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6d holographic anomaly match as a continuum limit.

Cremonesi, Stefano and Tomasiello, Alessandro (2016) '6d holographic anomaly match as a continuum limit.', Journal of high energy physics., 2016 (05). 031.

Abstract

An infinite class of analytic AdS7 × S3 solutions has recently been found. The S3 is distorted into a “crescent roll” shape by the presence of D8-branes. These solutions are conjectured to be dual to a class of “linear quivers”, with a large number of gauge groups coupled to (bi-)fundamental matter and tensor fields. In this paper we perform a precise quantitative check of this correspondence, showing that the a Weyl anomalies computed in field theory and gravity agree. In the holographic limit, where the number of gauge groups is large, the field theory result is a quadratic form in the gauge group ranks involving the inverse of the AN Cartan matrix C. The agreement can be understood as a continuum limit, using the fact that C is a lattice analogue of a second derivative. The discrete data of the field theory, summarized by two partitions, become in this limit the continuous functions in the geometry. Conversely, the geometry of the internal space gets discretized at the quantum level to the discrete data of the two partitions.

Item Type:Article
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Available under License - Creative Commons Attribution.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/JHEP05(2016)031
Publisher statement:This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Date accepted:26 April 2016
Date deposited:21 February 2017
Date of first online publication:05 May 2016
Date first made open access:No date available

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