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  • Open Access

Near-SUSY to non-SUSY crossover

Dan Kondo1,*, Hitoshi Murayama1,2,3,†,‡, and Bea Noether2,§

  • *Contact author: dan.kondo@ipmu.jp
  • †Contact author: hitoshi@berkeley.edu
  • ‡Professor at Hamamatsu.
  • §Contact author: bea_noether@berkeley.edu

Phys. Rev. D 112, 114021 – Published 15 December, 2025

DOI: https://doi.org/10.1103/9mjb-bp8g

Abstract

Gauge theories can be solved exactly slightly away from the supersymmetric (SUSY) limit softly broken by anomaly mediation when the size of SUSY breaking is much smaller than the dynamical scale (m≪Λ). We show empirical evidence that the near-SUSY limit is continuously connected to the non-SUSY limit (m≫Λ) in SU(Nc) gauge theories with Nf quarks in the fundamental representation. The evidence includes the behavior of quark bilinear condensate and gluon condensates, light hadron spectra, and consistency with the large Nc limit including the Witten-Veneziano relations between the topological susceptibility and mη′ and mπ. In addition, we present new predictions when Nf/Nc≳O(1).

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References (68)

  1. J. Chadwick, The existence of a neutron, Proc. R. Soc. A 136, 692 (1932).
  2. H. Yukawa, On the interaction of elementary particles I, Proc. Phys. Math. Soc. Jpn. 17, 48 (1935).
  3. S. H. Neddermeyer and C. D. Anderson, Note on the nature of cosmic ray particles, Phys. Rev. 51, 884 (1937).
  4. Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. 1, Phys. Rev. 122, 345 (1961).
  5. Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. II, Phys. Rev. 124, 246 (1961).
  6. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Microscopic theory of superconductivity, Phys. Rev. 106, 162 (1957).
  7. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  8. G. F. Chew and S. C. Frautschi, Regge trajectories and the principle of maximum strength for strong interactions, Phys. Rev. Lett. 8, 41 (1962).
  9. M. Gell-Mann, The eightfold way: A theory of strong interaction symmetry, https://inspirehep.net/literature/44998.
  10. M. Gell-Mann, A schematic model of baryons and mesons, Phys. Lett. 8, 214 (1964).
  11. G. Zweig, An SU(3) model for strong interaction symmetry and its breaking. Version 2, https://inspirehep.net/literature/4674.
  12. M. Y. Han and Y. Nambu, Three triplet model with double SU(3) symmetry, Phys. Rev. 139, B1006 (1965).
  13. H. Fritzsch, M. Gell-Mann, and H. Leutwyler, Advantages of the color octet gluon picture, Phys. Lett. 47B, 365 (1973).
  14. R. P. Feynman, Very high-energy collisions of hadrons, Phys. Rev. Lett. 23, 1415 (1969).
  15. D. J. Gross and F. Wilczek, Ultraviolet behavior of non-Abelian gauge theories, Phys. Rev. Lett. 30, 1343 (1973).
  16. H. D. Politzer, Reliable perturbative results for strong interactions?, Phys. Rev. Lett. 30, 1346 (1973).
  17. J. J. Aubert et al. (E598 Collaboration), Experimental observation of a heavy particle J, Phys. Rev. Lett. 33, 1404 (1974).
  18. J. E. Augustin et al. (SLAC-SP-017 Collaboration), Discovery of a narrow resonance in e+e− annihilation, Phys. Rev. Lett. 33, 1406 (1974).
  19. G. S. Abrams et al., The discovery of a second narrow resonance in e+e− annihilation, Phys. Rev. Lett. 33, 1453 (1974).
  20. G. Goldhaber et al., Observation in e+e− annihilation of a narrow state at 1865  MeV/c2 decaying to Kπ and Kπππ, Phys. Rev. Lett. 37, 255 (1976).
  21. S. Mandelstam, Vortices and quark confinement in non-Abelian gauge theories, Phys. Rep. 23, 245 (1976).
  22. K. G. Wilson, Confinement of quarks, Phys. Rev. D 10, 2445 (1974).
  23. T. Degrand and C. Detar, Lattice Methods for Quantum Chromodynamics (World Scientific Publishing Company, Singapore, 2006).
  24. C. Gattringer and C. B. Lang, Quantum Chromodynamics on the Lattice (Springer, Berlin, 2010), Vol. 788.
  25. L. Lellouch, Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance Computing: Lecture Notes of the Les Houches Summer School: Volume 93, 2009, Lecture Notes of the Les Houches Summer School (OUP, Oxford, 2011).
  26. N. Seiberg and E. Witten, Electric—magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory, Nucl. Phys. B426, 19 (1994); B430, 485(E) (1994).
  27. N. Seiberg, Exact results on the space of vacua of four-dimensional SUSY gauge theories, Phys. Rev. D 49, 6857 (1994).
  28. K. A. Intriligator, ‘Integrating in’ and exact superpotentials in 4-d, Phys. Lett. B 336, 409 (1994).
  29. K. A. Intriligator, R. G. Leigh, and N. Seiberg, Exact superpotentials in four-dimensions, Phys. Rev. D 50, 1092 (1994).
  30. K. A. Intriligator and P. Pouliot, Exact superpotentials, quantum vacua and duality in supersymmetric SP(NC) gauge theories, Phys. Lett. B 353, 471 (1995).
  31. K. A. Intriligator and N. Seiberg, Lectures on supersymmetric gauge theories and electric-magnetic duality, Nucl. Phys. B, Proc. Suppl. 45BC, 1 (1996).
  32. H. Murayama, Some exact results in QCD-like theories, Phys. Rev. Lett. 126, 251601 (2021).
  33. C. Csáki, H. Murayama, and O. Telem, Some exact results in chiral gauge theories, Phys. Rev. D 104, 065018 (2021).
  34. C. Csáki, H. Murayama, and O. Telem, More exact results on chiral gauge theories: The case of the symmetric tensor, Phys. Rev. D 105, 045007 (2022).
  35. C. Csáki, A. Gomes, H. Murayama, and O. Telem, Demonstration of confinement and chiral symmetry breaking in SO(Nc) gauge theories, Phys. Rev. Lett. 127, 251602 (2021).
  36. C. Csáki, A. Gomes, H. Murayama, and O. Telem, Phases of nonsupersymmetric gauge theories: The SO(Nc) case study, Phys. Rev. D 104, 114018 (2021).
  37. D. Kondo, H. Murayama, and C. Sylber, Dynamics of simplest chiral gauge theories, arXiv:2209.09287.
  38. J. M. Leedom, H. Murayama, G. Singh, B. Suter, and J. Wong, Exact results in chiral gauge theories with flavor, Phys. Rev. D 112, 025001 (2025).
  39. A. Goh, H. Murayama, G. Singh, B. Suter, and J. Wong, Dynamics of E6 chiral gauge theories, Phys. Rev. D 112, 045001 (2025).
  40. M. Dine and Y. Yu, Challenges to obtaining results for real QCD from SUSY QCD, arXiv:2205.00115.
  41. M. Dine, On the possibility of demonstrating confinement in non-supersymmetric theories by deforming confining supersymmetric theories, arXiv:2211.17134.
  42. S. P. Martin and J. D. Wells, Chiral symmetry breaking and effective Lagrangians for softly broken supersymmetric QCD, Phys. Rev. D 58, 115013 (1998).
  43. C. Csáki, A. Gomes, H. Murayama, B. Noether, D. R. Varier, and O. Telem, Guide to anomaly-mediated supersymmetry-breaking QCD, Phys. Rev. D 107, 054015 (2023).
  44. M. M. Parish, The BCS–BEC crossover, in Quantum Gas Experiments: Exploring Many-Body States (World Scientific, Singapore, 2015), pp. 179–197.
  45. Q. Chen, Z. Wang, R. Boyack, S. Yang, and K. Levin, When superconductivity crosses over: From BCS to BEC, Rev. Mod. Phys. 96, 025002 (2024).
  46. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
  47. D. Kondo, H. Murayama, B. Noether, and D. R. Varier, Broken conformal window, J. High Energy Phys. 04 (2025) 152.
  48. A. Luzio and L.-X. Xu, On the derivation of chiral symmetry breaking in QCD-like theories and s-confining theories, J. High Energy Phys. 08 (2022) 016.
  49. C. H. de Lima and D. Stolarski, On s-confining SUSY-QCD with anomaly mediation, J. High Energy Phys. 10 (2023) 020.
  50. C. Csáki, R. Tito D’Agnolo, R. S. Gupta, E. Kuflik, T. S. Roy, and M. Ruhdorfer, On the dynamical origin of the η′ potential and the axion mass, J. High Energy Phys. 10 (2023) 139.
  51. M. Bando, T. Kugo, S. Uehara, K. Yamawaki, and T. Yanagida, Is rho meson a dynamical gauge boson of hidden local symmetry?, Phys. Rev. Lett. 54, 1215 (1985).
  52. M. Bando, T. Kugo, and K. Yamawaki, On the vector mesons as dynamical gauge bosons of hidden local symmetries, Nucl. Phys. B259, 493 (1985).
  53. K. Yamawaki, Dynamical gauge boson of hidden local symmetry within the standard model, arXiv:1803.07271.
  54. K. Yamawaki, Proving rho meson is a dynamical gauge boson of hidden local symmetry, Symmetry 15, 2209 (2023).
  55. N. Arkani-Hamed and H. Murayama, Renormalization group invariance of exact results in supersymmetric gauge theories, Phys. Rev. D 57, 6638 (1998).
  56. E. Witten, Current algebra theorems for the U(1) Goldstone boson, Nucl. Phys. B156, 269 (1979).
  57. G. Veneziano, U(1) without instantons, Nucl. Phys. B159, 213 (1979).
  58. P. Dimopoulos et al., Topological susceptibility and η′ meson mass from Nf=2 lattice QCD at the physical point, Phys. Rev. D 99, 034511 (2019).
  59. G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B72, 461 (1974).
  60. G. Veneziano, Some aspects of a unified approach to gauge, dual and Gribov theories, Nucl. Phys. B117, 519 (1976).
  61. E. D’Hoker and E. Farhi, Decoupling a fermion whose mass is generated by a Yukawa coupling: The general case, Nucl. Phys. B248, 59 (1984).
  62. D. Kondo, R. McGehee, T. Melia, and H. Murayama, Linear sigma dark matter, J. High Energy Phys. 09 (2022) 041.
  63. R. L. Jaffe, Multi-quark hadrons. 1. The phenomenology of (2 quark 2 anti-quark) mesons, Phys. Rev. D 15, 267 (1977).
  64. R. A. Briceño, J. J. Dudek, R. G. Edwards, and D. J. Wilson, Isoscalar ππ scattering and the σ meson resonance from QCD, Phys. Rev. Lett. 118, 022002 (2017).
  65. R. A. Briceño, J. J. Dudek, R. G. Edwards, and D. J. Wilson, Isoscalar ππ,KK¯,ηη scattering and the σ,f0,f2 mesons from QCD, Phys. Rev. D 97, 054513 (2018).
  66. M. Lüscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B354, 531 (1991).
  67. J. R. Peláez, From controversy to precision on the sigma meson: A review on the status of the non-ordinary f0(500) resonance, Phys. Rep. 658, 1 (2016).
  68. K. Fujikawa and H. Suzuki, Anomalies, local counter terms and bosonization, Phys. Rep. 398, 221 (2004).

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