Phase structure of lattice \(\mathcal{N}=4\) super Yang-Mills. (English) Zbl 1397.81349
Summary: We make a first study of the phase diagram of four-dimensional \(\mathcal{N}=4\) super Yang-Mills theory regulated on a space-time lattice. The lattice formulation we employ is both gauge invariant and retains at all lattice spacings one exactly preserved supersymmetry charge. Our numerical results are consistent with the existence of a single deconfined phase at all observed values of the bare coupling.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
References:
| [1] | Kaplan, DB, Recent developments in lattice supersymmetry, Nucl. Phys. Proc. Suppl., 129, 109, (2004) · doi:10.1016/S0920-5632(03)02512-X |
| [2] | Giedt, J., Deconstruction and other approaches to supersymmetric lattice field theories, Int. J. Mod. Phys., A 21, 3039, (2006) · Zbl 1102.81061 |
| [3] | Catterall, S.; Kaplan, DB; Ünsal, M., Exact lattice supersymmetry, Phys. Rept., 484, 71, (2009) · doi:10.1016/j.physrep.2009.09.001 |
| [4] | Joseph, A., Supersymmetric Yang-Mills theories with exact supersymmetry on the lattice, Int. J. Mod. Phys., A 26, 5057, (2011) · Zbl 1263.81254 |
| [5] | Sugino, F., A lattice formulation of super Yang-Mills theories with exact supersymmetry, JHEP, 01, 015, (2004) · Zbl 1243.81125 · doi:10.1088/1126-6708/2004/01/015 |
| [6] | Sugino, F., Super Yang-Mills theories on the two-dimensional lattice with exact supersymmetry, JHEP, 03, 067, (2004) · doi:10.1088/1126-6708/2004/03/067 |
| [7] | D’Adda, A.; Kanamori, I.; Kawamoto, N.; Nagata, K., Exact extended supersymmetry on a lattice: twisted \(N\) = 2 super Yang-Mills in two dimensions, Phys. Lett., B 633, 645, (2006) · Zbl 1247.81464 |
| [8] | D’Adda, A.; Kanamori, I.; Kawamoto, N.; Nagata, K., Exact extended supersymmetry on a lattice: twisted \(N\) = 4 super Yang-Mills in three dimensions, Nucl. Phys., B 798, 168, (2008) · Zbl 1234.81103 · doi:10.1016/j.nuclphysb.2008.01.026 |
| [9] | Kanamori, I.; Suzuki, H., Restoration of supersymmetry on the lattice: two-dimensional \(N\) = (2,2) supersymmetric Yang-Mills theory, Nucl. Phys., B 811, 420, (2009) · Zbl 1194.81233 · doi:10.1016/j.nuclphysb.2008.11.021 |
| [10] | Hanada, M.; Kanamori, I., Lattice study of two-dimensional \(N\) = (2, 2) super Yang-Mills at large-\(N\), Phys. Rev., D 80, 065014, (2009) |
| [11] | Hanada, M.; Matsuura, S.; Sugino, F., Two-dimensional lattice for four-dimensional \(N\) = 4 supersymmetric Yang-Mills, Prog. Theor. Phys., 126, 597, (2011) · Zbl 1248.81140 · doi:10.1143/PTP.126.597 |
| [12] | Hanada, M., A proposal of a fine tuning free formulation of 4d N = 4 super Yang-Mills, JHEP, 11, 112, (2010) · Zbl 1294.81108 · doi:10.1007/JHEP11(2010)112 |
| [13] | Hanada, M.; Matsuura, S.; Sugino, F., Non-perturbative construction of 2\(D\) and 4\(D\) supersymmetric Yang-Mills theories with 8 supercharges, Nucl. Phys., B 857, 335, (2012) · Zbl 1246.81129 · doi:10.1016/j.nuclphysb.2011.12.014 |
| [14] | Maldacena, JM, Wilson loops in large-\(N\) field theories, Phys. Rev. Lett., 80, 4859, (1998) · Zbl 0947.81128 · doi:10.1103/PhysRevLett.80.4859 |
| [15] | Ünsal, M., Twisted supersymmetric gauge theories and orbifold lattices, JHEP, 10, 089, (2006) · doi:10.1088/1126-6708/2006/10/089 |
| [16] | Damgaard, PH; Matsuura, S., Relations among supersymmetric lattice gauge theories via orbifolding, JHEP, 08, 087, (2007) · Zbl 1326.81201 · doi:10.1088/1126-6708/2007/08/087 |
| [17] | Catterall, S., From twisted supersymmetry to orbifold lattices, JHEP, 01, 048, (2008) · doi:10.1088/1126-6708/2008/01/048 |
| [18] | Takimi, T., Relationship between various supersymmetric lattice models, JHEP, 07, 010, (2007) · doi:10.1088/1126-6708/2007/07/010 |
| [19] | Witten, E., Topological quantum field theory, Commun. Math. Phys., 117, 353, (1988) · Zbl 0656.53078 · doi:10.1007/BF01223371 |
| [20] | Elitzur, S.; Rabinovici, E.; Schwimmer, A., Supersymmetric models on the lattice, Phys. Lett., B 119, 165, (1982) |
| [21] | Marcus, N., The other topological twisting of \(N\) = 4 Yang-Mills, Nucl. Phys., B 452, 331, (1995) · Zbl 0925.81348 · doi:10.1016/0550-3213(95)00389-A |
| [22] | Kapustin, A.; Witten, E., Electric-magnetic duality and the geometric Langlands program, Commun. Num. Theor. Phys., 1, 1, (2007) · Zbl 1128.22013 |
| [23] | Aratyn, H.; Goto, M.; Zimerman, A., A lattice gauge theory for fields in the adjoint representation, Nuovo Cim., A 84, 255, (1984) · doi:10.1007/BF02778189 |
| [24] | Cohen, AG; Kaplan, DB; Katz, E.; Ünsal, M., Supersymmetry on a Euclidean space-time lattice. 1. A target theory with four supercharges, JHEP, 08, 024, (2003) · doi:10.1088/1126-6708/2003/08/024 |
| [25] | Cohen, AG; Kaplan, DB; Katz, E.; Ünsal, M., Supersymmetry on a Euclidean space-time lattice. 2. target theories with eight supercharges, JHEP, 12, 031, (2003) · doi:10.1088/1126-6708/2003/12/031 |
| [26] | Kaplan, DB; Ünsal, M., A Euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges, JHEP, 09, 042, (2005) · doi:10.1088/1126-6708/2005/09/042 |
| [27] | Damgaard, PH; Matsuura, S., Geometry of orbifolded supersymmetric lattice gauge theories, Phys. Lett., B 661, 52, (2008) · Zbl 1246.81179 |
| [28] | Rabin, JM, Homology theory of lattice fermion doubling, Nucl. Phys., B 201, 315, (1982) · doi:10.1016/0550-3213(82)90434-5 |
| [29] | Becher, P.; Joos, H., The Dirac-Kähler equation and fermions on the lattice, Z. Phys., C 15, 343, (1982) |
| [30] | Banks, T.; Dothan, Y.; Horn, D., Geometric fermions, Phys. Lett., B 117, 413, (1982) |
| [31] | Kanamori, I., Lattice formulation of two-dimensional \(N\) = (2, 2) super Yang-Mills with SU(\(N\)) gauge group, JHEP, 07, 021, (2012) · Zbl 1397.81380 · doi:10.1007/JHEP07(2012)021 |
| [32] | Hanada, M.; Kanamori, I., Absence of sign problem in two-dimensional \(N\) = (2, 2) super Yang-Mills on lattice, JHEP, 01, 058, (2011) · Zbl 1214.81155 · doi:10.1007/JHEP01(2011)058 |
| [33] | Catterall, S.; Galvez, R.; Joseph, A.; Mehta, D., On the sign problem in 2\(D\) lattice super Yang-Mills, JHEP, 01, 108, (2012) · Zbl 1306.81085 · doi:10.1007/JHEP01(2012)108 |
| [34] | 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]. |
| [35] | 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]. |
| [36] | Catterall, S.; Dzienkowski, E.; Giedt, J.; Joseph, A.; Wells, R., Perturbative renormalization of lattice \(N\) = 4 super Yang-Mills theory, JHEP, 04, 074, (2011) · Zbl 1250.81069 · doi:10.1007/JHEP04(2011)074 |
| [37] | D. Mehta, Lattice vs. continuum: landau gauge fixing and ’t Hooft-Polyakov monopoles, Ph.D. thesis, The University of Adelaide, Adelaide, Australia (2009). |
| [38] | L. von Smekal, A. Jorkowski, D. Mehta and A. Sternbeck, Lattice Landau gauge via stereographic projection, PoS(CONFINEMENT8)048 [arXiv:0812.2992] [INSPIRE]. |
| [39] | L. von Smekal, D. Mehta, A. Sternbeck and A.G. Williams, Modified lattice Landau gauge, PoS(LATTICE 2007)382 [arXiv:0710.2410] [INSPIRE]. |
| [40] | Catterall, S.; Joseph, A., An object oriented code for simulating supersymmetric Yang-Mills theories, Comput. Phys. Commun., 183, 1336, (2012) · doi:10.1016/j.cpc.2012.01.024 |
| [41] | R. Galvez and G. van Anders, Accelerating the solution of families of shifted linear systems with CUDA, arXiv:1102.2143 [INSPIRE]. |
| [42] | Krauth, W.; Staudacher, M., Eigenvalue distributions in Yang-Mills integrals, Phys. Lett., B 453, 253, (1999) · Zbl 1058.81731 |
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.
