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SU(2) gauge theory with one and two adjoint fermions toward the continuum limit

Andreas Athenodorou1,*, Ed Bennett2,†, Georg Bergner3,‡, Pietro Butti4,5,6,§, Julian Lenz2,7,∥, and Biagio Lucini8,9,¶

  • *Contact author: a.athenodorou@cyi.ac.cy
  • †Contact author: e.j.bennett@swansea.ac.uk
  • ‡Contact author: georg.bergner@uni-jena.de
  • §Contact author: pbutti@sdu.dk.es
  • ∥Contact author: j.lenz@hzdr.de
  • Contact author: b.lucini@qmul.ac.uk
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Phys. Rev. D 113, 074505 – Published 8 April, 2026

DOI: https://doi.org/10.1103/z6bp-cckl

Abstract

We provide an extended lattice study of the SU(2) gauge theory coupled to one Dirac fermion flavor (Nf=1) transforming in the adjoint representation as the continuum limit is approached. This investigation is supplemented by results obtained for the SU(2) gauge theory with two Dirac fermion flavors (Nf=2) transforming in the adjoint representation, for which we perform numerical investigations at three values of the lattice spacing. The purpose of our study is to advance the characterization of the infrared properties of both theories, which previous investigations have concluded to be in the conformal window. For both, we determine the mass spectrum and the anomalous dimension of the fermion condensate using finite-size hyperscaling of the spectrum, mode number analysis of the Dirac operator (for which we improve on our previous proposal) and the ratio of masses of the lightest spin-2 particle over the lightest scalar. All methods provide a consistent picture, with the anomalous dimension of the condensate γ* decreasing significantly as one approaches the continuum limit for the Nf=1 theory towards a value consistent with γ*=0.170(6), while for Nf=2 the anomalous dimension converges more rapidly with β to a value of γ*=0.291(9). A chiral perturbation theory analysis shows that the infrared behavior of both theories is incompatible with the breaking of chiral symmetry.

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References (134)

  1. S. Weinberg, Implications of dynamical symmetry breaking, Phys. Rev. D 13, 974 (1976), 19, 1277(A) (1979).
  2. L. Susskind, Dynamics of spontaneous symmetry breaking in the Weinberg-Salam theory, Phys. Rev. D 20, 2619 (1979).
  3. E. Eichten and K. D. Lane, Dynamical breaking of weak interaction symmetries, Phys. Lett. 90B, 125 (1980).
  4. B. Holdom, Raising the sideways scale, Phys. Rev. D 24, 1441 (1981).
  5. B. Holdom, Techniodor, Phys. Lett. 150B, 301 (1985).
  6. K. Yamawaki, M. Bando, and K.-i. Matumoto, Scale invariant technicolor model and a Technidilaton, Phys. Rev. Lett. 56, 1335 (1986).
  7. T. W. Appelquist, D. Karabali, and L. C. R. Wijewardhana, Chiral hierarchies and the flavor changing neutral current problem in technicolor, Phys. Rev. Lett. 57, 957 (1986).
  8. D. B. Kaplan and H. Georgi, SU(2)×U(1) breaking by vacuum misalignment, Phys. Lett. 136B, 183 (1984).
  9. H. Georgi, Sneaking up on composite models, Phys. Lett. 151B, 57 (1985).
  10. M. J. Dugan, H. Georgi, and D. B. Kaplan, Anatomy of a composite Higgs model, Nucl. Phys. B254, 299 (1985).
  11. J. Barnard, T. Gherghetta, and T. S. Ray, UV descriptions of composite Higgs models without elementary scalars, J. High Energy Phys. 02 (2014) 002.
  12. G. Ferretti and D. Karateev, Fermionic UV completions of composite Higgs models, J. High Energy Phys. 03 (2014) 077.
  13. G. Ferretti, Gauge theories of partial compositeness: Scenarios for Run-II of the LHC, J. High Energy Phys. 06 (2016) 107.
  14. G. Cacciapaglia, G. Ferretti, T. Flacke, and H. Serôdio, Light scalars in composite Higgs models, Front. Phys. 7, 22 (2019).
  15. F. Sannino and M. Shifman, Effective Lagrangians for orientifold theories, Phys. Rev. D 69, 125004 (2004).
  16. F. Sannino and K. Tuominen, Orientifold theory dynamics and symmetry breaking, Phys. Rev. D 71, 051901 (2005).
  17. 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, 055001 (2005).
  18. D. D. Dietrich and F. Sannino, Conformal window of SU(N) gauge theories with fermions in higher dimensional representations, Phys. Rev. D 75, 085018 (2007).
  19. N. Evans and K. S. Rigatos, Chiral symmetry breaking and confinement: Separating the scales, Phys. Rev. D 103, 094022 (2021).
  20. J.-W. Lee, Conformal window from conformal expansion, Phys. Rev. D 103, 076006 (2021).
  21. G. Aad et al. (ATLAS Collaboration), Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716, 1 (2012).
  22. S. Chatrchyan et al. (CMS Collaboration), Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716, 30 (2012).
  23. L. Del Debbio, B. Lucini, A. Patella, C. Pica, and A. Rago, Conformal versus confining scenario in SU(2) with adjoint fermions, Phys. Rev. D 80, 074507 (2009).
  24. A. J. Hietanen, K. Rummukainen, and K. Tuominen, Evolution of the coupling constant in SU(2) lattice gauge theory with two adjoint fermions, Phys. Rev. D 80, 094504 (2009).
  25. Z. Fodor, K. Holland, J. Kuti, D. Nogradi, and C. Schroeder, Nearly conformal gauge theories in finite volume, Phys. Lett. B 681, 353 (2009).
  26. F. Bursa, L. Del Debbio, L. Keegan, C. Pica, and T. Pickup, Mass anomalous dimension in SU(2) with two adjoint fermions, Phys. Rev. D 81, 014505 (2010).
  27. L. Del Debbio, B. Lucini, A. Patella, C. Pica, and A. Rago, Mesonic spectroscopy of minimal walking technicolor, Phys. Rev. D 82, 014509 (2010).
  28. L. Del Debbio, B. Lucini, A. Patella, C. Pica, and A. Rago, The infrared dynamics of minimal walking technicolor, Phys. Rev. D 82, 014510 (2010).
  29. Z. Fodor, K. Holland, J. Kuti, D. Nogradi, C. Schroeder, K. Holland, J. Kuti, D. Nogradi, and C. Schroeder, Twelve massless flavors and three colors below the conformal window, Phys. Lett. B 703, 348 (2011).
  30. F. Bursa, L. Del Debbio, D. Henty, E. Kerrane, B. Lucini, A. Patella, C. Pica, T. Pickup, and A. Rago, Improved lattice spectroscopy of minimal walking technicolor, Phys. Rev. D 84, 034506 (2011).
  31. S. Catterall, L. Del Debbio, J. Giedt, and L. Keegan, MCRG minimal walking technicolor, Phys. Rev. D 85, 094501 (2012).
  32. T. DeGrand, Y. Shamir, and B. Svetitsky, Infrared fixed point in SU(2) gauge theory with adjoint fermions, Phys. Rev. D 83, 074507 (2011).
  33. S. Catterall and F. Sannino, Minimal walking on the lattice, Phys. Rev. D 76, 034504 (2007).
  34. L. Del Debbio, A. Patella, and C. Pica, Higher representations on the lattice: Numerical simulations. SU(2) with adjoint fermions, Phys. Rev. D 81, 094503 (2010).
  35. A. J. Hietanen, J. Rantaharju, K. Rummukainen, and K. Tuominen, Spectrum of SU(2) lattice gauge theory with two adjoint Dirac flavours, J. High Energy Phys. 05 (2009) 025.
  36. S. Catterall, J. Giedt, F. Sannino, and J. Schneible, Phase diagram of SU(2) with 2 flavors of dynamical adjoint quarks, J. High Energy Phys. 11 (2008) 009.
  37. L. Del Debbio, B. Lucini, C. Pica, A. Patella, A. Rago, and S. Roman, Large-volume results in SU(2) with adjoint fermions, in Proceedings of the 31st International Symposium on Lattice Field Theory (2013), 10.22323/1.187.0067.
  38. A. Hasenfratz, D. Schaich, and A. Veernala, Nonperturbative β function of eight-flavor SU(3) gauge theory, J. High Energy Phys. 06 (2015) 143.
  39. A. Athenodorou, E. Bennett, G. Bergner, and B. Lucini, Infrared regime of SU(2) with one adjoint Dirac flavor, Phys. Rev. D 91, 114508 (2015).
  40. T. Appelquist et al., Strongly interacting dynamics and the search for new physics at the LHC, Phys. Rev. D 93, 114514 (2016).
  41. A. Hasenfratz and D. Schaich, Nonperturbative β function of twelve-flavor SU(3) gauge theory, J. High Energy Phys. 02 (2018) 132.
  42. G. Bergner, P. Giudice, I. Montvay, G. Münster, and S. Piemonte, Spectrum and mass anomalous dimension of SU(2) adjoint QCD with two Dirac flavors, Phys. Rev. D 96, 034504 (2017).
  43. G. Bergner, P. Giudice, G. Münster, P. Scior, I. Montvay, and S. Piemonte, Low energy properties of SU(2) gauge theory with Nf=3/2 flavours of adjoint fermions, J. High Energy Phys. 01 (2018) 119.
  44. A. Athenodorou, E. Bennett, G. Bergner, and B. Lucini, Investigating the conformal behavior of SU(2) with one adjoint Dirac flavor, Phys. Rev. D 104, 074519 (2021).
  45. T. DeGrand, Y. Shamir, and B. Svetitsky, SU(4) lattice gauge theory with decuplet fermions: Schrödinger functional analysis, Phys. Rev. D 85, 074506 (2012).
  46. T. DeGrand, Y. Shamir, and B. Svetitsky, Near the sill of the conformal window: Gauge theories with fermions in two-index representations, Phys. Rev. D 88, 054505 (2013).
  47. T. DeGrand, Y. Liu, E. T. Neil, Y. Shamir, and B. Svetitsky, Spectroscopy of SU(4) gauge theory with two flavors of sextet fermions, Phys. Rev. D 91, 114502 (2015).
  48. T. DeGrand and Y. Shamir, One-loop anomalous dimension of top-partner hyperbaryons in a family of composite Higgs models, Phys. Rev. D 92, 075039 (2015).
  49. T. DeGrand, M. Golterman, E. T. Neil, and Y. Shamir, One-loop Chiral Perturbation Theory with two fermion representations, Phys. Rev. D 94, 025020 (2016).
  50. T. A. DeGrand, M. Golterman, W. I. Jay, E. T. Neil, Y. Shamir, and B. Svetitsky, Radiative contribution to the effective potential in composite Higgs models from lattice gauge theory, Phys. Rev. D 94, 054501 (2016).
  51. V. Ayyar, T. DeGrand, M. Golterman, D. C. Hackett, W. I. Jay, E. T. Neil, Y. Shamir, and B. Svetitsky, Spectroscopy of SU(4) composite Higgs theory with two distinct fermion representations, Phys. Rev. D 97, 074505 (2018).
  52. E. Bennett, D. K. Hong, J.-W. Lee, C. J. D. Lin, B. Lucini, M. Piai, and D. Vadacchino, Sp(4) gauge theory on the lattice: Towards SU(4)/Sp(4) composite Higgs (and beyond), J. High Energy Phys. 03 (2018) 185.
  53. V. Ayyar, T. Degrand, D. C. Hackett, W. I. Jay, E. T. Neil, Y. Shamir, and B. Svetitsky, Baryon spectrum of SU(4) composite Higgs theory with two distinct fermion representations, Phys. Rev. D 97, 114505 (2018).
  54. V. Ayyar, T. DeGrand, D. C. Hackett, W. I. Jay, E. T. Neil, Y. Shamir, and B. Svetitsky, Finite-temperature phase structure of SU(4) gauge theory with multiple fermion representations, Phys. Rev. D 97, 114502 (2018).
  55. V. Ayyar, T. DeGrand, D. C. Hackett, W. I. Jay, E. T. Neil, Y. Shamir, and B. Svetitsky, Partial compositeness and baryon matrix elements on the lattice, Phys. Rev. D 99, 094502 (2019).
  56. E. Bennett, D. K. Hong, J.-W. Lee, C. J. D. Lin, B. Lucini, M. Piai, and D. Vadacchino, Sp(4) gauge theories on the lattice: Nf=2 dynamical fundamental fermions, J. High Energy Phys. 12 (2019) 053.
  57. E. Bennett, D. K. Hong, J.-W. Lee, C.-J. D. Lin, B. Lucini, M. Mesiti, M. Piai, J. Rantaharju, and D. Vadacchino, Sp(4) gauge theories on the lattice: Quenched fundamental and antisymmetric fermions, Phys. Rev. D 101, 074516 (2020).
  58. G. Cossu, L. Del Debbio, M. Panero, and D. Preti, Strong dynamics with matter in multiple representations: SU(4) gauge theory with fundamental and sextet fermions, Eur. Phys. J. C 79, 638 (2019).
  59. E. Bennett, D. K. Hong, H. Hsiao, J.-W. Lee, C. J. D. Lin, B. Lucini, M. Mesiti, M. Piai, and D. Vadacchino, Lattice studies of the Sp(4) gauge theory with two fundamental and three antisymmetric Dirac fermions, Phys. Rev. D 106, 014501 (2022).
  60. L. Del Debbio, A. Lupo, M. Panero, and N. Tantalo, Multi-representation dynamics of SU(4) composite Higgs models: Chiral limit and spectral reconstructions, Eur. Phys. J. C 83, 220 (2023).
  61. E. Bennett, J. Holligan, D. K. Hong, H. Hsiao, J.-W. Lee, C. J. D. Lin, B. Lucini, M. Mesiti, M. Piai, and D. Vadacchino, Sp(2N) lattice gauge theories and extensions of the standard model of particle physics, Universe 9, 236 (2023).
  62. E. Bennett et al., Symplectic lattice gauge theories in the grid framework: Approaching the conformal window, Phys. Rev. D 108, 094508 (2023).
  63. A. Maas and F. Zierler, Strong isospin breaking in Sp(4) gauge theory, Proc. Sci., LATTICE2021 (2022) 130 [arXiv:2109.14377].
  64. F. Zierler and A. Maas, Sp(4) SIMP dark matter on the lattice, Proc. Sci., LHCP2021 (2021) 162.
  65. S. Kulkarni, A. Maas, S. Mee, M. Nikolic, J. Pradler, and F. Zierler, Low-energy effective description of dark Sp(4) theories, SciPost Phys. 14, 044 (2023).
  66. B. Lucini, Strongly interacting dynamics beyond the standard model on a spacetime lattice, Phil. Trans. R. Soc. A 368, 3657 (2010).
  67. L. Del Debbio and R. Zwicky, Hyperscaling relations in mass-deformed conformal gauge theories, Phys. Rev. D 82, 014502 (2010).
  68. T. Appelquist, J. Ingoldby, and M. Piai, Dilaton EFT framework for lattice data, J. High Energy Phys. 07 (2017) 035.
  69. T. Appelquist, J. Ingoldby, and M. Piai, Dilaton potential and lattice data, Phys. Rev. D 101, 075025 (2020).
  70. A. Patella, A precise determination of the psibar-psi anomalous dimension in conformal gauge theories, Phys. Rev. D 86, 025006 (2012).
  71. Z. Fodor, K. Holland, J. Kuti, D. Nogradi, and C. H. Wong, The Yang-Mills gradient flow in finite volume, J. High Energy Phys. 11 (2012) 007.
  72. M. García Pérez, A. González-Arroyo, L. Keegan, and M. Okawa, Mass anomalous dimension of Adjoint QCD at large N from twisted volume reduction, J. High Energy Phys. 08 (2015) 034.
  73. C. Pica, Beyond the standard model: Charting fundamental interactions via lattice simulations, Proc. Sci., LATTICE2016 (2016) 015 [arXiv:1701.07782].
  74. O. Witzel, Review on composite Higgs models, Proc. Sci., LATTICE2018 (2019) 006 [arXiv:1901.08216].
  75. M. García Pérez, Prospects for large N gauge theories on the lattice, Proc. Sci., LATTICE2019 (2020) 276 [arXiv:2001.10859].
  76. T. Appelquist, J. Ingoldby, and M. Piai, Dilaton effective field theory, Universe 9, 10 (2023).
  77. K. Rummukainen and K. Tuominen, Lattice computations for beyond standard model physics, Universe 8, 188 (2022).
  78. J.-W. Lee, Strongly coupled gauge theories towards physics beyond the standard model, Proc. Sci., LATTICE2023 (2024) 118.
  79. W. E. Caswell, Asymptotic behavior of nonabelian gauge theories to two loop order, Phys. Rev. Lett. 33, 244 (1974).
  80. T. Banks and A. Zaks, On the phase structure of vector-like gauge theories with massless fermions, Nucl. Phys. B196, 189 (1982).
  81. N. Seiberg, Electric—magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B435, 129 (1995).
  82. M. Unsal, Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions, Phys. Rev. D 80, 065001 (2009).
  83. G. Basar, A. Cherman, D. Dorigoni, and M. Ünsal, Volume independence in the large N limit and an emergent fermionic symmetry, Phys. Rev. Lett. 111, 121601 (2013).
  84. M. M. Anber and E. Poppitz, Two-flavor adjoint QCD, Phys. Rev. D 98, 034026 (2018).
  85. Z. Bi and T. Senthil, Adventure in topological phase transitions in 3+1 -D: Non-Abelian deconfined quantum criticalities and a possible duality, Phys. Rev. X 9, 021034 (2019).
  86. C. Córdova and T. T. Dumitrescu, Candidate phases for SU(2) adjoint QCD4 with two flavors from N=2 supersymmetric Yang-Mills theory, SciPost Phys. 16, 139 (2024).
  87. Z. Wan and J. Wang, Adjoint QCD4, deconfined critical phenomena, symmetry-enriched topological quantum field theory, and higher symmetry-extension, Phys. Rev. D 99, 065013 (2019).
  88. E. Poppitz and T. A. Ryttov, Possible new phase for adjoint QCD, Phys. Rev. D 100, 091901 (2019).
  89. Z. Bi, A. Grebe, G. Kanwar, P. Ledwith, D. Murphy, and M. L. Wagman, Lattice analysis of SU(2) with 1 adjoint Dirac flavor, Proc. Sci., LATTICE2019 (2019) 127 [arXiv:1912.11723].
  90. G. Bergner, J. C. Lopez, S. Piemonte, and I. S. Calero, Lattice simulations of adjoint QCD with one Dirac overlap fermion, Phys. Rev. D 106, 094507 (2022).
  91. G. Bergner and S. Piemonte, Lattice simulations of a gauge theory with mixed adjoint-fundamental matter, Phys. Rev. D 103, 014503 (2021); 107, 019902(E) (2023).
  92. T. A. Ryttov and F. Sannino, Ultra minimal technicolor and its dark matter TIMP, Phys. Rev. D 78, 115010 (2008).
  93. E. Bennett, A. Athenodorou, G. Bergner, P. Butti, and B. Lucini, Update on SU(2) with one adjoint Dirac flavor, Proc. Sci., LATTICE2022 (2023) 204 [arXiv:2212.09173].
  94. A. D. Kennedy, I. Horvath, and S. Sint, A new exact method for dynamical fermion computations with nonlocal actions, Nucl. Phys. B, Proc. Suppl. 73, 834 (1999).
  95. C. Pica and HiRep contributors, HiRep, https://github.com/claudiopica/HiRep.
  96. A. Yamaguchi, P. Boyle, G. Cossu, G. Filaci, C. Lehner, and A. Portelli, Grid: OneCode and FourAPIs, Proc. Sci., LATTICE2021 (2022) 035 [arXiv:2203.06777].
  97. P. Boyle and Grid Contributors, Grid, https://github.com/paboyle/Grid.
  98. S. Martins, E. Kjellgren, E. Molinaro, C. Pica, and A. Rago, GPU-accelerated higher representations of Wilson fermions with HiRep, Proc. Sci., EuroPLEx2023 (2024) 035 [arXiv:2405.19294].
  99. M. Luscher, Topology of lattice gauge fields, Commun. Math. Phys. 85, 39 (1982).
  100. C. Alexandrou, A. Athenodorou, K. Cichy, A. Dromard, E. Garcia-Ramos, K. Jansen, U. Wenger, and F. Zimmermann, Comparison of topological charge definitions in Lattice QCD, Eur. Phys. J. C 80, 424 (2020).
  101. M. Lüscher, Properties and uses of the Wilson flow in lattice QCD, J. High Energy Phys. 08 (2010) 071; 03 (2014) 092(E).
  102. E. Bennett and B. Lucini, Topology of minimal walking technicolor, Eur. Phys. J. C 73, 2426 (2013).
  103. S. Borsányi, S. Dürr, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, and C. McNeile (BMW Collaboration), High-precision scale setting in lattice QCD, J. High Energy Phys. 09 (2012) 010.
  104. A. Athenodorou and M. Teper, The glueball spectrum of SU(3) gauge theory in 3+1 dimensions, J. High Energy Phys. 11 (2020) 172.
  105. M. Luscher and P. Weisz, Definition and general properties of the transfer matrix in continuum limit improved lattice gauge theories, Nucl. Phys. B240, 349 (1984).
  106. M. Luscher and U. Wolff, How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation, Nucl. Phys. B339, 222 (1990).
  107. B. Berg and A. Billoire, Glueball spectroscopy in four-dimensional SU(3) lattice gauge theory. 1, Nucl. Phys. B221, 109 (1983).
  108. B. Lucini, M. Teper, and U. Wenger, Glueballs and k-strings in SU(N) gauge theories: Calculations with improved operators, J. High Energy Phys. 06 (2004) 012.
  109. M. Teper, An improved method for lattice Glueball calculations, Phys. Lett. B 183, 345 (1987).
  110. A. Athenodorou, B. Bringoltz, and M. Teper, Closed flux tubes and their string description in D=3+1 SU(N) gauge theories, J. High Energy Phys. 02 (2011) 030.
  111. P. Goddard, J. Goldstone, C. Rebbi, and C. Thorn, Quantum dynamics of a massless relativistic string, Nucl. Phys. B56, 109 (1973).
  112. L. Del Debbio, B. Lucini, A. Patella, and C. Pica, Quenched mesonic spectrum at large N, J. High Energy Phys. 03 (2008) 062.
  113. F. Joswig, S. Kuberski, J. T. Kuhlmann, and J. Neuendorf, pyerrors: A python framework for error analysis of Monte Carlo data, Comput. Phys. Commun. 288, 108750 (2023).
  114. U. Wolff (ALPHA Collaboration), Monte Carlo errors with less errors, Comput. Phys. Commun. 156, 143 (2004); 176, 383(E) (2007).
  115. G. Bergner, T. Berheide, G. Munster, U. D. Ozugurel, D. Sandbrink, and I. Montvay, The gluino-glue particle and finite size effects in supersymmetric Yang-Mills theory, J. High Energy Phys. 09 (2012) 108.
  116. S. Ali, G. Bergner, H. Gerber, P. Giudice, I. Montvay, G. Münster, S. Piemonte, and P. Scior, The light bound states of N=1 supersymmetric SU(3) Yang-Mills theory on the lattice, J. High Energy Phys. 03 (2018) 113.
  117. A. Cheng, A. Hasenfratz, G. Petropoulos, and D. Schaich, Scale-dependent mass anomalous dimension from Dirac eigenmodes, J. High Energy Phys. 07 (2013) 061.
  118. G. Lepage, B. Clark, C. Davies, K. Hornbostel, P. Mackenzie, C. Morningstar, and H. Trottier, Constrained curve fitting, Nucl. Phys. B, Proc. Suppl. 106–107, 12 (2002).
  119. W. I. Jay and E. T. Neil, Bayesian model averaging for analysis of lattice field theory results, Phys. Rev. D 103, 114502 (2021).
  120. J. Frison, Towards fully Bayesian analyses in Lattice QCD, arXiv:2302.06550.
  121. S. Borsanyi, S. Durr, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, L. Lellouch, T. Lippert, A. Portelli, K. K. Szabo, and B. C. Toth, Ab initio calculation of the neutron-proton mass difference, Science 347, 1452 (2015).
  122. G. Boyd, J. Engels, F. Karsch, E. Laermann, C. Legeland, M. Lutgemeier, and B. Petersson, Thermodynamics of SU(3) lattice gauge theory, Nucl. Phys. B469, 419 (1996).
  123. B. Lucini, M. Teper, and U. Wenger, Properties of the deconfining phase transition in SU(N) gauge theories, J. High Energy Phys. 02 (2005) 033.
  124. A. Athenodorou, E. Bennett, G. Bergner, D. Elander, C. J. D. Lin, B. Lucini, and M. Piai, Large mass hierarchies from strongly-coupled dynamics, J. High Energy Phys. 06 (2016) 114.
  125. B. Lucini and M. Teper, SU(N) gauge theories in four-dimensions: Exploring the approach to N=infinity, J. High Energy Phys. 06 (2001) 050.
  126. A. Gonzalez Arroyo and C. P. Korthals Altes, The spectrum of Yang-Mills theory in a small twisted box, Nucl. Phys. B311, 433 (1988).
  127. D. Daniel, A. Gonzalez-Arroyo, C. P. Korthals Altes, and B. Soderberg, Energy spectrum of SU(2) Yang-Mills fields with space—like symmetric twist, Phys. Lett. B 221, 136 (1989).
  128. D. Daniel, A. Gonzalez-Arroyo, and C. P. Korthals Altes, The energy levels of lattice gauge theory in a small twisted box, Phys. Lett. B 251, 559 (1990).
  129. R. C. Brower, H. Neff, and K. Orginos, The Möbius domain wall fermion algorithm, Comput. Phys. Commun. 220, 1 (2017).
  130. A. Hasenfratz, Y. Shamir, and B. Svetitsky, Taming lattice artifacts with Pauli-Villars fields, Phys. Rev. D 104, 074509 (2021).
  131. www.dirac.ac.uk.
  132. A. Athenodorou, E. Bennett, G. Bergner, P. Butti, J. Lenz, and B. Lucini, SU(2) gauge theory with one and two adjoint fermions towards the continuum limit—data release, 10.5281/zenodo.18837336(2024).
  133. A. Athenodorou, E. Bennett, G. Bergner, and B. Lucini, Investigating the conformal behaviour of SU(2) with one adjoint dirac flavor—data release, 10.5281/zenodo.5139618(2021).
  134. A. Athenodorou, E. Bennett, G. Bergner, P. Butti, J. Lenz, and B. Lucini, SU(2) gauge theory with one and two adjoint fermions towards the continuum limit—analysis workflow, 10.5281/zenodo.18851517(2024).

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Phys. Rev. D 113, 074505– Published 8 April, 2026
  • Received 12 September 2024
  • Revised 5 February 2026
  • Accepted 2 March 2026
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