Are there any theorems restricting possible QG candidates?

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String theory, being such a theoretically successful theory as it is but with no experiment to single it out as THE model among alternatives, Im left to wonder, which models can be excluded? Are there essential no-go theorems regarding the physics of a theory for QG?
Im aware of the Coleman-Mandula theorem, but are there also restrictions to, say, which geometrical objects that, when quantized, could give rise to fruitful models of our universe?

Thanks.

// Curious
 
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arXiv:gr-qc/0306083 (gr-qc)
[Submitted on 18 Jun 2003 (v1), last revised 19 Jun 2003 (this version, v2)]
A Note On The Chern-Simons And Kodama Wavefunctions
Edward Witten
 
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FAQ: Are there any theorems restricting possible QG candidates?

What are the main challenges in formulating a theory of Quantum Gravity (QG)?

One of the main challenges in formulating a theory of Quantum Gravity is reconciling the principles of quantum mechanics, which govern the very small, with general relativity, which governs the very large. These two frameworks are fundamentally different in how they describe spacetime and gravitational interactions. Additionally, there are technical difficulties such as the problem of non-renormalizability in quantum field theories of gravity and the lack of experimental data to guide the development of such a theory.

Are there any no-go theorems that restrict possible QG candidates?

Yes, there are several no-go theorems that restrict possible candidates for Quantum Gravity. One prominent example is the Coleman-Mandula theorem, which limits the ways in which spacetime symmetries and internal symmetries can be combined in a quantum field theory. Another example is the Weinberg-Witten theorem, which places constraints on the types of massless particles that can exist in a relativistic quantum field theory. These theorems help narrow down the landscape of viable QG theories.

What is the significance of the AdS/CFT correspondence in QG research?

The AdS/CFT correspondence, also known as the holographic principle, is significant because it provides a concrete realization of how a theory of quantum gravity in a higher-dimensional spacetime (Anti-de Sitter space) can be equivalent to a lower-dimensional conformal field theory (CFT) without gravity. This duality offers valuable insights and computational tools for studying quantum gravity, particularly in regimes where traditional methods fail. It has also inspired new approaches to understanding black holes, quantum entanglement, and the nature of spacetime.

How do string theory and loop quantum gravity differ as QG candidates?

String theory and loop quantum gravity (LQG) are two leading candidates for a theory of Quantum Gravity, but they differ significantly in their approaches. String theory posits that the fundamental constituents of the universe are one-dimensional "strings" rather than point particles, and it naturally incorporates gravity through the vibration modes of these strings. It also requires additional spatial dimensions for consistency. In contrast, LQG attempts to quantize spacetime itself using a background-independent framework, focusing on discrete structures called spin networks. While string theory has had success in unifying all fundamental forces and predicting new phenomena, LQG provides a more direct approach to quantizing spacetime geometry.

What role do black holes play in the study of Quantum Gravity?

Black holes play a crucial role in the study of Quantum Gravity because they represent extreme environments where both quantum effects and gravitational effects are significant. The study of black hole thermodynamics, particularly the discovery of Hawking radiation, has provided

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