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Candidate Phases for SU(2) Adjoint QCD$_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
by Clay Córdova, Thomas T. Dumitrescu
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Submission summary
| Authors (as registered SciPost users): | Clay Córdova · Thomas Dumitrescu |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1806.09592v2 (pdf) |
| Date accepted: | 2024-05-13 |
| Date submitted: | 2024-05-07 16:24 |
| Submitted by: | Córdova, Clay |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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 $\mathcal{N}=2$ 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 $\mathcal{N}=2$ theories. Since every vacuum on the Coulomb branch of the $\mathcal{N}=2$ 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 $\mathbb{CP}^1$ sigma model, which we analyze in detail. Certain topological couplings that are likely to be present in this $\mathbb{CP}^1$ 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 $\mathcal{N}=2$ theory and conjecture that the $\mathbb{CP}^1$ phase eventually becomes dominant.
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List of changes
We thank the referees for their comments. In response we have made the following changes:
1) corrected all identified typos
2) added the final paragraph of the introduction with reference to more recent work
3) corrected mistake on page 4: 4Nc-> 2NfNc
4) corrected footnote 55
5) added footnote 60 about the biholomorphism between the u plane and the tau plane (with related references)
Finally with regard to the questions about different global forms of the gauge group, eg SO(3) we have not investigated the question in detail, but view it as an interesting topic for future investigations, both in this model and in more general theories with gauge group lie algebra SU(N).
Published as SciPost Phys. 16, 139 (2024)