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Remarks on QCD 4 with fundamental and adjoint matter

Anber, Mohamed M.; Lohitsiri, Nakarin; Sulejmanpasic, Tin

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We study 4-dimensional SU(N) gauge theory with one adjoint Weyl fermion and fundamental matter — either bosonic or fermionic. Symmetries, their ’t Hooft anomalies, and the Vafa-Witten-Weingarten theorems strongly constrain the possible bulk phases. The first part of the paper is dedicated to a single fundamental fermion or boson. As long as the adjoint Weyl fermion is massless, this theory always possesses a ℤ2Nχ chiral symmetry, which breaks spontaneously, supporting N vacua and domain walls between them for a generic mass of the matter fields. We argue, however, that the domain walls generically undergo a phase transition, and we establish the corresponding 3d gauge theories on the walls. The rest of the paper is dedicated to studying the multi-flavor fundamental matter. Here, the phases crucially depend on the ratio of the number of colors and the number of fundamental flavors. We also discuss the limiting scenarios of heavy adjoint and fundamentals, which align neatly with our current understanding of QCD and N = 1 super Yang-Mills theory.


Anber, M. M., Lohitsiri, N., & Sulejmanpasic, T. (2023). Remarks on QCD 4 with fundamental and adjoint matter. Journal of High Energy Physics, 2023(12), Article 63.

Journal Article Type Article
Acceptance Date Nov 27, 2023
Online Publication Date Dec 12, 2023
Publication Date 2023-12
Deposit Date Dec 20, 2023
Publicly Available Date Dec 20, 2023
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2023
Issue 12
Article Number 63
Keywords Anomalies in Field and String Theories, Discrete Symmetries, Confinement, Nonperturbative Effects
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