Remarks on QCD4 with fundamental and adjoint matter

Mohamed Anber (Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, UK) ; Nakarin Lohitsiri (Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, UK) ; Tin Sulejmanpasic (Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, UK)

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 2 N χ $$ {\mathbb{Z}}_{2N}^{\chi } $$ 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 $$ \mathcal{N} $$ = 1 super Yang-Mills theory.

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      "surname": "Sulejmanpasic", 
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  "abstracts": [
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      "source": "Springer", 
      "value": "We study 4-dimensional SU(N) gauge theory with one adjoint Weyl fermion and fundamental matter \u2014 either bosonic or fermionic. Symmetries, their \u2019t 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   <math> <msubsup> <mi>\u2124</mi> <mrow> <mn>2</mn> <mi>N</mi> </mrow> <mi>\u03c7</mi> </msubsup> </math>  $$ {\\mathbb{Z}}_{2N}^{\\chi } $$  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   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 1 super Yang-Mills theory."
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Published on:
12 December 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 12
Pages 1-62
DOI:
https://doi.org/10.1007/JHEP12(2023)063
arXiv:
2306.01849
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

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