Abstract
We study a three-dimensional \( \mathcal{N} \) = 2 supersymmetric G2 gauge theory with and without fundamental matters. We find that a classical Coulomb branch of the moduli space of vacua is partly lifted by monopole-instantons and the quantum Coulomb moduli space would be described by a complex one-dimensional space. Depending on the number of the matters in a fundamental representation, the low-energy dynamics of the theory shows various phases like s-confinement or quantum merging of the Coulomb and the Higgs branches. We also investigate superconformal indices as an independent check of our analysis.
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References
N. Seiberg, Exact results on the space of vacua of four-dimensional SUSY gauge theories, Phys. Rev. D 49 (1994) 6857 [hep-th/9402044] [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
N. Seiberg, The power of duality: Exact results in 4-D SUSY field theory, Int. J. Mod. Phys. A 16 (2001) 4365 [hep-th/9506077] [INSPIRE].
K. Holland, P. Minkowski, M. Pepe and U.J. Wiese, Confinement without a center: The exceptional group G(2), Nucl. Phys. Proc. Suppl. 119 (2003) 652 [hep-lat/0209093] [INSPIRE].
K. Holland, P. Minkowski, M. Pepe and U.J. Wiese, Exceptional confinement in G 2 gauge theory, Nucl. Phys. B 668 (2003) 207 [hep-lat/0302023] [INSPIRE].
M. Pepe and U.J. Wiese, Exceptional Deconfinement in G 2 Gauge Theory, Nucl. Phys. B 768 (2007) 21 [hep-lat/0610076] [INSPIRE].
G. Cossu, M. D’Elia, A. Di Giacomo, B. Lucini and C. Pica, G 2 gauge theory at finite temperature, JHEP 10 (2007) 100 [arXiv:0709.0669] [INSPIRE].
B.H. Wellegehausen, A. Wipf and C. Wozar, Casimir Scaling and String Breaking in G 2 Gluodynamics, Phys. Rev. D 83 (2011) 016001 [arXiv:1006.2305] [INSPIRE].
M. Bruno, M. Caselle, M. Panero and R. Pellegrini, Exceptional thermodynamics: the equation of state of G 2 gauge theory, JHEP 03 (2015) 057 [arXiv:1409.8305] [INSPIRE].
E. Poppitz, T. Schäfer and M. Ünsal, Universal mechanism of (semi-classical) deconfinement and theta-dependence for all simple groups, JHEP 03 (2013) 087 [arXiv:1212.1238] [INSPIRE].
M. Alishahiha, F. Ardalan and F. Mansouri, The moduli space of the supersymmetric G 2 Yang-Mills theory, Phys. Lett. B 381 (1996) 446 [hep-th/9512005] [INSPIRE].
K. Landsteiner, J.M. Pierre and S.B. Giddings, On the moduli space of N = 2 supersymmetric G 2 gauge theory, Phys. Rev. D 55 (1997) 2367 [hep-th/9609059] [INSPIRE].
I. Pesando, Exact results for the supersymmetric G 2 gauge theories, Mod. Phys. Lett. A 10 (1995) 1871 [hep-th/9506139] [INSPIRE].
S.B. Giddings and J.M. Pierre, Some exact results in supersymmetric theories based on exceptional groups, Phys. Rev. D 52 (1995) 6065 [hep-th/9506196] [INSPIRE].
A.V. Smilga, 6+1 vacua in supersymmetric QCD with G 2 gauge group, Phys. Rev. D 58 (1998) 105014 [hep-th/9801078] [INSPIRE].
N.M. Davies, T.J. Hollowood and V.V. Khoze, Monopoles, affine algebras and the gluino condensate, J. Math. Phys. 44 (2003) 3640 [hep-th/0006011] [INSPIRE].
M. Alishahiha, J. de Boer, A.E. Mosaffa and J. Wijnhout, N = 1 G 2 SYM theory and compactification to three-dimensions, JHEP 09 (2003) 066 [hep-th/0308120] [INSPIRE].
O. Saito, The glueball superpotential for G 2, arXiv:0711.1456 [INSPIRE].
A. Bourget and J. Troost, On the \( \mathcal{N} \) = 1∗ gauge theory on a circle and elliptic integrable systems, JHEP 01 (2016) 097 [arXiv:1511.03116] [INSPIRE].
P. Ramond, Superalgebras in N = 1 gauge theories, Phys. Lett. B 390 (1997) 179 [hep-th/9608077] [INSPIRE].
J. Distler and A. Karch, N = 1 dualities for exceptional gauge groups and quantum global symmetries, Fortsch. Phys. 45 (1997) 517 [hep-th/9611088] [INSPIRE].
A. Karch, More on N = 1 selfdualities and exceptional gauge groups, Phys. Lett. B 405 (1997) 280 [hep-th/9702179] [INSPIRE].
P.L. Cho, Moduli in exceptional SUSY gauge theories, Phys. Rev. D 57 (1998) 5214 [hep-th/9712116] [INSPIRE].
P. Pouliot, Spectroscopy of gauge theories based on exceptional Lie groups, J. Phys. A 34 (2001) 8631 [hep-th/0107151] [INSPIRE].
C. Csáki and H. Murayama, Discrete anomaly matching, Nucl. Phys. B 515 (1998) 114 [hep-th/9710105] [INSPIRE].
U.H. Danielsson and B. Sundborg, Exceptional equivalences in N = 2 supersymmetric Yang-Mills theory, Phys. Lett. B 370 (1996) 83 [hep-th/9511180] [INSPIRE].
M.R. Abolhasani, M. Alishahiha and A.M. Ghezelbash, The moduli space and monodromies of the N = 2 supersymmetric Yang-Mills theory with any Lie gauge groups, Nucl. Phys. B 480 (1996) 279 [hep-th/9606043] [INSPIRE].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, JHEP 07 (2013) 149 [arXiv:1305.3924] [INSPIRE].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities for orthogonal groups, JHEP 08 (2013) 099 [arXiv:1307.0511] [INSPIRE].
P. Pouliot, Chiral duals of nonchiral SUSY gauge theories, Phys. Lett. B 359 (1995) 108 [hep-th/9507018] [INSPIRE].
E. Witten, Constraints on Supersymmetry Breaking, Nucl. Phys. B 202 (1982) 253 [INSPIRE].
A. Yu. Morozov, M.A. Olshanetsky and M.A. Shifman, Gluino Condensate in Supersymmetric Gluodynamics, Sov. Phys. JETP 67 (1988) 222 [INSPIRE].
E. Witten, Toroidal compactification without vector structure, JHEP 02 (1998) 006 [hep-th/9712028] [INSPIRE].
E.J. Weinberg and P. Yi, Magnetic Monopole Dynamics, Supersymmetry and Duality, Phys. Rept. 438 (2007) 65 [hep-th/0609055] [INSPIRE].
Ya. Shnir and G. Zhilin, G2 monopoles, Phys. Rev. D 92 (2015) 045025 [arXiv:1508.01871] [INSPIRE].
R. Matsudo and K.-I. Kondo, Gauge-covariant decomposition and magnetic monopole for G 2 Yang-Mills field, Phys. Rev. D 94 (2016) 045004 [arXiv:1602.06086] [INSPIRE].
K.-M. Lee and P. Yi, Monopoles and instantons on partially compactified D-branes, Phys. Rev. D 56 (1997) 3711 [hep-th/9702107] [INSPIRE].
K.-M. Lee, Instantons and magnetic monopoles on R 3 × S 1 with arbitrary simple gauge groups, Phys. Lett. B 426 (1998) 323 [hep-th/9802012] [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].
C. Callias, Index Theorems on Open Spaces, Commun. Math. Phys. 62 (1978) 213 [INSPIRE].
E.J. Weinberg, Fundamental Monopoles and Multi-Monopole Solutions for Arbitrary Simple Gauge Groups, Nucl. Phys. B 167 (1980) 500 [INSPIRE].
J. de Boer, K. Hori and Y. Oz, Dynamics of N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 500 (1997) 163 [hep-th/9703100] [INSPIRE].
I. Affleck, J.A. Harvey and E. Witten, Instantons and (Super)Symmetry Breaking in (2+1)-Dimensions, Nucl. Phys. B 206 (1982) 413 [INSPIRE].
K. Intriligator and N. Seiberg, Aspects of 3d N = 2 Chern-Simons-Matter Theories, JHEP 07 (2013) 079 [arXiv:1305.1633] [INSPIRE].
O. Aharony, A. Hanany, K.A. Intriligator, N. Seiberg and M.J. Strassler, Aspects of N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 499 (1997) 67 [hep-th/9703110] [INSPIRE].
W. Nahm, Selfdual monopoles and calorons, in Group Theoretical Methods in Physics: Proceedings, 12th International Colloquium, Trieste, Italy, September 5-11, 1983.
J. Bhattacharya and S. Minwalla, Superconformal Indices for N = 6 Chern Simons Theories, JHEP 01 (2009) 014 [arXiv:0806.3251] [INSPIRE].
S. Kim, The complete superconformal index for N = 6 Chern-Simons theory, Nucl. Phys. B 821 (2009) 241 [Erratum ibid. B 864 (2012) 884] [arXiv:0903.4172] [INSPIRE].
Y. Imamura and S. Yokoyama, Index for three dimensional superconformal field theories with general R-charge assignments, JHEP 04 (2011) 007 [arXiv:1101.0557] [INSPIRE].
Y. Imamura, D. Yokoyama and S. Yokoyama, Superconformal index for large-N quiver Chern-Simons theories, JHEP 08 (2011) 011 [arXiv:1102.0621] [INSPIRE].
A. Kapustin and B. Willett, Generalized Superconformal Index for Three Dimensional Field Theories, arXiv:1106.2484 [INSPIRE].
D. Bashkirov, Aharony duality and monopole operators in three dimensions, arXiv:1106.4110 [INSPIRE].
A. Kapustin, H. Kim and J. Park, Dualities for 3d Theories with Tensor Matter, JHEP 12 (2011) 087 [arXiv:1110.2547] [INSPIRE].
H. Kim and J. Park, Aharony Dualities for 3d Theories with Adjoint Matter, JHEP 06 (2013) 106 [arXiv:1302.3645] [INSPIRE].
V.P. Spiridonov and G.S. Vartanov, Elliptic Hypergeometry of Supersymmetric Dualities, Commun. Math. Phys. 304 (2011) 797 [arXiv:0910.5944] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
P. Goddard, J. Nuyts and D.I. Olive, Gauge Theories and Magnetic Charge, Nucl. Phys. B 125 (1977) 1 [INSPIRE].
S. Cremonesi, The Hilbert series of 3d \( \mathcal{N} \) = 2 Yang-Mills theories with vectorlike matter, J. Phys. A 48 (2015) 455401 [arXiv:1505.02409] [INSPIRE].
A. Hanany, C. Hwang, H. Kim, J. Park and R.-K. Seong, Hilbert Series for Theories with Aharony Duals, JHEP 11 (2015) 132 [arXiv:1505.02160] [INSPIRE].
S. Benvenuti, B. Feng, A. Hanany and Y.-H. He, Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics, JHEP 11 (2007) 050 [hep-th/0608050] [INSPIRE].
B. Feng, A. Hanany and Y.-H. He, Counting gauge invariants: The Plethystic program, JHEP 03 (2007) 090 [hep-th/0701063] [INSPIRE].
P. Pouliot, Molien function for duality, JHEP 01 (1999) 021 [hep-th/9812015] [INSPIRE].
C. Csáki, M. Martone, Y. Shirman, P. Tanedo and J. Terning, Dynamics of 3D SUSY Gauge Theories with Antisymmetric Matter, JHEP 08 (2014) 141 [arXiv:1406.6684] [INSPIRE].
A. Amariti, C. Csáki, M. Martone and N. R.-L. Lorier, From 4D to 3D chiral theories: Dressing the monopoles, Phys. Rev. D 93 (2016) 105027 [arXiv:1506.01017] [INSPIRE].
R.E. Behrends, J. Dreitlein, C. Fronsdal and W. Lee, Simple Groups and Strong Interaction Symmetries, Rev. Mod. Phys. 34 (1962) 1 [Erratum ibid. 34 (1962) 584] [INSPIRE].
R. Slansky, Group Theory for Unified Model Building, Phys. Rept. 79 (1981) 1 [INSPIRE].
R. Arenas, Constructing a Matrix Representation of the Lie Group G 2, MSc Thesis, Department of Mathematics, Harvey Mudd college, Claremont, California, U.S.A., (2005).
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Nii, K., Sekiguchi, Y. Low-energy dynamics of 3d \( \mathcal{N} \) = 2 G2 supersymmetric gauge theory. J. High Energ. Phys. 2018, 158 (2018). https://doi.org/10.1007/JHEP02(2018)158
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DOI: https://doi.org/10.1007/JHEP02(2018)158