R-R背景場下的D膜理論

Abstract

本篇論文主要研究在Ramond-Ramond（R-R）背景場下D膜(D-brane)的有效場論。由於R-R背景場的存在，這樣的理論在背景場的方向會有體積保持不變的對稱性（volume-preserving diffeomorphism），這是這理論的主要特徵之一。之所以會研究這樣的理論，起源於最近有關M5膜在大C背景場的有效場論的研究。高一維度的理論可以透過丟掉場在這一維度的自由度，來得到低一維度在低能量極限的有效場論。因此這樣的分析方法常常會有一些多餘的場殘留在低一維度的理論中。要如何分辨哪些場是理論所必須的，而哪些場又是可以被積掉的，是這研究的核心部分。在這篇論文中，我們發現原先所預期出現的規範場被隱藏在某些場內，我們使用了對偶變換的方法來使這樣的規範場在理論中變的明顯。接著我們討論了在這樣的變換下，要如何求出規範場的規範對稱變換以及超對稱變換。我們研究了在規範對稱性以及體積保持不變性之下的協變量（covariant variables）應是什麼樣子的，並利用它們來使理論易於推廣到不同的情形。最後我們利用這理論所具有的超對稱去討論這理論的拓樸性質，即理論所允許的孤立子解。

In this paper, we try to understand the low energy effective theory of Dp-brane in large R-R (p-1)-form field background. To construct the effective theory, we start with the M5-brane theory in large C-field background. The C-field background defines the 3-dimensional volume form in M5-brane theory. Hence, the M5-brane theory can be described as a Nambu-Poisson-bracket gauge theory with volume-preserving diffeomorphism symmetry (VPD). After doing double dimensional reduction, we obtain the effective theory of D4-brane in large C-field background. This theory has both the usual U(1) gauge symmetry and the new symmetry VPD. The VPD two-form gauge potential can be understood as the electric-magnetic dual of the one-form gauge field in the D4- brane theory. This theory is described by the one-form gauge field and the dual two-form gauge field at the same time. These results can be generalized to Dp-branes cases. In the last part of thesis, we study the supersymmetry (SUSY) algebra in this theory. We can calculate the central charges from the SUSY algebra in this theory, then we can know the possible topological quantities in this system. This interesting system may help us to understand M-theory, the models with volume-preserving diffeomorphism, the suitable low energy description of Dp-branes in different field backgrounds, some new soliton solutions, and so on.