论文标题
双重大规模（超级）P形式的有效动作
Effective actions for dual massive (super) p-forms
论文作者
论文摘要
在$ d $尺寸中，众所周知，弯曲空间中无数$ p $形式的模型是$ p> 1 $的可简化量规理论，因此无法使用标准的Faddeev-Popov方案进行其协变量量化。但是，增加了质量术语，还引入了由此产生的$ p $形式模型的Stueckelberg重新制定，最终以一种不可约的规程理论，可以定量Faddeev和Popov。在Hodge-de Rham运算符的功能决定因素方面，我们为大规模$ p $ p $ form有效的动作得出一个紧凑的表达式。然后，我们证明有效的动作$γ^{（m）} _ p $和$γ^{（m）} _ {d-p-1} $因拓扑不变性而有所不同。这是无数情况下已知结果的概括，即有效的动作$γ_p$和$γ_{d-p-2} $ comincide modulo是拓扑术语。最后，我们的分析扩展到了大量的超级$ p $ - 形式与背景$ {\ cal n} = 1 $在四个维度上的超级重力。具体而言，我们研究了以下大量超级$ p $ - 形式的量子动力学：（i）矢量多重动力学； （ii）张量多重； （iii）三型多重。证明大规模矢量和张量多重的有效作用一致。大规模三型的有效作用被证明是对应于两个巨大标量多重组的那些拓扑术语的总和。
In $d$ dimensions, the model for a massless $p$-form in curved space is known to be a reducible gauge theory for $p>1$, and therefore its covariant quantisation cannot be carried out using the standard Faddeev-Popov scheme. However, adding a mass term and also introducing a Stueckelberg reformulation of the resulting $p$-form model, one ends up with an irreducible gauge theory which can be quantised à la Faddeev and Popov. We derive a compact expression for the massive $p$-form effective action, $Γ^{(m)}_p$, in terms of the functional determinants of Hodge-de Rham operators. We then show that the effective actions $Γ^{(m)}_p$ and $Γ^{(m)}_{d-p-1}$ differ by a topological invariant. This is a generalisation of the known result in the massless case that the effective actions $Γ_p$ and $Γ_{d-p-2}$ coincide modulo a topological term. Finally, our analysis is extended to the case of massive super $p$-forms coupled to background ${\cal N}=1$ supergravity in four dimensions. Specifically, we study the quantum dynamics of the following massive super $p$-forms: (i) vector multiplet; (ii) tensor multiplet; and (iii) three-form multiplet. It is demonstrated that the effective actions of the massive vector and tensor multiplets coincide. The effective action of the massive three-form is shown to be a sum of those corresponding to two massive scalar multiplets, modulo a topological term.
