Abstract
Supersymmetry (SUSY) has been proposed to be a central concept for the physics beyond the standard model and for a description of the strong interactions in the context of the AdS/CFT correspondence. A deeper understanding of these developments requires the knowledge of the properties of supersymmetric models at finite temperatures. We present a Monte Carlo investigation of the finite temperature phase diagram of the \( \mathcal{N}=1 \) supersymmetric Yang-Mills theory (SYM) regularised on a space-time lattice. The model is in many aspects similar to QCD: quark confinement and fermion condensation occur in the low temperature regime of both theories. A comparison to QCD is therefore possible. The simulations show that for \( \mathcal{N}=1 \) SYM the deconfinement temperature has a mild dependence on the fermion mass. The analysis of the chiral condensate susceptibility supports the possibility that chiral symmetry is restored near the deconfinement phase transition.
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References
J. Engels, J. Fingberg and M. Weber, Finite Size Scaling Analysis of SU(2) Lattice Gauge Theory in (3+1)-dimensions, Nucl. Phys. B 332 (1990) 737 [INSPIRE].
B. Lucini, M. Teper and U. Wenger, The Deconfinement transition in SU(N) gauge theories, Phys. Lett. B 545 (2002) 197 [hep-lat/0206029] [INSPIRE].
Y. Aoki, G. Endrodi, Z. Fodor, S.D. Katz and K.K. Szabo, The Order of the quantum chromodynamics transition predicted by the standard model of particle physics, Nature 443 (2006) 675 [hep-lat/0611014] [INSPIRE].
Y. Aoki, Z. Fodor, S.D. Katz and K.K. Szabo, The Equation of state in lattice QCD: With physical quark masses towards the continuum limit, JHEP 01 (2006) 089 [hep-lat/0510084] [INSPIRE].
A. Bazavov, T. Bhattacharya, M. Cheng, N.H. Christ, C. DeTar et al., Equation of state and QCD transition at finite temperature, Phys. Rev. D 80 (2009) 014504 [arXiv:0903.4379] [INSPIRE].
Y. Aoki, Z. Fodor, S.D. Katz and K.K. Szabo, The QCD transition temperature: Results with physical masses in the continuum limit, Phys. Lett. B 643 (2006) 46 [hep-lat/0609068] [INSPIRE].
Wuppertal-Budapest collaboration, S. Borsányi et al., Is there still any T c mystery in lattice QCD? Results with physical masses in the continuum limit III, JHEP 09 (2010) 073 [arXiv:1005.3508] [INSPIRE].
J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser and A. Karch, From gauge-string duality to strong interactions: A Pedestrian’s Guide, Ann. Rev. Nucl. Part. Sci. 59 (2009) 145 [arXiv:0901.0935] [INSPIRE].
L. Girardello, M.T. Grisaru and P. Salomonson, Temperature and Supersymmetry, Nucl. Phys. B 178 (1981) 331 [INSPIRE].
T.E. Clark and S.T. Love, Supersymmetry at finite temperature, Nucl. Phys. B 217 (1983) 349 [INSPIRE].
A.K. Das, Supersymmetry and Finite Temperature, Physica A 158 (1989) 1 [INSPIRE].
O. Aharony, J. Sonnenschein and S. Yankielowicz, A Holographic model of deconfinement and chiral symmetry restoration, Annals Phys. 322 (2007) 1420 [hep-th/0604161] [INSPIRE].
A. Armoni, M. Shifman and G. Veneziano, From super Yang-Mills theory to QCD: Planar equivalence and its implications, World Scientific, 2004, hep-th/0403071 [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].
L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, The Supergravity dual of N = 1 super Yang-Mills theory, Nucl. Phys. B 569 (2000) 451 [hep-th/9909047] [INSPIRE].
I. Montvay, An algorithm for gluinos on the lattice, Nucl. Phys. B 466 (1996) 259 [hep-lat/9510042] [INSPIRE].
G. Veneziano and S. Yankielowicz, An Effective Lagrangian for the Pure N = 1 Supersymmetric Yang-Mills Theory, Phys. Lett. B 113 (1982) 231 [INSPIRE].
G.R. Farrar, G. Gabadadze and M. Schwetz, On the effective action of N = 1 supersymmetric Yang-Mills theory, Phys. Rev. D 58 (1998) 015009 [hep-th/9711166] [INSPIRE].
G. Bergner, T. Berheide, G. Munster, U.D. Ozugurel, D. Sandbrink et al., The gluino-glue particle and finite size effects in supersymmetric Yang-Mills theory, JHEP 09 (2012) 108 [arXiv:1206.2341] [INSPIRE].
G. Bergner, I. Montvay, G. Münster, U.D. Özugurel and D. Sandbrink, Towards the spectrum of low-lying particles in supersymmetric Yang-Mills theory, JHEP 11 (2013) 061 [arXiv:1304.2168] [INSPIRE].
G. Bergner, Complete supersymmetry on the lattice and a No-Go theorem, JHEP 01 (2010) 024 [arXiv:0909.4791] [INSPIRE].
M. Kato, M. Sakamoto and H. So, Taming the Leibniz Rule on the Lattice, JHEP 05 (2008) 057 [arXiv:0803.3121] [INSPIRE].
G. Curci and G. Veneziano, Supersymmetry and the Lattice: A Reconciliation?, Nucl. Phys. B 292 (1987) 555 [INSPIRE].
H. Suzuki, Supersymmetry, chiral symmetry and the generalized BRS transformation in lattice formulations of 4D \( \mathcal{N}=1 \) SYM, Nucl. Phys. B 861 (2012) 290 [arXiv:1202.2598] [INSPIRE].
G. Münster and H. Stüwe, The mass of the adjoint pion in \( \mathcal{N}=1 \) supersymmetric Yang-Mills theory, JHEP 05 (2014) 034 [arXiv:1402.6616] [INSPIRE].
D. Amati, K. Konishi, Y. Meurice, G.C. Rossi and G. Veneziano, Nonperturbative Aspects in Supersymmetric Gauge Theories, Phys. Rept. 162 (1988) 169 [INSPIRE].
B. Svetitsky and L.G. Yaffe, Critical Behavior at Finite Temperature Confinement Transitions, Nucl. Phys. B 210 (1982) 423 [INSPIRE].
DESY-Munster collaboration, R. Kirchner, I. Montvay, J. Westphalen, S. Luckmann and K. Spanderen, Evidence for discrete chiral symmetry breaking in N = 1 supersymmetric Yang-Mills theory, Phys. Lett. B 446 (1999) 209 [hep-lat/9810062] [INSPIRE].
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].
G. Bergner and J. Wuilloud, Acceleration of the Arnoldi method and real eigenvalues of the non-Hermitian Wilson-Dirac operator, Comput. Phys. Commun. 183 (2012) 299 [arXiv:1104.1363] [INSPIRE].
R. Sommer, A New way to set the energy scale in lattice gauge theories and its applications to the static force and α s in SU(2) Yang-Mills theory, Nucl. Phys. B 411 (1994) 839 [hep-lat/9310022] [INSPIRE].
S. Borsányi, S. Dürr, Z. Fodor, C. Hölbling, S.D. Katz et al., High-precision scale setting in lattice QCD, JHEP 09 (2012) 010 [arXiv:1203.4469] [INSPIRE].
V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Exact Gell-Mann-Low Function of Supersymmetric Yang-Mills Theories from Instanton Calculus, Nucl. Phys. B 229 (1983) 381 [INSPIRE].
A.K. De, A. Harindranath and J. Maiti, On Scale Determination in Lattice QCD with Dynamical Quarks, arXiv:0803.1281 [INSPIRE].
S. Necco and R. Sommer, The N(f) = 0 heavy quark potential from short to intermediate distances, Nucl. Phys. B 622 (2002) 328 [hep-lat/0108008] [INSPIRE].
A.M. Ferrenberg and D.P. Landau, Critical behavior of the three-dimensional Ising model: A high-resolution Monte Carlo study, Phys. Rev. B 44 (1991) 5081.
G. Cella, G. Curci, R. Tripiccione and A. Vicere, Scaling, asymptotic scaling and Symanzik improvement. Deconfinement temperature in SU(2) pure gauge theory, Phys. Rev. D 49 (1994) 511 [hep-lat/9306011] [INSPIRE].
F. Karsch and M. Lutgemeier, Deconfinement and chiral symmetry restoration in an SU(3) gauge theory with adjoint fermions, Nucl. Phys. B 550 (1999) 449 [hep-lat/9812023] [INSPIRE].
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Bergner, G., Giudice, P., Münster, G. et al. Phase structure of the \( \mathcal{N}=1 \) supersymmetric Yang-Mills theory at finite temperature. J. High Energ. Phys. 2014, 49 (2014). https://doi.org/10.1007/JHEP11(2014)049
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DOI: https://doi.org/10.1007/JHEP11(2014)049