Cascading from $$\mathscr{N}$$ = 2 supersymmetric Yang–Mills theory to confinement and chiral symmetry breaking in adjoint QCD

Journal Article · Sat Nov 08 00:00:00 EST 2025 · Physics Reports

DOI:https://doi.org/10.1016/j.physrep.2025.10.007· OSTI ID:3006238

D’Hoker, Eric ^[1]; Dumitrescu, Thomas T. ^[1]; Gerchkovitz, Efrat ^[2]; Nardoni, Emily ^[3]

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1. Univ. of California, Los Angeles, CA (United States)
2. Weizmann Institute of Science, Rehovot (Israel)
3. Vassar College, Poughkeepsie, NY (United States)

We argue that adjoint QCD in 3 + 1 dimensions, with any SU(N) gauge group and two Weyl fermion flavors (i.e. one adjoint Dirac fermion), confines and spontaneously breaks its chiral symmetries via the condensation of a fermion bilinear. We flow to this theory from pure $$\mathscr{N}$$ = 2 SUSY Yang–Mills theory with the same gauge group, by giving a SUSY-breaking mass M to the scalars in the $$\mathscr{N}$$ = 2 vector multiplet. This flow can be analyzed rigorously at small M, where it leads to a deconfined vacuum at the origin of the $$\mathscr{N}$$ = 2 Coulomb branch. The analysis can be extended to all M using an Abelian dual description that arises from the N multi-monopole points of the $$\mathscr{N}$$ = 2 theory. At each such point, there are N −1 hypermultiplet Higgs fields h$$^{i=1,2}_m$$, which are SU(2)_R doublets. We provide a detailed study of the phase diagram as a function of M, by analyzing the semi-classical phases of the dual using a combination of analytic and numerical techniques. The result is a cascade of first-order phase transitions, along which the Higgs fields h i m successively turn on, and which interpolates between the Coulomb branch at small M, where all h$$^{i}_m$$ = 0, and a maximal Higgs branch, where all h$$^{i}_m$$ ≠ 0, at sufficiently large M. We show that this maximal Higgs branch precisely matches the confining and chiral symmetry breaking phase of two-flavor adjoint QCD, including its broken and unbroken symmetries, its massless spectrum, and the expected large-N scaling of various observables. The spontaneous breaking pattern SU(2)_R → U(1)_R, consistent with the Vafa–Witten theorem, is ensured by an intricate alignment mechanism for the h$$^{i}_m$$ in the dual, and leads to a CP¹ sigma model of increasing radius along the cascade.

• Research Organization: Univ. of California, Los Angeles, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0009937; SC0020421; SC0025534
• OSTI ID: 3006238
• Journal Information: Physics Reports, Journal Name: Physics Reports Vol. 1158; ISSN 0370-1573
• Publisher: Elsevier
• Country of Publication: United States
• Language: English