Elementary Constituents Conjecture: Cobordism Classes Trivialized by Generators with Tension at Most Order 1 in Planck Units

The fundamental nature of space itself presents a long-standing challenge in theoretical physics, and recent work addresses this by investigating the building blocks of extended objects known as cobordism defects. Vinicius Nevoa, Sanjay Raman, and Cumrun Vafa, all from Harvard University, propose a compelling conjecture that these defects are surprisingly simple, being generated by elementary constituents with minimal energy, at most comparable to the Planck scale. This research unites concepts from both the geometry of space and the dynamics of these defects, offering new insights into the boundaries of consistent theoretical physics, a field known as the Swampland program. By suggesting a fundamental limit on the energy required to create these objects, the team’s work potentially simplifies the landscape of possible universes and provides a crucial step towards a more complete understanding of spacetime itself.

The research proposes that, for any extended object, its intrinsic tension always remains at or below the Planck scale, a fundamental limit in physics. This work unites concepts from geometry and dynamics within the framework of cobordism defects, a key area of investigation within the Swampland program, which seeks to define the boundaries of consistent physical theories. The investigation reviews the cobordism conjecture and explores how introducing symmetry affects the classification of these defects, further examining the relationship between topological charges and their geometric properties. Specific examples within M-theory and involving Type II D-branes are presented to illustrate the conjecture’s applicability.

Swampland Constraints And Quantum Gravity Consistency

This document explores the theoretical landscape of string theory, M-theory, and the Swampland, the region of parameter space where seemingly consistent theories are incompatible with quantum gravity. It investigates the constraints on consistent theories, particularly focusing on the Weak Gravity Conjecture, cobordism, and the geometry of moduli spaces. A central goal is to understand the criteria that determine whether a theory is viable for describing our universe. The research is highly theoretical, pushing the boundaries of our understanding of fundamental physics. The document emphasizes the Swampland and the Distance Conjecture, which suggests that the distance in moduli space between two theories relates to the distance in parameter space, implying a geometric structure within the Swampland.

Cobordism, a mathematical tool classifying spaces based on their boundaries, imposes strong constraints on consistent theories. The Weak Gravity Conjecture, suggesting gravity must be strong enough to allow black hole formation, also plays a crucial role. Moduli spaces, which parameterize the possible shapes of physical systems, are central to understanding the Swampland, as certain regions are more stable than others. The research delves into heterotic strings and branes, exploring how charge quantization is constrained by the Weak Gravity Conjecture and cobordism. Understanding the Swampland requires exploring non-supersymmetric theories. Cobordism provides a powerful tool for analyzing consistency, and the geometry of moduli spaces is crucial for understanding the Swampland. In essence, the document is a highly technical exploration of the boundaries of theoretical physics, seeking to understand the criteria that determine whether a theory is a viable candidate for describing our universe.

Cobordism Defects Resolve to Planckian Tension

This work presents a compelling conjecture regarding the trivialization of cobordism classes in quantum gravity, proposing that these classes are always resolved by elementary generators with tension at or below the Planck scale. Researchers investigated the relationship between cobordism defects and the absence of global symmetries, motivated by the attractor mechanism and detailed analysis of several examples. The central claim is that any configuration in quantum gravity can be connected to any other via a finite action process, formalized by the Cobordism Conjecture. The team rigorously examined the implications of this conjecture for effective field theories, demonstrating that a non-vanishing bordism group, representing a potential global symmetry, necessitates the existence of dynamical, singular branes.

Specifically, they predict the existence of (D-d-1)-dimensional branes that resolve the bordism charge associated with a given non-trivial group, where D is the dimension of spacetime and d is the dimension of the manifold in question. These branes, termed “bordism defects”, are predicted to carry charge and couple to higher gauge fields, analogous to magnetic monopoles trivializing a specific bordism class. Researchers explored two scenarios for non-vanishing bordism groups: symmetry breaking and symmetry gauging. In the case of symmetry breaking, the study predicts the existence of singular branes with tension at or below the Planck scale, effectively resolving the topological charge. This work establishes a framework for understanding topological charges in quantum gravity and provides concrete predictions for the spectrum of defects expected in a complete theory, offering a novel perspective on the Cobordism Conjecture and its implications for fundamental physics.

Cobordism Defects And Minimal Tension Generators

This research establishes a compelling connection between cobordism defects and fundamental principles within string theory and quantum gravity. Scientists demonstrate that these defects, which represent boundaries in higher-dimensional spaces, can be consistently described by elementary generators possessing remarkably low tension, at or below the Planck scale. This finding addresses a long-standing question regarding the nature of these defects and their role in defining the boundaries of effective field theories. The team’s analysis reveals that the tension of these generators is not arbitrary, but is actively minimized by a mechanism akin to the attractor flow observed near black holes.

This attractor mechanism guides the relevant fields in the theory towards configurations that reduce the tension of the defect, ensuring that even objects initially possessing higher tension will naturally evolve towards a low-energy state. Importantly, the researchers show this principle applies to fundamental objects in M-theory, such as M2- and M5-branes, confirming the consistency of the proposed framework. The authors acknowledge that determining the precise numerical value defining “order 1” tension remains an open question. Future research will likely focus on refining the quantitative understanding of these tension bounds and exploring the implications for the broader landscape of string theory and quantum gravity.