Abstract
We construct two-dimensional \( \mathcal{N} \) =(2, 2) supersymmetric gauge theories on a Euclidean spacetime lattice with matter in the two-index symmetric and anti-symmetric representations of SU(N c ) color group. These lattice theories preserve a subset of the supercharges exact at finite lattice spacing. The method of topological twisting is used to construct such theories in the continuum and then the geometric discretization scheme is used to formulate them on the lattice. The lattice theories obtained this way are gauge in variant, free from fermion doubling problem and exact supersymmetric at finite lattice spacing. We hope that these lattice constructions further motivate the nonperturbative explorations of models inspired by technicolor, orbifolding and orientifolding in string theories and the Corrigan-Ramond limit.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
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].
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].
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].
S. Catterall, D.B. Kaplan and M. Ünsal, Exact lattice supersymmetry, Phys. Rept. 484 (2009) 71 [arXiv:0903.4881] [INSPIRE].
S. Catterall, E. Dzienkowski, J. Giedt, A. Joseph and R. Wells, Perturbative renormalization of lattice N = 4 super Yang-Mills theory, JHEP 04 (2011) 074 [arXiv:1102.1725] [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].
S. Catterall, J. Giedt and A. Joseph, Twisted supersymmetries in lattice \( \mathcal{N} \) = 4 super Yang-Mills theory, JHEP 10 (2013) 166 [arXiv:1306.3891] [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].
S. Matsuura and F. Sugino, Lattice Formulation for 2d N = (2,2), (4,4) Super Yang-Mills Theories without Admissibility Conditions, arXiv:1402.0952 [INSPIRE].
S. Catterall, D. Schaich, P.H. Damgaard, T. DeGrand and J. Giedt, N = 4 Supersymmetry on a Space-Time Lattice, arXiv:1405.0644 [INSPIRE].
D.J. Weir, S. Catterall and D. Mehta, Eigenvalue spectrum of lattice N = 4 super Yang-Mills, arXiv:1311.3676 [INSPIRE].
S. Catterall, P.H. Damgaard, T. Degrand, R. Galvez and D. Mehta, Phase Structure of Lattice N = 4 Super Yang-Mills, JHEP 11 (2012) 072 [arXiv:1209.5285] [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 \( \mathcal{N} \)=(2, 2) and \( \mathcal{N} \)=(8, 8) lattice super Yang-Mills theories, PoS(LATTICE 2011)064 [arXiv:1201.1924] [INSPIRE].
S. Catterall, A. Joseph and T. Wiseman, Gauge theory duals of black hole — black string transitions of gravitational theories on a circle, J. Phys.: Conf. Ser. 462 (2013) 012022 [arXiv:1009.0529] [INSPIRE].
S. Catterall, A. Joseph and T. Wiseman, Thermal phases of D1-branes on a circle from lattice super Yang-Mills, JHEP 12 (2010) 022 [arXiv:1008.4964] [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].
A. Joseph, Lattice formulation of three-dimensional \( \mathcal{N} \)= 4 gauge theory with fundamental matter fields, JHEP 09 (2013) 046 [arXiv:1307.3281] [INSPIRE].
A. Joseph, Supersymmetric quiver gauge theories on the lattice, JHEP 01 (2014) 093 [arXiv:1311.5111] [INSPIRE].
E. Witten, Topological Quantum Field Theory, Commun. Math. Phys. 117 (1988) 353 [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.H. Zimerman, A Lattice Gauge Theory for Fields in the Adjoint Representation, Nuovo Cim. A 84 (1984) 255 [INSPIRE].
P. Cvitanovic, Group theory for Feynman diagrams in non-Abelian gauge theories, Phys. Rev. D 14 (1976) 1536 [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 and A. Joseph, An Object oriented code for simulating supersymmetric Yang-Mills theories, Comput. Phys. Commun. 183 (2012) 1336 [arXiv:1108.1503] [INSPIRE].
E. Corrigan and P. Ramond, A Note on the Quark Content of Large Color Groups, Phys. Lett. B 87 (1979) 73 [INSPIRE].
A. Armoni, M. Shifman and G. Veneziano, Exact results in nonsupersymmetric large-N orientifold field theories, Nucl. Phys. B 667 (2003) 170 [hep-th/0302163] [INSPIRE].
A. Armoni, M. Shifman and G. Veneziano, SUSY relics in one flavor QCD from a new 1/N expansion, Phys. Rev. Lett. 91 (2003) 191601 [hep-th/0307097] [INSPIRE].
D.D. Dietrich, F. Sannino and K. Tuominen, Light composite Higgs from higher representations versus electroweak precision measurements: Predictions for CERN LHC, Phys. Rev. D 72 (2005) 055001 [hep-ph/0505059] [INSPIRE].
I. Affleck, M. Dine and N. Seiberg, Dynamical Supersymmetry Breaking in Chiral Theories, Phys. Lett. B 137 (1984) 187 [INSPIRE].
Y. Meurice and G. Veneziano, SUSY vacua versus chiral fermions, Phys. Lett. B 141 (1984) 69 [INSPIRE].
R.G. Leigh, L. Randall and R. Rattazzi, Unity of supersymmetry breaking models, Nucl. Phys. B 501 (1997) 375 [hep-ph/9704246] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1403.4390
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Joseph, A. Two-dimensional \( \mathcal{N} \) = (2, 2) lattice gauge theories with matter in higher representations. J. High Energ. Phys. 2014, 67 (2014). https://doi.org/10.1007/JHEP07(2014)067
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2014)067