箱中Cecotti-Fendley-Intriligator-Vafa指数
Cecotti-Fendley-Intriligator-Vafa Index in a Box
摘要：
重新讨论了二维${\mathcal N} =(2,2)$模型中的Cecotti-Fendley-Intriligator-Vafa（CFIV）指数。我们解决的问题，“小学”（非拓扑）的激发在一个扭结的解决方案，在一个扭结部门（使用Wess-Zumino或Landau-Ginzburg模型与两个真空为例）。换句话说，我们将自己限制在大- $β$极限。通过一个大的盒子，明智地选择边界条件的激发光谱在经典的水平扭结的BPS饱和。边界条件的设计，以这样一种方式，即一半的超对称性被保存以及BPS扭结本身，和相关的零模式。激发光谱获得质量间隙。所有（离散化的）激发态以四维多重态（两个玻色子态+两个费米子态）进入。他们对$\mathrm{ind}_{\rm CFIV}$的贡献一级一级地消失。基态贡献产生$|\mathrm{ind}_{\rm CFIV}|=1$。
英文摘要：
The Cecotti-Fendley-Intriligator-Vafa (CFIV) index in two-dimensional ${\mathcal N} =(2,2)$ models is revisited. We address the problem of "elementary" (nontopological) excitations over a kink solution, in the one-kink sector (using the Wess-Zumino or Landau-Ginzburg models with two vacua as examples). In other words, we limit ourselves to the large-$β$ limit. The excitation spectrum over the BPS-saturated at the classical level kink is discretized through a large box with judiciously chosen boundary conditions. The boundary conditions are designed in such a way that half of supersymmetry is preserved as well as the BPS kink itself, and relevant zero modes. The excitation spectrum acquires a mass gap. All (discretized) excited states enter in four-dimensional multiplets (two bosonic states + two fermionic). Their contribution to $\mathrm{ind}_{\rm CFIV}$ vanishes level by level. The ground state contribution produces $|\mathrm{ind}_{\rm CFIV}|=1$.
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