发表机构
Yukawa Institute for Theoretical Physics, Kyoto University; Princeton University; Institute for Advanced Study（京都大学汤川理论物理研究所; 普林斯顿大学; 高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出例外 $m=12$ $\mathcal N=1$ 超共形最小模型的 Landau-Ginzburg 描述，通过超势 $W=g_1XY^2/2+g_2X^3/6$ 在 $g_1/g_2=3/2$ 处实现，并利用融合环和重整化群流验证其性质。
AI 中文摘要
具有 $m=12$ 和例外模不变式 $(E_6,D_8)$ 的 $\mathcal N=1$ 超共形最小模型是超-$W_3$ 代数的幺正最小模型。我们提出其 Landau-Ginzburg 描述，使用两个实标量超场和三次超势 ${\cal W}=g_1 XY^2/2 + g_2X^3/6$。对于 $g_1=g_2$，已知该超势描述两个 $m=3$ $\mathcal N=1$ 超共形最小模型的乘积，即具有 $(D_6,E_6)$ 模不变式的 $m=10$ 模型。例外的 $m=12$ 超共形最小模型在同一理论的不同不动点处实现。检验此 Landau-Ginzburg 描述需要最小模型的融合环，我们通过扩展代数的模数据获得该融合环。融合环具有由手征费米子宇称给出的 $\mathbb Z_2$ 分级，而普通融合系数无法确定该分级。此分级与共轭复合后，给出 Landau-Ginzburg 理论的 R-宇称 $\mathbb Z_2^{R}$ 的生成元。然后我们将具有超势 $\cal W$ 的理论视为 $d=4-\epsilon$ 中的 Gross-Neveu-Yukawa 模型，并发现一个弱耦合的红外不动点，其中 $g_1/g_2=3/2+\mathcal O(\epsilon)$，在该不动点处超对称涌现。我们还描述了从该不动点到 $g_1=g_2$ 的解耦不动点的重整化群流。耦合不动点处的算符维度，延拓到 $d=2$，与 $m=12$ 超共形最小模型中的值近似一致。最后，我们估计了新的相互作用 $d=3$ $\mathcal N=1$ 超共形场论中的标度维度。
英文摘要
The $\mathcal N=1$ superconformal minimal model with $m=12$ and the exceptional modular invariant $(E_6,D_8)$ is the unitary minimal model of the super-$W_3$ algebra. We propose its Landau-Ginzburg description using two real scalar superfields with the cubic superpotential ${\cal W}=g_1 XY^2/2 + g_2X^3/6$. For $g_1=g_2$, this superpotential is known to describe a product of two $m=3$ $\mathcal N=1$ superconformal minimal models, which is the $m=10$ model with the $(D_6,E_6)$ modular invariant. The exceptional $m=12$ superconformal minimal model is realized at a different fixed point of the same theory. Testing this Landau-Ginzburg description requires the fusion ring of the minimal model, which we obtain from the modular data of the extended algebra. The fusion ring has a $\mathbb Z_2$ grading by chiral fermion parity that the ordinary fusion coefficients do not determine. This grading, composed with conjugation, gives the generator of the R-parity $\mathbb Z_2^{R}$ of the Landau-Ginzburg theory. We then treat the theory with superpotential $\cal W$ as a Gross-Neveu-Yukawa model in $d=4-ε$ and find a weakly coupled infrared fixed point with $g_1/g_2=3/2+\mathcal O(ε)$, at which supersymmetry emerges. We also describe the renormalization group flow from this fixed point to the decoupled fixed point with $g_1=g_2$. The operator dimensions at the coupled fixed point, continued to $d=2$, agree approximately with their values in the $m=12$ superconformal minimal model. Finally, we estimate the scaling dimensions in the new interacting $d=3$ $\mathcal N=1$ superconformal field theory.
Comments63 pages, 1 figure, v2: minor improvement, reference added
