×

Geometry and dynamics of a coupled 4\(D\)-2\(D\) quantum field theory. (English) Zbl 1388.81709

Summary: Geometric and dynamical aspects of a coupled \(4D\)-\(2D\) interacting quantum field theory – the gauged nonabelian vortex – are investigated. The fluctuations of the internal \(2D\) nonabelian vortex zeromodes excite the massless \(4D\) Yang-Mills modes and in general give rise to divergent energies. This means that the well-known \(2D\) \(\mathbb {CP}^{N-1}\) zeromodes associated with a nonAbelian vortex become nonnormalizable. Moreover, all sorts of global, topological \(4D\) effects such as the nonabelian Aharonov-Bohm effect come into play. These topological global features and the dynamical properties associated with the fluctuation of the \(2D\) vortex moduli modes are intimately correlated, as shown concretely here in a \(\mathrm{U}_0(1)\times\mathrm{SU}_l(N)\times\mathrm{SU}_r(N)\) model with scalar fields in a bifundamental representation of the two \(\mathrm{SU}(N)\) factor gauge groups.

MSC:

81T45 Topological field theories in quantum mechanics
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] R. Auzzi, S. Bolognesi, J. Evslin, K. Konishi and A. Yung, Non-Abelian superconductors: vortices and confinement \[inN=2 \mathcal{N}=2\] SQCD, Nucl. Phys.B 673 (2003) 187 [hep-th/0307287] [INSPIRE]. · Zbl 1058.81580 · doi:10.1016/j.nuclphysb.2003.09.029
[2] A. Hanany and D. Tong, Vortices, instantons and branes, JHEP07 (2003) 037 [hep-th/0306150] [INSPIRE]. · doi:10.1088/1126-6708/2003/07/037
[3] M. Shifman and A. Yung, Non-Abelian string junctions as confined monopoles, Phys. Rev.D 70 (2004) 045004 [hep-th/0403149] [INSPIRE].
[4] A. Gorsky, M. Shifman and A. Yung, Non-Abelian Meissner effect in Yang-Mills theories at weak coupling, Phys. Rev.D 71 (2005) 045010 [hep-th/0412082] [INSPIRE].
[5] S.B. Gudnason, Y. Jiang and K. Konishi, Non-Abelian vortex dynamics: effective world-sheet action, JHEP08 (2010) 012 [arXiv:1007.2116] [INSPIRE]. · Zbl 1291.81251 · doi:10.1007/JHEP08(2010)012
[6] Z. Komargodski, Vector mesons and an interpretation of Seiberg duality, JHEP02 (2011) 019 [arXiv:1010.4105] [INSPIRE]. · Zbl 1294.81288
[7] G. Carlino, K. Konishi and H. Murayama, Dynamical symmetry breaking in supersymmetric SU(nc) and USp(2nc) gauge theories, Nucl. Phys.B 590 (2000) 37 [hep-th/0005076] [INSPIRE]. · Zbl 0991.81044 · doi:10.1016/S0550-3213(00)00482-X
[8] M.G. Alford, K. Rajagopal and F. Wilczek, Color flavor locking and chiral symmetry breaking in high density QCD, Nucl. Phys.B 537 (1999) 443 [hep-ph/9804403] [INSPIRE]. · doi:10.1016/S0550-3213(98)00668-3
[9] M.G. Alford, K. Benson, S.R. Coleman, J. March-Russell and F. Wilczek, The interactions and excitations of non-Abelian vortices, Phys. Rev. Lett.64 (1990) 1632 [Erratum ibid.65 (1990) 668] [INSPIRE]. · Zbl 1050.81560
[10] M.G. Alford, K. Benson, S.R. Coleman, J. March-Russell and F. Wilczek, Zero modes of non-Abelian vortices, Nucl. Phys.B 349 (1991) 414 [INSPIRE]. · doi:10.1016/0550-3213(91)90331-Q
[11] M.G. Alford, K.-M. Lee, J. March-Russell and J. Preskill, Quantum field theory of non-Abelian strings and vortices, Nucl. Phys.B 384 (1992) 251 [hep-th/9112038] [INSPIRE]. · doi:10.1016/0550-3213(92)90468-Q
[12] H.-K. Lo and J. Preskill, Non-Abelian vortices and non-Abelian statistics, Phys. Rev.D 48 (1993) 4821 [hep-th/9306006] [INSPIRE].
[13] M. Bucher and A. Goldhaber, SO(10) cosmic strings and SU(3)colorCheshire charge, Phys. Rev.D 49 (1994) 4167 [hep-ph/9310262] [INSPIRE].
[14] K. Konishi, M. Nitta and W. Vinci, Supersymmetry breaking on gauged non-Abelian vortices, JHEP09 (2012) 014 [arXiv:1206.4546] [INSPIRE]. · Zbl 1397.81101 · doi:10.1007/JHEP09(2012)014
[15] J. Evslin, K. Konishi, M. Nitta, K. Ohashi and W. Vinci, Non-Abelian vortices with an Aharonov-Bohm effect, JHEP01 (2014) 086 [arXiv:1310.1224] [INSPIRE]. · doi:10.1007/JHEP01(2014)086
[16] S. Bolognesi, C. Chatterjee, S.B. Gudnason and K. Konishi, Vortex zero modes, large flux limit and Ambjørn-Nielsen-Olesen magnetic instabilities, JHEP10 (2014) 101 [arXiv:1408.1572] [INSPIRE]. · doi:10.1007/JHEP10(2014)101
[17] S. Bolognesi, C. Chatterjee and K. Konishi, Non-Abelian vortices, large winding limits and Aharonov-Bohm effects, JHEP04 (2015) 143 [arXiv:1503.00517] [INSPIRE]. · Zbl 1388.81101 · doi:10.1007/JHEP04(2015)143
[18] F. Delduc and G. Valent, Classical and quantum structure of the compact Kählerian σ models, Nucl. Phys.B 253 (1985) 494 [INSPIRE]. · doi:10.1016/0550-3213(85)90544-9
[19] N.K. Nielsen and P. Olesen, An unstable Yang-Mills field mode, Nucl. Phys.B 144 (1978) 376 [INSPIRE]. · doi:10.1016/0550-3213(78)90377-2
[20] J. Ambjørn and P. Olesen, On electroweak magnetism, Nucl. Phys.B 315 (1989) 606 [INSPIRE]. · doi:10.1016/0550-3213(89)90004-7
[21] J. Ambjørn and P. Olesen, A condensate solution of the electroweak theory which interpolates between the broken and the symmetric phase, Nucl. Phys.B 330 (1990) 193 [INSPIRE]. · doi:10.1016/0550-3213(90)90307-Y
[22] P.C. Nelson and A. Manohar, Global color is not always defined, Phys. Rev. Lett.50 (1983) 943 [INSPIRE]. · doi:10.1103/PhysRevLett.50.943
[23] A.P. Balachandran et al., Monopole topology and the problem of color, Phys. Rev. Lett.50 (1983) 1553 [INSPIRE]. · doi:10.1103/PhysRevLett.50.1553
[24] A.S. Schwarz, Field theories with no local conservation of the electric charge, Nucl. Phys.B 208 (1982) 141 [INSPIRE]. · doi:10.1016/0550-3213(82)90190-0
[25] A.S. Schwarz and Y.S. Tyupkin, Grand unification and mirror particles, Nucl. Phys.B 209 (1982) 427 [INSPIRE]. · doi:10.1016/0550-3213(82)90265-6
[26] L. Seveso, Gauged non-Abelian vortices: topology and dynamics of a coupled 2D-4D quantum field theory, Master Thesis, University of Pisa, Pisa Italy (2015).
[27] M. Eto et al., Multiple layer structure of non-Abelian vortex, Phys. Lett.B 678 (2009) 254 [arXiv:0903.1518] [INSPIRE]. · doi:10.1016/j.physletb.2009.05.061
[28] N. Dorey, The BPS spectra of two-dimensional supersymmetric gauge theories with twisted mass terms, JHEP11 (1998) 005 [hep-th/9806056] [INSPIRE]. · Zbl 0949.81060
[29] C.M. Hull, A. Karlhede, U. Lindström and M. Roček, Nonlinear σ models and their gauging in and out of superspace, Nucl. Phys.B 266 (1986) 1 [INSPIRE]. · doi:10.1016/0550-3213(86)90175-6
[30] D. Gaiotto, S. Gukov and N. Seiberg, Surface defects and resolvents, JHEP09 (2013) 070 [arXiv:1307.2578] [INSPIRE]. · doi:10.1007/JHEP09(2013)070
[31] E. Witten, Superconducting strings, Nucl. Phys.B 249 (1985) 557 [INSPIRE]. · doi:10.1016/0550-3213(85)90022-7
[32] M. Shifman and A. Yung, Non-Abelian semilocal strings \[inN=2 \mathcal{N}=2\] supersymmetric QCD, Phys. Rev.D 73 (2006) 125012 [hep-th/0603134] [INSPIRE].
[33] M. Eto et al., On the moduli space of semilocal strings and lumps, Phys. Rev.D 76 (2007) 105002 [arXiv:0704.2218] [INSPIRE].
[34] M. Shifman, W. Vinci and A. Yung, Effective world-sheet theory for non-Abelian semilocal strings \[inN=2 \mathcal{N}=2\] supersymmetric QCD, Phys. Rev.D 83 (2011) 125017 [arXiv:1104.2077] [INSPIRE].
[35] P. Koroteev, M. Shifman, W. Vinci and A. Yung, Quantum dynamics of low-energy theory on semilocal non-Abelian strings, Phys. Rev.D 84 (2011) 065018 [arXiv:1107.3779] [INSPIRE].
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.