Candidate phases for SU(2) adjoint QCD$$_4$$ with two flavors from $$\mathcal{N}=2$$ supersymmetric Yang-Mills theory

Journal Article · Wed May 29 00:00:00 EDT 2024 · SciPost Physics

DOI:https://doi.org/10.21468/scipostphys.16.5.139· OSTI ID:2478701

Córdova, Clay ^[1]; Dumitrescu, Thomas ^[2]

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1. Institute for Advanced Study, Princeton, NJ (United States); University of California, Los Angeles
2. Harvard University, Cambridge, MA (United States)

We study four-dimensional adjoint QCD with gauge group SU(2) and two Weyl fermion flavors, which has an SU(2)_R chiral symmetry. The infrared behavior of this theory is not firmly established. We explore candidate infrared phases by embedding adjoint QCD into N = 2 supersymmetric Yang-Mills theory deformed by a supersymmetry-breaking scalar mass M that preserves all global symmetries and 't Hooft anomalies. This includes 't Hooft anomalies that are only visible when the theory is placed on manifolds that do not admit a spin structure. The consistency of this procedure is guaranteed by a nonabelian spin-charge relation involving the SU(2)_R symmetry that is familiar from topologically twisted N = 2 theories. Since every vacuum on the Coulomb branch of the N = 2 theory necessarily matches all 't Hooft anomalies, we can generate candidate phases for adjoint QCD by deforming the theories in these vacua while preserving all symmetries and 't Hooft anomalies. One such deformation is the supersymmetry-breaking scalar mass M itself, which can be reliably analyzed when M is small. In this regime it gives rise to an exotic Coulomb phase without chiral symmetry breaking. By contrast, the theory near the monopole and dyon points can be deformed to realize a candidate phase with monopole-induced confinement and chiral symmetry breaking. The low-energy theory consists of two copies of a CP¹ sigma model, which we analyze in detail. Certain topological couplings that are likely to be present in this CP¹ model turn the confining solitonic string of the model into a topological insulator. We also examine the behavior of various candidate phases under fermion mass deformations. We speculate on the possible large-M behavior of the deformed N = 2 theory and conjecture that the CP¹ phase eventually becomes dominant.

• Research Organization: University of California, Los Angeles, CA (United States)
• Sponsoring Organization: John Templeton Foundation; National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0009988; SC0020421
• OSTI ID: 2478701
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 5 Vol. 16; ISSN 2542-4653
• Publisher: SciPost Foundation
• Country of Publication: United States
• Language: English