论文标题
在广义的Legendre Transform中重新访问Atiyah-Hitchin歧管
Revisiting Atiyah-Hitchin manifold in the generalized Legendre transform
论文作者
论文摘要
我们在广义的Legendre Transform方法中重新审视了Atiyah-Hitchin歧管的构造。这最初是由Ivanov和Rocek研究的，随后由IONAS对此进行了更多的研究，在后者中，计算了Kähler电位的显式形式和KählerMetric。前者和后者之间存在区别。在广义的Legendre变换方法中，由一个函数与全体形态坐标的轮廓集成构建了Kähler电位。后者中轮廓的选择与前者的选择不同，前者的差异可能会在Kähler的潜力中产生差异，并最终在Kähler指标中产生差异。我们表明，前者仅发出真正的Kähler潜力，这与其定义一致，而后者产生了复杂的潜力。我们从伊万诺夫和罗切克首次考虑的轮廓方面，根据霍顿 - 希钦歧管的摩尔形坐标来获得kähler的潜力和指标。
We revisit construction of the Atiyah-Hitchin manifold in the generalized Legendre transform approach. This is originally studied by Ivanov and Rocek and is subsequently investigated more by Ionas, in the latter of which the explicit forms of the Kähler potential and the Kähler metric are calculated. There is a difference between the former and the latter. In the generalized Legendre transform approach, a Kähler potential is constructed from the contour integration of one function with holomorphic coordinates. The choice of the contour in the latter is different from the former's one, whose difference may yield a discrepancy in the Kähler potential and eventually in the Kähler metric. We show that the former only gives the real Kähler potential, which is consistent with its definition, while the latter yields the complex one. We derive the Kähler potential and the metric for the Atiyah-Hitchin manifold in terms of holomorphic coordinates for the contour considered by Ivanov and Roček for the first time.
