[Paper Review] 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 PhysicsPhysics and Astronomy81 references79 citations

TL;DR

The paper provides an overview of the string landscape and swampland, surveys conjectures distinguishing viable low-energy theories with gravity, and discusses dualities and holography, highlighting a missing corner in string dualities and the push toward a direct quantum gravity definition.

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).

Motivation & Objective

• 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.

Proposed method

• 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.

Experimental results

Research questions

• 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?

Key findings

• 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.