AI 中文总结
本文研究三维CFT中与大荷相关的算子塔，利用模空间EFT证明了受弱引力猜想启发的α₀≤0界，还计算了多个三维N=1理论的α₁与α₀，发现α₁无除平凡界外的普适界。
AI 中文摘要
在arXiv:2406.19441中已证明，对于具有模空间且沿该空间U(1)对称性自发破缺的三维共形场论（CFTs），大荷Q下的最小标度维数满足Δ_min(Q)=α₁Q+α₀+O(1/Q)。受全息沼泽地纲领的启发，我们研究系数α_i的可能界。对于α₀，弱引力猜想（WGC）提出CFT荷凸性猜想，要求α₀≤0的界。利用模空间有效场论（EFT），我们对投影后的Δ_min(Q)证明了该界——投影后的Δ_min(Q)通过固定单一电荷Q并在允许其他所有电荷变化的情况下最小化维数得到。这提供了一个可利用CFT方法明确证明的、受WGC启发的界。另一方面，我们表明除平凡界α₁≥0外，α₁不存在普适界。我们还通过ε展开和大N方法，在多个新的三维N=1理论中计算了α₁和α₀。
英文摘要
In arXiv:2406.19441, it was shown that for 3d CFTs with a moduli space along which a $U(1)$ symmetry is spontaneously broken, the minimum scaling dimension at large charge $Q$ scales as $Δ_{\min}(Q)=α_1 Q+α_0+O(1/Q)$. Motivated by the holographic swampland program, we study possible bounds on the coefficients $α_i$. For $α_0$, the weak gravity conjecture motivates the CFT charge convexity conjecture, which requires the bound $α_0\leq 0$. Using the moduli space EFT we prove this bound for the $\textit{projected}$ $Δ_{\min}(Q)$, obtained by fixing a single charge $Q$ and minimizing the dimension while allowing all other charges to vary. This provides a WGC-motivated bound that is explicitly provable using CFT methods. On the other hand, we show that $α_1$ admits no universal bound apart from the trivial bound $α_1\geq 0$. We also compute $α_1$ and $α_0$ in several new 3d $\mathcal{N}=1$ theories via the $ε$-expansion and large-$N$ methods.
