论文标题
在最小Argyres-Douglas理论的受保护范围内
On the Protected Spectrum of the Minimal Argyres-Douglas Theory
论文作者
论文摘要
尽管具有超对称性的力量，但很难找到相互作用的超符号野外理论（SCFT）的精确闭合形式表达式。在本文中，我们朝着解决方案迈出了“最简单”的交互4D $ \ MATHCAL {N} = 2 $ SCFT：最小的Argyres-Douglas（MAD）理论。我们提出了两个结果，这些结果超出了众所周知的库仑分支和舒尔部门。首先，我们发现包含手性的多重构图的精确闭合形式谱相对于任何$ \ MATHCAL {n} = 1 \ subset \ Mathcal {n} = 2 $ superconformentormangra。我们认为，这个“完整的”手性部门（FCS）与Unitarity允许的具有库仑分支的理论一样简单，直到续约$ u（1）_r $量子数字，而有限的状态消失了，MAD FC是对免费$ \ nath Calculian fc fcs of Math Calcal f c f c f c f c f c的fc。用超宪法表示理论的语言，这仅留下差不多理解的$ \ bar {\ mathcal {c}} _ {r，r，r（j，\ bar j）} $多倍数的频谱。我们的第二个结果阐明了这些可观察到的东西：我们找到了$ \ bar {\ mathcal {c}} _ {0，r（j，j，0）} $倍数的$ \ bar {\ mathcal {c}} _ {\ mathcal {c}}的确切答案。我们认为，这个子部门也与Unitarity允许的具有库仑分支的理论一样简单，并且在自由$ \ Mathcal {n} = 2 $ Abelian Gauge理论的相应扇区上有一个自然图。这些结果激发了对疯狂理论的完整当地运营商代数的猜想。
Despite the power of supersymmetry, finding exact closed-form expressions for the protected operator spectra of interacting superconformal field theories (SCFTs) is difficult. In this paper, we take a step towards a solution for the "simplest" interacting 4D $\mathcal{N}=2$ SCFT: the minimal Argyres-Douglas (MAD) theory. We present two results that go beyond the well-understood Coulomb branch and Schur sectors. First, we find the exact closed-form spectrum of multiplets containing operators that are chiral with respect to any $\mathcal{N}=1\subset\mathcal{N}=2$ superconformal subalgebra. We argue that this "full" chiral sector (FCS) is as simple as allowed by unitarity for a theory with a Coulomb branch and that, up to a rescaling of $U(1)_r$ quantum numbers and the vanishing of a finite number of states, the MAD FCS is isospectral to the FCS of the free $\mathcal{N}=2$ Abelian gauge theory. In the language of superconformal representation theory, this leaves only the spectrum of the poorly understood $\bar{\mathcal{C}}_{R,r(j,\bar j)}$ multiplets to be determined. Our second result sheds light on these observables: we find an exact closed-form answer for the number of $\bar{\mathcal{C}}_{0,r(j,0)}$ multiplets, for any $r$ and $j$, in the MAD theory. We argue that this sub-sector is also as simple as allowed by unitarity for a theory with a Coulomb branch and that there is a natural map to the corresponding sector of the free $\mathcal{N}=2$ Abelian gauge theory. These results motivate a conjecture on the full local operator algebra of the MAD theory.
