Hunting 3d $\mathcal{N}=1$ SQED in the $ε$-expansion
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917725330210816 |
|---|---|
| author | Breitstein, Yacov-Nir Sharon, Adar |
| author_facet | Breitstein, Yacov-Nir Sharon, Adar |
| contents | It was recently shown that $3d$ $\mathcal{N}=1$ supersymmetric Wess-Zumino models can be studied in the $ε$-expansion by analytically continuing the number of fermionic degrees of freedom to be half-integer. In this work we study the extension of this strategy to gauge theories. We consider $U(1)$ gauge theories with $N_g$ neutral Majorana fermions $χ_a$, $N_f$ charge-1 bosons $ϕ_i$ and $N_f\times N_g$ charge-1 Dirac fermions $ψ_{ia}$ in the $d=4-2ε$ expansion. Analytically continuing to $N_g=\frac12$ schematically matches the Lagrangian and matter content of $3d$ $\mathcal{N}=1$ SQED, and we check whether this match can be made rigorous. We compute anomalous dimensions of $χ_a$ up to two loops and of meson operators up to one loop at the fixed points, and compare to expectations from SUSY. While we find obstructions to SUSY at small $N_f$, at large $N_f$ the observables approach the expected values at a SUSY fixed point. This may allow for checks of $3d$ $\mathcal{N}=1$ IR dualities between gauge theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07148 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hunting 3d $\mathcal{N}=1$ SQED in the $ε$-expansion Breitstein, Yacov-Nir Sharon, Adar High Energy Physics - Theory It was recently shown that $3d$ $\mathcal{N}=1$ supersymmetric Wess-Zumino models can be studied in the $ε$-expansion by analytically continuing the number of fermionic degrees of freedom to be half-integer. In this work we study the extension of this strategy to gauge theories. We consider $U(1)$ gauge theories with $N_g$ neutral Majorana fermions $χ_a$, $N_f$ charge-1 bosons $ϕ_i$ and $N_f\times N_g$ charge-1 Dirac fermions $ψ_{ia}$ in the $d=4-2ε$ expansion. Analytically continuing to $N_g=\frac12$ schematically matches the Lagrangian and matter content of $3d$ $\mathcal{N}=1$ SQED, and we check whether this match can be made rigorous. We compute anomalous dimensions of $χ_a$ up to two loops and of meson operators up to one loop at the fixed points, and compare to expectations from SUSY. While we find obstructions to SUSY at small $N_f$, at large $N_f$ the observables approach the expected values at a SUSY fixed point. This may allow for checks of $3d$ $\mathcal{N}=1$ IR dualities between gauge theories. |
| title | Hunting 3d $\mathcal{N}=1$ SQED in the $ε$-expansion |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.07148 |