Volume 42-3  修士論文

On Orbifolds in Closed Superstring Field Theory

張 湘杭 (ルートヴィヒ・マクシミリアン大学ミュンヘン)

素粒子論研究・電子版 Vol. 42 (2024) No. 3

2024年3月27日受理

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概要

In this thesis we study the deformation of orbifold conformal field theories (CFT) in the framework of closed superstring field theory (superSFT). In particular, we consider the type II theory on $\mathbb{C}_4/\mathbb{Z}_2$ and its possible deformation of massless modes to the nearby theory on a smoothed-out manifold. This process is described by so-called ‟resolving" or ‟blowing-up" in algebraic geometry. Description of orbifold CFT is based on twist field [Dixon et al, Nucl. Phys. B, 282, 13(1987)] that changes the periodic boundary condition to anti-periodic one. This allows us to explore the moduli space of marginal deformations corresponding to the twist modes. By analysing the equation of motion of closed bosonic SFT, we show that the blowing-up is obstructed at the second order. Furtherly, we move on to superstrings. Since computation shows the second-order obstruction vanishes, it is possible to derive the blown-up metric in terms of the twisted moduli. We note that, although the initial orbifold theory posesses a $\mathcal{N}=2$ superconformal symmetry, the blown-up mode is not necessarily Kähler, indicating a broken superconformal symmetry. This makes sense because the closed superSFT is defined on a generic $\mathcal{N}=1$ superconformal string background. We carry on the analysis to the third order, where we find out that due to the chiral structure of the closed superSFT, the third-order obstruction is simply reduced to zero. This is unlike the open-string case [Mattiello, PhD thesis(2019)].