[論文レビュー] The String Landscape, the Swampland, and the Missing Corner

T. Daniel Brennan, Federico Carta+1 more|arXiv (Cornell University)|Nov 2, 2017

Black Holes and Theoretical Physics参考文献 81被引用数 79

ひとこと要約

この論文は、ストリング・ランドスケープと swampland の概観を提供し、重力と結合させたときに多くが一見矛盾なく見える低エネルギー理論を区別する予想を調査し、双対性とホログラフィーを論じ、ストリング双対性の欠けたコーナーと直接的な量子重力定義へ向けた推進を強調する。

ABSTRACT

We give a brief overview of the string landscape and techniques used to construct string compactifications. We then explain how this motivates the notion of the swampland and review a number of conjectures that attempt to characterize theories in the swampland. We also compare holography in the context of superstrings with the similar, but much simpler case of topological string theory. For topological strings, there is a direct definition of topological gravity based on a sum over a "quantum gravitational foam." In this context, holography is the statement of an identification between a gravity and gauge theory, both of which are defined independently of one another. This points to a missing corner in string dualities which suggests the search for a direct definition of quantum theory of gravity rather than relying on its strongly coupled holographic dual as an adequate substitute (Based on TASI 2017 lectures given by C. Vafa).

研究の動機と目的

• Summarize the landscape of low-energy theories arising from string compactifications and why many appear consistent yet fail when coupled to gravity.
• Discuss conjectures that distinguish the swampland from the landscape and their potential physical predictions.
• Review how dualities relate compactifications across dimensions and SUSY levels, and contrast holography in topological strings with full string theory.
• Illustrate the need for a direct definition of quantum gravity beyond holographic duals by comparing topological and full string theories.

提案手法

• Review of string theory compactifications and the role of SUSY in preserving stability.
• Use of the adiabatic principle to relate dualities across dimensions and fibered geometries.
• Discussion of Calabi-Yau, G2, Spin(7), and other holonomy manifolds as compactification spaces.
• Comparison of holography in topological strings (gravity ≈ non-commutative U(1) gauge theory dual to CS theory) with the absence of a direct quantum gravity definition in full string theory.
• framing of the swampland conjectures as criteria distinguishing viable theories from inconsistent ones.

実験結果

リサーチクエスチョン

• RQ1 What criteria can distinguish theories in the string landscape from those in the swampland when coupled to gravity?
• RQ2 How do various string dualities persist under compactification across dimensions and SUSY levels, and what does this imply about the underlying theory?
• RQ3 What can topological string theory teach us about holography and the quest for a direct definition of quantum gravity?
• RQ4 What is the nature of the 'missing corner' in string dualities, and how might a direct quantum gravity formulation be realized?

主な発見

• A set of conjectures aims to separate the swampland from the landscape and may lead to concrete observable predictions.
• Compactifications preserving different amounts and chiralities of SUSY relate via dualities; adiabatic methods connect higher-dimensional dualities to lower-dimensional ones.
• Topological string theory provides a holographic dictionary via a quantum gravitational foam described by a non-commutative U(1) gauge theory dual to a Chern-Simons theory, offering a contrast to full string holography.
• In full string theory, a direct definition of quantum gravity is missing, and holography serves as a substitute rather than a fundamental construction.
• Calabi-Yau and related holonomy manifolds critically determine preserved SUSY and the resulting 4D physics, guiding landscape vs. swampland considerations.
• The lectures emphasize that many compactifications with identical SUSY and dimensions should be dual, illustrating a tight web of interconnected string theories.