Abstract
We construct lattice action for three-dimensional \( \mathcal{N}=4 \) supersymmetric gauge theory with matter fields in the fundamental representation.
Similar content being viewed by others
References
D.B. Kaplan, Recent developments in lattice supersymmetry, Nucl. Phys. Proc. Suppl. 129 (2004) 109 [hep-lat/0309099] [INSPIRE].
J. Giedt, Deconstruction and other approaches to supersymmetric lattice field theories, Int. J. Mod. Phys. A 21 (2006) 3039 [hep-lat/0602007] [INSPIRE].
S. Catterall, D.B. Kaplan and M. Ünsal, Exact lattice supersymmetry, Phys. Rept. 484 (2009) 71 [arXiv:0903.4881] [INSPIRE].
A. Joseph, Supersymmetric Yang-Mills theories with exact supersymmetry on the lattice, Int. J. Mod. Phys. A 26 (2011) 5057 [arXiv:1110.5983] [INSPIRE].
D.B. Kaplan, E. Katz and M. Ünsal, Supersymmetry on a spatial lattice, JHEP 05 (2003) 037 [hep-lat/0206019] [INSPIRE].
A.G. Cohen, D.B. Kaplan, E. Katz and M. Ünsal, Supersymmetry on a euclidean space-time lattice. 1. A target theory with four supercharges, JHEP 08 (2003) 024 [hep-lat/0302017] [INSPIRE].
A.G. Cohen, D.B. Kaplan, E. Katz and M. Ünsal, Supersymmetry on a euclidean space-time lattice. 2. Target theories with eight supercharges, JHEP 12 (2003) 031 [hep-lat/0307012] [INSPIRE].
D.B. Kaplan and M. Ünsal, A euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges, JHEP 09 (2005) 042 [hep-lat/0503039] [INSPIRE].
S. Catterall, A geometrical approach to N = 2 super Yang-Mills theory on the two dimensional lattice, JHEP 11 (2004) 006 [hep-lat/0410052] [INSPIRE].
S. Catterall, Lattice formulation of N = 4 super Yang-Mills theory, JHEP 06 (2005) 027 [hep-lat/0503036] [INSPIRE].
S. Catterall, Simulations of N = 2 super Yang-Mills theory in two dimensions, JHEP 03 (2006) 032 [hep-lat/0602004] [INSPIRE].
S. Catterall, Dirac-Kähler fermions and exact lattice supersymmetry, PoS(LAT2005)006 [hep-lat/0509136] [INSPIRE].
A. Feo, Supersymmetry on the lattice, Nucl. Phys. Proc. Suppl. 119 (2003) 198 [hep-lat/0210015] [INSPIRE].
J.W. Elliott and G.D. Moore, Three dimensional N = 2 supersymmetry on the lattice, JHEP 11 (2005) 010 [hep-lat/0509032] [INSPIRE].
F. Sugino, A lattice formulation of super Yang-Mills theories with exact supersymmetry, JHEP 01 (2004) 015 [hep-lat/0311021] [INSPIRE].
F. Sugino, Super Yang-Mills theories on the two-dimensional lattice with exact supersymmetry, JHEP 03 (2004) 067 [hep-lat/0401017] [INSPIRE].
A. D’Adda, I. Kanamori, N. Kawamoto and K. Nagata, Exact extended supersymmetry on a lattice: Twisted N = 2 super Yang-Mills in two dimensions, Phys. Lett. B 633 (2006) 645 [hep-lat/0507029] [INSPIRE].
A. D’Adda, I. Kanamori, N. Kawamoto and K. Nagata, Exact Extended supersymmetry on a lattice: twisted N = 4 super Yang-Mills in three dimensions, Nucl. Phys. B 798 (2008) 168 [arXiv:0707.3533] [INSPIRE].
I. Kanamori and H. Suzuki, Restoration of supersymmetry on the lattice: Two-dimensional N = (2,2) supersymmetric Yang-Mills theory, Nucl. Phys. B 811 (2009) 420 [arXiv:0809.2856] [INSPIRE].
M. Hanada and I. Kanamori, Lattice study of two-dimensional N = (2, 2) super Yang-Mills at large-N, Phys. Rev. D 80 (2009) 065014 [arXiv:0907.4966] [INSPIRE].
M. Hanada, S. Matsuura and F. Sugino, Two-dimensional lattice for four-dimensional N = 4 supersymmetric Yang-Mills, Prog. Theor. Phys. 126 (2011) 597 [arXiv:1004.5513] [INSPIRE].
M. Hanada, A proposal of a fine tuning free formulation of 4D N = 4 super Yang-Mills, JHEP 11 (2010) 112 [arXiv:1009.0901] [INSPIRE].
M. Hanada, S. Matsuura and F. Sugino, Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges, Nucl. Phys. B 857 (2012) 335 [arXiv:1109.6807] [INSPIRE].
M. Ünsal, Twisted supersymmetric gauge theories and orbifold lattices, JHEP 10 (2006) 089 [hep-th/0603046] [INSPIRE].
S. Catterall, From twisted supersymmetry to orbifold lattices, JHEP 01 (2008) 048 [arXiv:0712.2532] [INSPIRE].
M.G. Endres and D.B. Kaplan, Lattice formulation of (2, 2) supersymmetric gauge theories with matter fields, JHEP 10 (2006) 076 [hep-lat/0604012] [INSPIRE].
J. Giedt, Quiver lattice supersymmetric matter: D1/D5 branes and AdS 3 /CFT 2, hep-lat/0605004 [INSPIRE].
J. Giedt, A deconstruction lattice description of the D1/D5 brane world-volume gauge theory, Adv. High Energy Phys. 2011 (2011) 241419.
S. Matsuura, Two-dimensional N = (2, 2) supersymmetric lattice gauge theory with matter fields in the fundamental representation, JHEP 07 (2008) 127 [arXiv:0805.4491] [INSPIRE].
M. Blau and G. Thompson, Aspects of N (T) ≥ two topological gauge theories and D-branes, Nucl. Phys. B 492 (1997) 545 [hep-th/9612143] [INSPIRE].
J.M. Rabin, Homology theory of lattice fermion doubling, Nucl. Phys. B 201 (1982) 315 [INSPIRE].
P. Becher and H. Joos, The Dirac-Kähler equation and fermions on the lattice, Z. Phys. C 15 (1982) 343 [INSPIRE].
T. Banks, Y. Dothan and D. Horn, Geometric fermions, Phys. Lett. B 117 (1982) 413 [INSPIRE].
H. Aratyn, M. Goto and A. Zimerman, A lattice gauge theory for fields in the adjoint representation, Nuovo Cim. A 84 (1984) 255 [INSPIRE].
N. Marcus, The other topological twisting of N = 4 Yang-Mills, Nucl. Phys. B 452 (1995) 331 [hep-th/9506002] [INSPIRE].
P.H. Damgaard and S. Matsuura, Classification of supersymmetric lattice gauge theories by orbifolding, JHEP 07 (2007) 051 [arXiv:0704.2696] [INSPIRE].
P.H. Damgaard and S. Matsuura, Geometry of orbifolded supersymmetric lattice gauge theories, Phys. Lett. B 661 (2008) 52 [arXiv:0801.2936] [INSPIRE].
S. Catterall, R. Galvez, A. Joseph and D. Mehta, On the sign problem in 2D lattice super Yang-Mills, JHEP 01 (2012) 108 [arXiv:1112.3588] [INSPIRE].
D. Mehta, S. Catterall, R. Galvez and A. Joseph, Supersymmetric gauge theories on the lattice: pfaffian phases and the Neuberger 0/0 problem, PoS(LATTICE 2011)078 [arXiv:1112.5413] [INSPIRE].
R. Galvez, S. Catterall, A. Joseph and D. Mehta, Investigating the sign problem for two-dimensional \( \mathcal{N}=\left( {2,2} \right) \) and \( \mathcal{N}=\left( {8,8} \right) \) lattice super Yang-Mills theories, PoS(LATTICE 2011)064 [arXiv:1201.1924] [INSPIRE].
S. Catterall, J. Giedt and A. Joseph, Twisted supersymmetries in lattice \( \mathcal{N}=4 \) super Yang-Mills theory, arXiv:1306.3891 [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].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
J. de Boer, K. Hori, H. Ooguri and Y. Oz, Mirror symmetry in three-dimensional gauge theories, quivers and D-branes, Nucl. Phys. B 493 (1997) 101 [hep-th/9611063] [INSPIRE].
J. de Boer, K. Hori, H. Ooguri, Y. Oz and Z. Yin, Mirror symmetry in three-dimensional theories, SL(2, \( \mathbb{Z} \)) and D-brane moduli spaces, Nucl. Phys. B 493 (1997) 148 [hep-th/9612131] [INSPIRE].
A. Kapustin and M.J. Strassler, On mirror symmetry in three-dimensional Abelian gauge theories, JHEP 04 (1999) 021 [hep-th/9902033] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1307.3281
Rights and permissions
About this article
Cite this article
Joseph, A. Lattice formulation of three-dimensional \( \mathcal{N}=4 \) gauge theory with fundamental matter fields. J. High Energ. Phys. 2013, 46 (2013). https://doi.org/10.1007/JHEP09(2013)046
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2013)046