在ε-展开中寻找3d N=1 SQED
Hunting 3d $\mathcal{N}=1$ SQED in the $ε$-expansion
AI总结：
本文通过ε-展开研究3d N=1 SQED，将费米子自由度解析延拓至半整数，计算异常维度并与SUSY预期比较，发现大N_f下观测量接近SUSY固定点，为检验红外对偶提供可能。
摘要：
最近研究表明，通过解析延拓费米子自由度数为半整数，可以在ε-展开中研究3d N=1超对称Wess-Zumino模型。本文研究将该策略扩展到规范理论。我们考虑在d=4-2ε展开中的U(1)规范理论，包含N_g个中性Majorana费米子χ_a、N_f个电荷为1的玻色子ϕ_i以及N_f×N_g个电荷为1的Dirac费米子ψ_{ia}。解析延拓至N_g=1/2在形式上与3d N=1 SQED的拉格朗日量和物质内容匹配，我们检验该匹配能否严格成立。我们计算了不动点处χ_a的异常维度至两圈，以及介子算符的异常维度至一圈，并与SUSY预期进行比较。虽然在小N_f时发现SUSY存在阻碍，但在大N_f时观测量接近SUSY不动点处的预期值。这可能允许对3d N=1规范理论之间的红外对偶进行检验。
英文摘要：
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.
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