The String Landscape, the Swampland, and the Missing Corner (1711.00864v3)

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).

• The paper presents a detailed analysis of the string landscape, elucidating how compactification and dualities shape low-energy effective theories from string theory.
• It formulates swampland criteria that exclude gravitationally inconsistent models by addressing issues like the absence of continuous global symmetries.
• The authors explore topological string theory as a promising framework to directly formulate quantum gravity beyond the holographic approach.

An Overview of "The String Landscape, the Swampland, and the Missing Corner"

The paper authored by T. Daniel Brennan, Federico Cartab, and Cumrun Vafa offers a comprehensive examination of the conceptual frameworks within string theory, particularly focusing on the notions of the string landscape and the swampland. This manuscript, elaborating upon lectures delivered by C. Vafa at TASI 2017, is structured into three significant sections corresponding to their respective thematic lectures.

The first lecture section explores the string landscape, a vast collection of low-energy physics theories derived from string theory compactifications. The discussion covers the foundational aspects of string theories, their compactifications, and the duality relationships between different forms such as Type I, Type IIA, IIB, and heterotic strings. The authors examine how compact manifolds, like Calabi-Yau (CY) manifolds, serve as the compactification arenas, emphasizing the centrality of supersymmetry in preserving physical consistency across down-scaling processes to four dimensions. The exploration of compactification singularities, as well as the role of branes in complex systems like F-theory, further contextualizes the landscape's vast scale and variety. Dualities, as analyzed in this paper, are affirmed as robust frameworks that support these intricate structures, often echoed in conjectures of equivalency across compactified dimensions with shared characteristics.

Transitioning to the second lecture segment, the paper navigates the tricky waters of the swampland, which encapsulates seemingly consistent low-energy theories that, due to gravitational inconsistencies, fail to arise from string compactifications. A series of swampland conjectures are outlined, presenting criteria for discerning which effective field theories (EFTs) couple meaningfully to gravity. A core conjecture addressed is the absence of continuous global symmetries within consistent quantum gravity frameworks. The authors present several philosophical and theoretical reasons barring global symmetries, including black hole physics and the conservation of information. The conjectures concerning the necessity of all charge spectra, compactness of moduli spaces, and the entropic structure of black holes form a complex narrative on consistent quantum theory's demands. Such arguments offer a framework for exclusions within quantum theory and advocate for emergent constraints on models like de Sitter spacetime and non-supersymmetric AdS/CFT.

In the third and final lecture segment, the discussion shifts toward the "Missing Corner" of string theory—devoted to establishing a direct formulation of quantum gravity. By contrasting the inadequacies of holography as a definitive description of quantum gravity, the authors poise topological string theory as a conceptual apparatus with promising potentiality. This paper exposes topological string theory as a distilled model, mirroring broader string theory qualities and admitting non-perturbative formulations integral to a direct understanding of quantum gravity. The exploration of concepts like geometric transitions and the large N duality in topological strings reflects on how aspects of string integration potentially stitch quantum gravity together.

Overall, this paper should be interpreted as a nuanced examination of string theory's theoretical space: both illuminating and questioning the abstract constructs binding theoretical physics to the observed universe. The discussion on landscape and swampland places a critical lens on how our universe may sit within an enormously complex fabric rife with constraints. Consequently, the implications for quantum gravity—articulated through topological string theory—highlight a domain of inquiry poised for deeper explorations and reinvestment in foundational string principles. The findings, while deeply theoretical, suggest a continued evolution of string theory; one seeking to unify its existing precepts with a tangible model for understanding quantum gravitational phenomena.