Model theory and the AdS/CFT correspondence

Jerzy Król

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arXiv · hep-th/0506003

Model theory and the AdS/CFT correspondence

Jerzy Król

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Abstract

We give arguments that exotic smooth structures on compact and noncompact 4-manifolds are essential for some approaches to quantum gravity. We rely on the recently developed model-theoretic approach to exotic smoothness in dimension four. It is possible to conjecture that exotic $R^4$'s play fundamental role in quantum gravity similarily as standard local 4-spacetime patches do for classical general relativity. Renormalization in gravity--field theory limit of AdS/CFT correspondence is reformulated in terms of exotic $R^4$'s. We show how doubly special relativity program can be related to some model-theoretic self-dual $R^4$'s. The relevance of the structures for the Maldacena conjecture is discussed, though explicit calculations refer to the would be noncompact smooth 4-invariants based on the intuitionistic logic.

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Jerzy Król. 2005-06-11. Model theory and the AdS/CFT correspondence. https://arxiv.org/abs/hep-th/0506003

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