arXiv 2205.079302022-05hep-th

关于极小Argyres-Douglas理论的保护谱

On the Protected Spectrum of the Minimal Argyres-Douglas Theory

Chinmaya Bhargava, Matthew Buican, Hongliang Jiang

备注：: 34 pages and 2 appendices; v2: references added and typos corrected
DOI：: 10.1007/JHEP08(2022)132

摘要：

尽管超对称性的力量，找到精确的封闭形式的表达相互作用的超共形场论（SCFT）的保护算子谱是困难的。在本文中，我们采取了一个解决方案的“最简单的”相互作用的4D $\mathcal{N}=2$ SCFT：最小的Argyres-Douglas（MAD）理论。我们提出了两个结果，超出了众所周知的库仑分支和舒尔部门。首先，我们找到了包含关于任何$\mathcal{N}=1\subset\mathcal{N}=2$超共形子代数的手征算子的多重态的精确闭合形式谱。我们认为，这个“完整的”手征部门（FCS）是简单的，因为允许与库仑分支的理论的么正性，并认为，到$U(1)_r$量子数的重新标度和有限数量的状态的消失，MAD FCS是等谱的自由$\mathcal{N}=2$阿贝尔规范理论的FCS。用超共形表示理论的语言来说，这只留下了人们知之甚少的$\bar{\mathcal{C}}_{R,r(j,\bar j)}$多重态的谱。我们的第二个结果揭示了这些可观的：我们找到了一个确切的封闭形式的答案，$\bar{\mathcal{C}}_{0,r(j,0)}$多重峰的数量，任何$r$和$j$，在MAD理论。我们认为，这个子部门也一样简单，允许的库仑分支理论的幺正性，并有一个自然的映射到相应的部门的自由$\mathcal{N}=2$阿贝尔规范理论。这些结果激发了人们对MAD理论的完整局部算子代数的猜想。

英文摘要：

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.

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英文摘要：

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