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arXiv 2202.08196hep-th
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离壳立方超多重态与$\mathcal{N}=2$高自旋规范超场的耦合

Off-shell cubic hypermultiplet couplings to $\mathcal{N}=2$ higher spin gauge superfields

Ioseph Buchbinder, Evgeny Ivanov, Nikita Zaigraev

备注：
0 + 37 pages, eqs. (3.68) corrected, without any impact on the subsequent formulas and results
发表信息：
JHEP 05 (2022) 104
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摘要：

我们构造了明显的$4D, \mathcal{N}=2$超对称和规范不变的离壳立方耦合的物质超多重态的更高整数自旋规范$\mathcal{N}=2$多重态arXiv：2109.07639 [hep-th]。超多重态由解析谐波$4D, \mathcal{N}=2$超场$q^{+}$描述，物理分量自旋为${\bf s} = (\frac{1}{2}\,, \;0)$，辅助场为无穷多个。所构造的立方耦合具有示意性结构$q^+ \hat{\cal H}^{++}_{(s)} q^+$，其中$\hat{\cal H}^{++}_{(s)}$是最高阶$({\bf s} - 1)$的微分分析算子，其容纳具有最高自旋${\bf s}$的无质量规范$\mathcal{N}=2$多重态。对于奇${\bf s}$，规范群生成元和耦合与超多重态内部${\rm SU}(2)_{PG}$对称性的${\rm U}(1)_{PG}$生成元成比例，因此如果${\rm SU}(2)_{PG}$不破缺，则不存在规范群生成元和耦合。如果这个${\rm U}(1)_{PG}$与$ 4D, \mathcal{N}=2$超对称性的中心电荷一致，则产生超多重态的质量，并且奇数${\bf s}$耦合在适当的无质量极限中消失。对于甚至${\bf s}$，高自旋规范变换和立方超场耦合都可以定义为有质量和无质量（中心电荷中性）的超多重态，而不包括${\rm U}(1)_{PG}$生成元。所有这些特征直接延伸到具有最大内部对称性${\rm USp}(2n) \times {\rm SU}(2)$的$n$超多重态的情况。

英文摘要：

We construct manifestly $4D, \mathcal{N}=2$ supersymmetric and gauge invariant off-shell cubic couplings of matter hypermultiplets to the higher integer spin gauge $\mathcal{N}=2$ multiplets introduced in arXiv:2109.07639 [hep-th]. The hypermultiplet is described by an analytic harmonic $4D, \mathcal{N}=2$ superfield $q^{+}$ with the physical component spins ${\bf s} = (\frac{1}{2}\,, \;0)$ and an infinite number of auxiliary fields. The cubic coupling constructed has the schematic structure $q^+ \hat{\cal H}^{++}_{(s)} q^+$, where $\hat{\cal H}^{++}_{(s)}$ is a differential analytic operator of the highest degree $({\bf s} - 1)$ accommodating the massless gauge $\mathcal{N}=2$ multiplet with the highest spin ${\bf s}$. For odd ${\bf s}$ the gauge group generators and couplings are proportional to ${\rm U}(1)_{PG}$ generator of the internal ${\rm SU}(2)_{PG}$ symmetry of the hypermultiplet and so do not exist if ${\rm SU}(2)_{PG}$ is unbroken. If this ${\rm U}(1)_{PG}$ is identified with the central charge of $ 4D, \mathcal{N}=2$ supersymmetry, a mass for the hypermultiplet is generated and the odd ${\bf s}$ couplings vanish in the proper massless limit. For even ${\bf s}$ the higher-spin gauge transformations and cubic superfield couplings can be defined for both massive and massless (central-charge neutral) hypermultiplets without including ${\rm U}(1)_{PG}$ generator. All these features directly extend to the case of $n$ hypermultiplets with the maximal internal symmetry ${\rm USp}(2n) \times {\rm SU}(2)$.

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