Related papers: Holography and local fields
These lecture notes aim to provide a pedagogical introduction to the AdS/CFT correspondence and its extensions to spacetimes with positive (de Sitter spacetime) and zero (flat spacetime) cosmological constant. We begin by explaining the…
The AdS/CFT correspondence, or holography, has provided numerous important insights into the behavior of strongly-coupled many-body systems. Crucially, it has provided a testing ground for the construction of new effective field theories,…
We sketch in this article a new theory, which we call Symplectic Field Theory or SFT, which provides an approach to Gromov-Witten invariants of symplectic manifolds and their Lagrangian submanifolds in the spirit of topological field…
$p$-adic Hodge Theory is one of the most powerful tools in modern Arithmetic Geometry. In this survey, we will review $p$-adic Hodge Theory for algebraic varieties, present current developments in $p$-adic Hodge Theory for analytic…
This report on the topics in the title was written for a lecture series at the Southwestern Center for Arithmetic Algebraic Geometry at the University of Arizona.It may serve as an introduction to certain conjectural relations between…
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
We discuss recent developments in $p$-adic geometry, ranging from foundational results such as the degeneration of the Hodge-to-de Rham spectral sequence for "compact $p$-adic manifolds" over new period maps on moduli spaces of abelian…
A rigorous (and simple) proof is given that there is a one-to-one correspondence between causal anti-deSitter covariant quantum field theories on anti-deSitter space and causal conformally covariant quantum field theories on its conformal…
This is a lecture note prepared for the SFT 9 workshop in Augsburg, Germany. The text describes a polyfold approach to the construction of symplectic field theory and focuses on the perturbation and transversality theory.
Using the AdS/CFT correspondence, we examine entanglement entropy for a boundary theory deformed by a relevant operator and establish two results. The first is that if there is a contribution which is logarithmic in the UV cut-off, then the…
The theory of locally analytic representations of $p$-adic Lie groups with $\mathbf{Q}_p$-coefficients is a powerful tool in $p$-adic Hodge theory and in the $p$-adic Langlands program. This perspective reveals important differential…
We give a brief expository discussion on the holographic correspondence of correlation functions in the large J limit of AdS/CFT conjecture. We first review our proposals on the interpretation of the so-called GKPW relation in the large J…
We give an introductory review of gauge/gravity duality, and associated ideas of holography, emphasising the conceptual aspects. The opening Sections gather the ingredients, viz. anti-de Sitter spacetime, conformal field theory and string…
Motivated by structural issues in the AdS-CFT correspondence, the theory of generalized free fields is reconsidered. A stress-energy tensor for the generalized free field is constructed as a limit of Wightman fields. Although this limit is…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
We show by means of the AdS/CFT correspondence in the context of quantum gravity how inter-representational relations - loosely speaking relations among different equivalent representations of one and the same physics - can play out as a…
This is a concise review of holographic superconductors and superfluids. We highlight some predictions of the holographic models and the emphasis is given to physical aspects rather than to the technical details, although some references to…
The correspondence between theories in anti-de Sitter space and conformal field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD which has scale invariance at short distances and color…
This thesis is an elaboration of recent results on the holographic re-construction of metric-like interactions in higher-spin gauge theories on anti-de Sitter space (AdS), employing their conjectured holographic duality with free conformal…
Motivated by the Langlands program in representation theory, number theory and geometry, the theory of representations of a reductive $p$-adic group over a coefficient ring different from the field of complex numbers has been widely…