2012-08-012024-05-18https://scholars.lib.ntu.edu.tw/handle/123456789/698016摘要：超弦理論是目前唯一有可能描述量子重力效應與粒子物理的自洽理論，也就是所謂的“萬有理論”。它可以幫助我們瞭解許多關於量子引力效應的問題，例如黑洞的訊息詭論的問題；它也可能讓我們回答關於宇宙論的大問題，例如暗能量是甚麼、宇宙的最初狀態是甚麼等等。弦論也促使現象學家討論一些新的現象學模型，例如非交換幾何、模世界、大額外空間等。在大強子對撞機的高能實驗結果、及世界上許多宇宙學觀測結果即將出爐、重新形塑下一代的物理學的這個新時代，我們的弦論研究將提供新的理論基礎，當作新一代物理學的架構和模式。 事實上，從弦論中發現的AdS/CFT對偶關係已經被廣泛用作建立物理模型的新理論架構，應用在許多其他的物理領域中，包括量子色動力學（QCD）、超導體、流體力學、量子霍爾效應等強關聯系統中。過去幾年來這個研究方向已經形成一個熱門趨勢；而臺大的學者在某些問題上走在世界的前沿（如AdS/QCD及全像超導），所以這個研究方向也將是我們努力的重點之一。 目前已知的五種超弦理論（分別稱作：type I, IIA, IIB, heterotic SO(32) 及 heterotic E8xE8 超弦理論）都被統一在一個假設的M理論中。除了因為M理論可以幫我們統一所有弦論，M理論的另一個好處是它可以把一些弦論中的對偶性轉換成幾何上的對稱性，讓我們比較容易瞭解這些對偶性的內容。近幾年M理論的研究有不少重要的進展，臺大的一些同仁也有參與其中的一些重要工作（M2膜及M5膜的等效理論）。我們將繼續研究M理論、以及M理論在數學上和物理上的意義。因為M理論可以將對偶性表達的更清楚，我們預期M理論在其他領域中的應用將比弦論更強而有力。 弦論除了在其他物理領域中有它的影響之外，它也被當作物理與數學研究的橋梁。弦論中的一些對偶性促發了數學中的一些重要發展。舉例來說，數學中卡拉比-丘空間在弦論中是十維時空中多出來的六維空間的幾何形態。透過弦論，數學中卡拉比-丘的幾何性質對應到基本粒子的物理性質。因此弦論中的對偶性建立了不同的卡拉比-丘空間的幾何及拓樸性質之間的關係。簡單的說，弦論就是數學與物理之間的對偶映射，把每一個數學問題對應到一個物理問題。除了過去已經獲得的成果，還有一大片未經開發的區域含有許多物理學家與數學家有共同興趣的問題，待我們去發掘開墾。目前世界上還有不少重要的物理學與數學的合作計畫在進行當中，我們相信還有更重要、影響層面更大的結果需要物理學家與數學家更密切更深入的合作纔會被發現。這是我們的研究計畫的另一個重點。 綜言之，我們的研究重點包含以下各項： 1. 弦論在粒子物理（現象學）即宇宙學的應用 2. AdS/CFT對偶性在凝態物理方面的應用 3. M理論的物理及應用 4. 弦論中數學與物理的交流合作 這些都是世界上一流研究機構所重視的研究方向，也是臺大研究團隊有所專精的領域。本計畫可以整合我們的研究工作、藉著新的合作平台與有效率的訪客計畫使得我們的研究視野更開闊、研究效率更高、成果更豐碩。<br> Abstract: String theory (or superstring theory) is at the moment the only candidate for a consistent theory of quantum gravity and fundamental particles (the so-called “theory of everything”). It helps us understand puzzles in quantum gravity such as the information paradox of black holes, and it also has the potential to answer big questions in cosmology, such as the origin of dark energy, and the initial state of the universe. String theory also motivates various phenomenological models in particle physics. Examples are non-commutative geometry, brane-worlds, large extra dimensions, etc. At the advent of the new era when high-energy experiments at LHC and cosmological observations throughout the globe are producing new data that will shape the next-generation physics, our string theory research will aim to provide new frameworks for developing next-generation theories. In fact, AdS/CFT duality discovered in string theory has already been used as a new theoretical framework to study various problems in other branches of physics, including quantum chromodynamics (QCD), superconductors, fluid dynamics, quantum Hall effects and other strongly correlated systems. This approach has been very popular in the past few years, and people at NTU have been playing a leading role on some of the topics (e.g. AdS/QCD and holographic superconductors). This is one of the directions we will focus on. A total of five superstring theories (called type I, IIA, IIB, heterotic SO(32) and heterotic E8xE8 superstrings) are known, and string theorists believe that they are all unified in a hypothetical theory called M theory. Understanding M theory is of great importance not only because of its role of unifying all string theories, but also because some of the dualities in string theories can be more easily understood as geometrical symmetries in M theory. In recent years, there has been a fast progress in the study of M theory, with researchers at NTU playing leading roles on some topics (effective theories of M2-branes and M5-branes). We will keep the momentum and explore M theory further, as well as the implications of M theory on mathematics and other branches of physics. As a more powerful framework for describing dualities, M theory will be more powerful than string theory in its many applications using dualities. In addition to its impact on other branches of physics, string theory has also been acting as the connection between physics and mathematics in the past few decades. Various dualities in string theory have triggered important developments in mathematics. For example, the study of Calabi-Yau spaces in mathematics is associated with the physical problem of compactification of the extra 6 dimensions in the 10 dimensional spacetime of string theory. Geometrical properties of Calabi-Yau space is reinterpreted as properties of particle physics via string theory. Hence dualities of string theory establish relations among geometrical and topological properties of Calabi-Yau spaces. In short, string theory serves as a duality map between physics and mathematics. Apart from the well-recognized progress in the past, there is still a huge area of common interest to both string theorists and mathematicians to be explored. There are many important on-going projects with physicists and mathematicians in collaboration. We feel that there are still greater results to be discovered via a deeper, more extensive collaboration between mathematicians and physicists. This is another direction we will emphasize in our sub-project. To summarize, the topics we will work on include 1. Application of string theory to particle phenomenology and cosmology. 2. Application of AdS/QCD to condensed matter physics. 3. Physics of M theory and its applications. 4. Joint problems in string theory and mathematics. These are exciting research directions emphasized by almost all first-class institutes all over the world, and we have strong manpower on each of these topics. The sub-project will facilitate our activities and put our efforts in coherence.超弦理論Ｍ理論Ｄ膜Ｍ膜代數幾何卡拉比-丘空間superstring theoryM theoryD-braneM-braneAlgebraic GeometryCalabi-Yau space