Abstract
We study intersecting brane systems that realize a class of singular monopole configurations in four-dimensional Yang-Mills-Higgs theory. Singular monopoles are solutions to the Bogomolny equation on \( {\mathrm{\mathbb{R}}}^3 \) with a prescribed number of singularities corresponding to the insertion of ’t Hooft defects. We use the brane construction to motivate a recent conjecture on the conditions for which the moduli space of solutions is non-empty. We also show how branes provide physical intuition for various aspects of the dimension formula derived in [1], including the contribution to the dimension from the defects and its invariance under Weyl reflections of the ’t Hooft charges. Along the way we uncover and illustrate new dynamical phenomena for the brane systems, including a description of smooth monopole extraction and bubbling from ’t Hooft defects.
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G.W. Moore, A.B. Royston and D. Van den Bleeken, Parameter counting for singular monopoles on \( {\mathrm{\mathbb{R}}}^3 \), arXiv:1404.5616 [INSPIRE].
A. Giveon and D. Kutasov, Brane dynamics and gauge theory, Rev. Mod. Phys. 71 (1999) 983 [hep-th/9802067] [INSPIRE].
D.-E. Diaconescu, D-branes, monopoles and Nahm equations, Nucl. Phys. B 503 (1997) 220 [hep-th/9608163] [INSPIRE].
A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].
S.A. Cherkis and A. Kapustin, Singular monopoles and supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 525 (1998) 215 [hep-th/9711145] [INSPIRE].
S.A. Cherkis and A. Kapustin, D(k) gravitational instantons and Nahm equations, Adv. Theor. Math. Phys. 2 (1999) 1287 [hep-th/9803112] [INSPIRE].
S.A. Cherkis and A. Kapustin, Singular monopoles and gravitational instantons, Commun. Math. Phys. 203 (1999) 713 [hep-th/9803160] [INSPIRE].
S.A. Cherkis and B. Durcan, Singular monopoles via the Nahm transform, JHEP 04 (2008) 070 [arXiv:0712.0850] [INSPIRE].
G.W. Gibbons, Born-Infeld particles and Dirichlet p-branes, Nucl. Phys. B 514 (1998) 603 [hep-th/9709027] [INSPIRE].
C.G. Callan and J.M. Maldacena, Brane death and dynamics from the Born-Infeld action, Nucl. Phys. B 513 (1998) 198 [hep-th/9708147] [INSPIRE].
D. Gaiotto and E. Witten, Supersymmetric boundary conditions in \( \mathcal{N}=4 \) super Yang-Mills theory, J. Statist. Phys. 135 (2009) 789 [arXiv:0804.2902] [INSPIRE].
E.J. Weinberg, Fundamental monopoles and multi-monopole solutions for arbitrary simple gauge groups, Nucl. Phys. B 167 (1980) 500 [INSPIRE].
A. Kapustin and E. Witten, Electric-magnetic duality and the geometric Langlands program, Commun. Num. Theor. Phys. 1 (2007) 1 [hep-th/0604151] [INSPIRE].
C.H. Taubes, Monopoles and maps from S 2 to S 2 : the topology of the configuration space, Commun. Math. Phys. 95 (1984) 345 [INSPIRE].
N.S. Manton and B.J. Schroers, Bundles over moduli spaces and the quantization of BPS monopoles, Annals Phys. 225 (1993) 290 [INSPIRE].
G. ’t Hooft, On the phase transition towards permanent quark confinement, Nucl. Phys. B 138 (1978) 1 [INSPIRE].
A. Kapustin, Wilson-’t Hooft operators in four-dimensional gauge theories and S-duality, Phys. Rev. D 74 (2006) 025005 [hep-th/0501015] [INSPIRE].
E.B. Bogomolny, Stability of classical solutions, Sov. J. Nucl. Phys. 24 (1976) 449 [INSPIRE].
M.K. Prasad and C.M. Sommerfield, An exact classical solution for the ’t Hooft monopole and the Julia-Zee dyon, Phys. Rev. Lett. 35 (1975) 760 [INSPIRE].
E.J. Weinberg, Parameter counting for multi-monopole solutions, Phys. Rev. D 20 (1979) 936 [INSPIRE].
C. Callias, Index theorems on open spaces, Commun. Math. Phys. 62 (1978) 213 [INSPIRE].
S. Sethi, M. Stern and E. Zaslow, Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories, Nucl. Phys. B 457 (1995) 484 [hep-th/9508117] [INSPIRE].
M. Cederwall, G. Ferretti, B.E.W. Nilsson and P. Salomonson, Low-energy dynamics of monopoles in N = 2 SYM with matter, Mod. Phys. Lett. A 11 (1996) 367 [hep-th/9508124] [INSPIRE].
J.P. Gauntlett and J.A. Harvey, S duality and the dyon spectrum in N = 2 super Yang-Mills theory, Nucl. Phys. B 463 (1996) 287 [hep-th/9508156] [INSPIRE].
M. Henningson, Discontinuous BPS spectra in N = 2 gauge theory, Nucl. Phys. B 461 (1996) 101 [hep-th/9510138] [INSPIRE].
E.J. Weinberg and P. Yi, Magnetic monopole dynamics, supersymmetry and duality, Phys. Rept. 438 (2007) 65 [hep-th/0609055] [INSPIRE].
A. Strominger, Open p-branes, Phys. Lett. B 383 (1996) 44 [hep-th/9512059] [INSPIRE].
M.B. Green and M. Gutperle, Comments on three-branes, Phys. Lett. B 377 (1996) 28 [hep-th/9602077] [INSPIRE].
M.R. Douglas and M. Li, D-brane realization of N = 2 super Yang-Mills theory in four-dimensions, hep-th/9604041 [INSPIRE].
A. Kapustin and S. Sethi, The Higgs branch of impurity theories, Adv. Theor. Math. Phys. 2 (1998) 571 [hep-th/9804027] [INSPIRE].
D. Tsimpis, Nahm equations and boundary conditions, Phys. Lett. B 433 (1998) 287 [hep-th/9804081] [INSPIRE].
X. Chen and E.J. Weinberg, ADHMN boundary conditions from removing monopoles, Phys. Rev. D 67 (2003) 065020 [hep-th/0212328] [INSPIRE].
S. Elitzur, A. Giveon, D. Kutasov and D. Tsabar, Branes, orientifolds and chiral gauge theories, Nucl. Phys. B 524 (1998) 251 [hep-th/9801020] [INSPIRE].
C.-h. Ahn and B.-H. Lee, SO/Sp monopoles and branes with orientifold three plane, Phys. Rev. D 59 (1999) 026001 [hep-th/9803069] [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Framed BPS states, Adv. Theor. Math. Phys. 17 (2013) 241 [arXiv:1006.0146] [INSPIRE].
O. Aharony, N. Seiberg and Y. Tachikawa, Reading between the lines of four-dimensional gauge theories, JHEP 08 (2013) 115 [arXiv:1305.0318] [INSPIRE].
K.-M. Lee, E.J. Weinberg and P. Yi, The moduli space of many BPS monopoles for arbitrary gauge groups, Phys. Rev. D 54 (1996) 1633 [hep-th/9602167] [INSPIRE].
R.S. Ward, Deformations of the imbedding of the SU(2) monopole solution in SU(3), Commun. Math. Phys. 86 (1982) 437 [INSPIRE].
C. Athorne, Cylindrically and spherically symmetric monopoles in SU(3) gauge theory, Commun. Math. Phys. 88 (1983) 43 [INSPIRE].
E.J. Weinberg and P. Yi, Explicit multimonopole solutions in SU(N) gauge theory, Phys. Rev. D 58 (1998) 046001 [hep-th/9803164] [INSPIRE].
S.A. Cherkis and B. Durcan, The ’t Hooft-Polyakov monopole in the presence of an ’t Hooft operator, Phys. Lett. B 671 (2009) 123 [arXiv:0711.2318] [INSPIRE].
N.R. Constable, R.C. Myers and O. Tafjord, The noncommutative bion core, Phys. Rev. D 61 (2000) 106009 [hep-th/9911136] [INSPIRE].
D. Gang, E. Koh and K. Lee, Line operator index on S 1 × S 3, JHEP 05 (2012) 007 [arXiv:1201.5539] [INSPIRE].
E. Poppitz and M. Ünsal, Index theorem for topological excitations on R 3 × S 1 and Chern-Simons theory, JHEP 03 (2009) 027 [arXiv:0812.2085] [INSPIRE].
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [INSPIRE].
R. Jackiw and C. Rebbi, Solitons with fermion number 1/2, Phys. Rev. D 13 (1976) 3398 [INSPIRE].
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Moore, G.W., Royston, A.B. & Van den Bleeken, D. Brane bending and monopole moduli. J. High Energ. Phys. 2014, 157 (2014). https://doi.org/10.1007/JHEP10(2014)157
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DOI: https://doi.org/10.1007/JHEP10(2014)157