Abstract
We study aspects of the large-N volume independence on \( {\mathbb{R}^3} \times {L^\Gamma } \), where L Γ is a Γ-site lattice for Yang-Mills theory with adjoint Wilson-fermions. We find the critical number of lattice sites above which the center-symmetry analysis on L Γ agrees with the one on the continuum S 1. For Wilson parameter set to one and Γ≥2, the two analyses agree. One-loop radiative corrections to Wilson-line masses are finite, reminiscent of the UV-insensitivity of the Higgs mass in deconstruction/Little-Higgs theories. Even for theories with Γ=1, volume independence in QCD(adj) may be guaranteed to work by tuning one low-energy effective field theory parameter. Within the parameter space of the theory, at most three operators of the 3d effective field theory exhibit one-loop UV-sensitivity. This opens the analytical prospect to study 4d non-perturbative physics by using lower dimensional field theories (d=3, in our example).
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References
T. Eguchi and H. Kawai, Reduction of dynamical degrees of freedom in the large-N gauge theory, Phys. Rev. Lett. 48 (1982) 1063 [SPIRES].
L.G. Yaffe, Large-N limits as classical mechanics, Rev. Mod. Phys. 54 (1982) 407 [SPIRES].
G. Bhanot, U.M. Heller and H. Neuberger, The quenched Eguchi-Kawai model, Phys. Lett. B 113 (1982) 47 [SPIRES].
B. Bringoltz, Solving two-dimensional large-N QCD with a nonzero density of baryons and arbitrary quark mass, Phys. Rev. D 79 (2009) 125006 [arXiv:0901.4035] [SPIRES].
P. Kovtun, M. Ünsal and L.G. Yaffe, Volume independence in large-N c QCD-like gauge theories, JHEP 06 (2007) 019 [hep-th/0702021] [SPIRES].
M. Ünsal, Phases of N c = ∞ QCD-like gauge theories on S 3 × S 1 and nonperturbative orbifold-orientifold equivalences, Phys. Rev. D 76 (2007) 025015 [hep-th/0703025] [SPIRES].
T.J. Hollowood and J.C. Myers, Finite volume phases of large-N gauge theories with massive adjoint fermions, JHEP 11 (2009) 008 [arXiv:0907.3665] [SPIRES].
B. Bringoltz, Large-N volume reduction of lattice QCD with adjoint Wilson fermions at weak-coupling, JHEP 06 (2009) 091 [arXiv:0905.2406] [SPIRES].
P.F. Bedaque, M.I. Buchoff, A. Cherman and R.P. Springer, Can fermions save large-N dimensional reduction?, JHEP 10 (2009) 070 [arXiv:0904.0277] [SPIRES].
G. Cossu and M. D’Elia, Finite size phase transitions in QCD with adjoint fermions, JHEP 07 (2009) 048 [arXiv:0904.1353] [SPIRES].
B. Bringoltz and S.R. Sharpe, Non-perturbative volume-reduction of large-N QCD with adjoint fermions, Phys. Rev. D 80 (2009) 065031 [arXiv:0906.3538] [SPIRES].
B. Bringoltz and S.R. Sharpe, Breakdown of large-N quenched reduction in SU(N) lattice gauge theories, Phys. Rev. D 78 (2008) 034507 [arXiv:0805.2146] [SPIRES].
M. Hanada, L. Mannelli and Y. Matsuo, Four-dimensional N = 1 super Yang-Mills from matrix model, Phys. Rev. D 80 (2009) 125001 [arXiv:0905.2995] [SPIRES].
M. Hanada, L. Mannelli and Y. Matsuo, Large-N reduced models of supersymmetric quiver, Chern-Simons gauge theories and ABJM, JHEP 11 (2009) 087 [arXiv:0907.4937] [SPIRES].
T. Ishii, G. Ishiki, S. Shimasaki and A. Tsuchiya, N = 4 super Yang-Mills from the plane wave matrix model, Phys. Rev. D 78 (2008) 106001 [arXiv:0807.2352] [SPIRES].
G. Ishiki, S.-W. Kim, J. Nishimura and A. Tsuchiya, Testing a novel large-N reduction for N = 4 super Yang-Mills theory on R × S 3, JHEP 09 (2009) 029 [arXiv:0907.1488] [SPIRES].
J. Kiskis, R. Narayanan and H. Neuberger, Does the crossover from perturbative to nonperturbative physics in QCD become a phase transition at infinite N?, Phys. Lett. B 574 (2003) 65 [hep-lat/0308033] [SPIRES].
H. Georgi and A. Pais, CP-violation as a quantum effect, Phys. Rev. D 10 (1974) 1246 [SPIRES].
H. Neuberger, Note on the effective potential in the 4 + 1 A-HCG model, unpublished (2001).
H.-C. Cheng, C.T. Hill, S. Pokorski and J. Wang, The standard model in the latticized bulk, Phys. Rev. D 64 (2001) 065007 [hep-th/0104179] [SPIRES].
N. Arkani-Hamed, A.G. Cohen and H. Georgi, Electroweak symmetry breaking from dimensional deconstruction, Phys. Lett. B 513 (2001) 232 [hep-ph/0105239] [SPIRES].
J. Giedt, E. Poppitz and M. Rozali, Deconstruction, lattice supersymmetry, anomalies and branes, JHEP 03 (2003) 035 [hep-th/0301048] [SPIRES].
N. Arkani-Hamed, A.G. Cohen and H. Georgi, Twisted supersymmetry and the topology of theory space, JHEP 07 (2002) 020 [hep-th/0109082] [SPIRES].
M. Ünsal and L.G. Yaffe, Center-stabilized Yang-Mills theory: confinement and large-N volume independence, Phys. Rev. D 78 (2008) 065035 [arXiv:0803.0344] [SPIRES].
P.N. Meisinger and M.C. Ogilvie, String tension scaling in high-temperature confined SU(N) gauge theories, arXiv:0905.3577 [SPIRES].
B. Bringoltz, Partial breakdown of center symmetry in large-N QCD with adjoint Wilson fermions, arXiv:0911.0352 [SPIRES].
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ArXiv ePrint: 0911.0358
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Poppitz, E., Ünsal, M. Comments on large-N volume independence. J. High Energ. Phys. 2010, 98 (2010). https://doi.org/10.1007/JHEP01(2010)098
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DOI: https://doi.org/10.1007/JHEP01(2010)098