Abstract
We discuss 1/2 BPS domain walls in the 3d \( \mathcal{N}=4 \) supersymmetric gauge theory which is self-dual under the 3d mirror symmetry. We find that if a BF-type coupling is introduced, invariance of the BPS domain wall under the duality transformation can be explicitly seen from the classical BPS equations. It has been known that particles and vortices are swapped under the 3d duality transformations. We show that Noether charges and vortex topological charges localized on the domain walls are correctly exchanged under the 3d mirror symmetry.
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References
M.E. Peskin, Mandelstam ’t Hooft duality in abelian lattice models, Annals Phys. 113 (1978) 122 [INSPIRE].
C. Dasgupta and B.I. Halperin, Phase transition in a lattice model of superconductivity, Phys. Rev. Lett. 47 (1981) 1556 [INSPIRE].
D.T. Son, Is the composite fermion a Dirac particle?, Phys. Rev. X 5 (2015) 031027 [arXiv:1502.03446] [INSPIRE].
A. Karch and D. Tong, Particle-vortex duality from 3D bosonization, Phys. Rev. X 6 (2016) 031043 [arXiv:1606.01893] [INSPIRE].
J. Murugan and H. Nastase, Particle-vortex duality in topological insulators and superconductors, JHEP 05 (2017) 159 [arXiv:1606.01912] [INSPIRE].
N. Seiberg, T. Senthil, C. Wang and E. Witten, A duality web in 2+1 dimensions and condensed matter physics, Annals Phys. 374 (2016) 395 [arXiv:1606.01989] [INSPIRE].
F. Benini, Three-dimensional dualities with bosons and fermions, JHEP 02 (2018) 068 [arXiv:1712.00020] [INSPIRE].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
E.R.C. Abraham and P.K. Townsend, Q kinks, Phys. Lett. B 291 (1992) 85 [INSPIRE].
E.R.C. Abraham and P.K. Townsend, More on Q kinks: a (1 + 1)-dimensional analog of dyons, Phys. Lett. B 295 (1992) 225 [INSPIRE].
J.P. Gauntlett, D. Tong and P.K. Townsend, Multidomain walls in massive supersymmetric σ-models, Phys. Rev. D 64 (2001) 025010 [hep-th/0012178] [INSPIRE].
D. Tong, The moduli space of BPS domain walls, Phys. Rev. D 66 (2002) 025013 [hep-th/0202012] [INSPIRE].
M. Shifman and A. Yung, Domain walls and flux tubes in N = 2 SQCD: D-brane prototypes, Phys. Rev. D 67 (2003) 125007 [hep-th/0212293] [INSPIRE].
D. Tong, Mirror mirror on the wall: on 2D black holes and Liouville theory, JHEP 04 (2003) 031 [hep-th/0303151] [INSPIRE].
Y. Isozumi, K. Ohashi and N. Sakai, Exact wall solutions in five-dimensional SUSY QED at finite coupling, JHEP 11 (2003) 060 [hep-th/0310189] [INSPIRE].
M. Eto et al., Multiple layer structure of non-abelian vortex, Phys. Lett. B 678 (2009) 254 [arXiv:0903.1518] [INSPIRE].
D. Tong, TASI lectures on solitons: Instantons, monopoles, vortices and kinks, hep-th/0509216 [INSPIRE].
M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Solitons in the Higgs phase: the moduli matrix approach, J. Phys. A 39 (2006) R315 [hep-th/0602170] [INSPIRE].
M. Shifman and A. Yung, Supersymmetric solitons and how they help us understand non-abelian gauge theories, Rev. Mod. Phys. 79 (2007) 1139 [hep-th/0703267] [INSPIRE].
A. Kapustin and M.J. Strassler, On mirror symmetry in three-dimensional Abelian gauge theories, JHEP 04 (1999) 021 [hep-th/9902033] [INSPIRE].
B. Collie and D. Tong, The partonic nature of instantons, JHEP 08 (2009) 006 [arXiv:0905.2267] [INSPIRE].
J.P. Gauntlett, R. Portugues, D. Tong and P.K. Townsend, D-brane solitons in supersymmetric σ-models, Phys. Rev. D 63 (2001) 085002 [hep-th/0008221] [INSPIRE].
M. Eto and K. Hashimoto, Speed limit in internal space of domain walls via all-order effective action of moduli motion, Phys. Rev. D 93 (2016) 065058 [arXiv:1508.00433] [INSPIRE].
M. Eto, J-kink domain walls and the DBI action, JHEP 06 (2015) 160 [arXiv:1504.00753] [INSPIRE].
M. Eto et al., Non-abelian vortices on cylinder: duality between vortices and walls, Phys. Rev. D 73 (2006) 085008 [hep-th/0601181] [INSPIRE].
M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Webs of walls, Phys. Rev. D 72 (2005)085004 [hep-th/0506135] [INSPIRE].
M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Non-abelian webs of walls, Phys. Lett. B 632 (2006) 384 [hep-th/0508241] [INSPIRE].
M. Eto, Y. Isozumi, M. Nitta and K. Ohashi, 1/2, 1/4 and 1/8 BPS equations in SUSY Yang-Mills-Higgs systems: field theoretical brane configurations, Nucl. Phys. B 752 (2006) 140 [hep-th/0506257] [INSPIRE].
M. Eto et al., Effective action of domain wall networks, Phys. Rev. D 75 (2007) 045010 [hep-th/0612003] [INSPIRE].
M. Eto et al., Dynamics of domain wall networks, Phys. Rev. D 76 (2007) 125025 [arXiv:0707.3267] [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].
G.W. Gibbons, P. Rychenkova and R. Goto, Hyper-Kähler quotient construction of BPS monopole moduli spaces, Commun. Math. Phys. 186 (1997) 585 [hep-th/9608085] [INSPIRE].
E. Witten, Branes, instantons, and Taub-NUT spaces, JHEP 06 (2009) 067 [arXiv:0902.0948] [INSPIRE].
M. Shifman and A. Yung, Localization of nonAbelian gauge fields on domain walls at weak coupling (D-brane prototypes II), Phys. Rev. D 70 (2004) 025013 [hep-th/0312257] [INSPIRE].
Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Construction of non-Abelian walls and their complete moduli space, Phys. Rev. Lett. 93 (2004) 161601 [hep-th/0404198] [INSPIRE].
Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Non-Abelian walls in supersymmetric gauge theories, Phys. Rev. D 70 (2004) 125014 [hep-th/0405194] [INSPIRE].
M. Eto, Y. Isozumi, M. Nitta, K. Ohashi, K. Ohta and N. Sakai, D-brane construction for non-Abelian walls, Phys. Rev. D 71 (2005) 125006 [hep-th/0412024] [INSPIRE].
A. Hanany and D. Tong, On monopoles and domain walls, Commun. Math. Phys. 266 (2006)647 [hep-th/0507140] [INSPIRE].
M. Naganuma, M. Nitta and N. Sakai, BPS lumps and their intersections in N = 2 SUSY nonlinear σ-models, Grav. Cosmol. 8 (2002) 129 [hep-th/0108133] [INSPIRE].
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Eto, M., Fujimori, T. & Nitta, M. Domain wall and three dimensional duality. J. High Energ. Phys. 2018, 35 (2018). https://doi.org/10.1007/JHEP06(2018)035
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DOI: https://doi.org/10.1007/JHEP06(2018)035