As already noticed for the Abelian case, non-Abelian kinks must correspond to non-Abelian monopoles of the unbroken phase of SU(N) Yang-Mills.We show, in some special cases, that the moduli spaces of the two objects are in one-to-one correspondence. We argue that the correspondence holds in the most general case.The consequence of our result is two-fold. First, it gives an alternative way to construct non-Abelian monopoles, in addition to other well-known techniques (Nahm transform, spectral curves, rational maps). Second, it opens the way to the study of the quantum physics of non-Abelian monopoles, by considering the simpler non-Abelian kinks.

AB - We use the moduli matrix approach to study the moduli space of 1/4 BPS kinks supported by vortices in the Higgs phase of N=2 supersymmetric U(N) gauge theories when non-zero masses for the matter hypermultiplets are introduced. We focus on the case of degenerate masses. In these special cases vortices acquire new orientational degrees of freedom, and become "non-Abelian". Kinks acquire new degrees of freedom too, and we will refer to them as "non-Abelian". As already noticed for the Abelian case, non-Abelian kinks must correspond to non-Abelian monopoles of the unbroken phase of SU(N) Yang-Mills.We show, in some special cases, that the moduli spaces of the two objects are in one-to-one correspondence. We argue that the correspondence holds in the most general case.The consequence of our result is two-fold. First, it gives an alternative way to construct non-Abelian monopoles, in addition to other well-known techniques (Nahm transform, spectral curves, rational maps). Second, it opens the way to the study of the quantum physics of non-Abelian monopoles, by considering the simpler non-Abelian kinks.

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U2 - 10.1016/j.nuclphysb.2011.02.014

DO - 10.1016/j.nuclphysb.2011.02.014

M3 - Article

AN - SCOPUS:79953065386

VL - 848

SP - 121

EP - 154

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1

ER -