Abstract
We study two-dimensional \( \mathcal{N}=\left(4,4\right) \) supersymmetric gauge theories which do not have classical Higgs branches, but are believed to have isolated quantum Higgs vacua. We provide arguments for the existence of such vacua based on brane dynamics in string theory and the supersymmetric partition sums of the gauge theories.
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References
E. Witten, On the conformal field theory of the Higgs branch, JHEP 07 (1997) 003 [hep-th/9707093] [INSPIRE].
M.R. Douglas, J. Polchinski and A. Strominger, Probing five-dimensional black holes with D-branes, JHEP 12 (1997) 003 [hep-th/9703031] [INSPIRE].
F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic genera of two-dimensional N = 2 gauge theories with rank-one gauge groups, Lett. Math. Phys. 104 (2014) 465 [arXiv:1305.0533] [INSPIRE].
F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic genera of 2D \( \mathcal{N}=2 \) gauge theories, Commun. Math. Phys. 333 (2015) 1241 [arXiv:1308.4896] [INSPIRE].
A. Gadde and S. Gukov, 2D index and surface operators, JHEP 03 (2014) 080 [arXiv:1305.0266] [INSPIRE].
A. Giveon and D. Kutasov, Brane dynamics and gauge theory, Rev. Mod. Phys. 71 (1999) 983 [hep-th/9802067] [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].
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].
E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].
I. Antoniadis and B. Pioline, Higgs branch, hyperKahler quotient and duality in SUSY N = 2 Yang-Mills theories, Int. J. Mod. Phys. A 12 (1997) 4907 [hep-th/9607058] [INSPIRE].
F. Benini and S. Cremonesi, Partition functions of \( \mathcal{N}=\left(2,2\right) \) gauge theories on S2 and vortices, Commun. Math. Phys. 334 (2015) 1483 [arXiv:1206.2356] [INSPIRE].
N. Doroud, J. Gomis, B. Le Floch and S. Lee, Exact results in D = 2 supersymmetric gauge theories, JHEP 05 (2013) 093 [arXiv:1206.2606] [INSPIRE].
S. Elitzur, A. Giveon and D. Kutasov, Branes and N = 1 duality in string theory, Phys. Lett. B 400 (1997) 269 [hep-th/9702014] [INSPIRE].
K. Hosomichi and S. Lee, Self-dual strings and 2D SYM, JHEP 01 (2015) 076 [arXiv:1406.1802] [INSPIRE].
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ArXiv ePrint: 1406.6000
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Harvey, J.A., Kutasov, D. & Lee, S. Comments on quantum Higgs vacua. J. High Energ. Phys. 2015, 71 (2015). https://doi.org/10.1007/JHEP07(2015)071
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DOI: https://doi.org/10.1007/JHEP07(2015)071