2015/12/31 by Stefano Cremonesi, Alessandro Tomasiello
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Anomaly (physics) #Black Holes and Theoretical Physics #Gauge theory #Lattice (music) #Lattice gauge theory #Limit (mathematics) #Noncommutative and Quantum Gravity Theories #Quadratic equation #Quantum field theory #Supersymmetric gauge theory #Tensor (intrinsic definition) #Tensor field #hep-th
paper · pdf · doi:10.1007/jhep05(2016)031
33 pages, 7 figures; v2: references added, minor changes; v3: typos fixed, details added in section 2.2.3
openalex publication_date 2016/05/01 · openalex created_date 2016/06/24 · arxiv created 2016/09/28 · arxiv updated 2016/09/29 · openalex updated_date 2026/08/05
An infinite class of analytic AdS7 × S 3 solutions has recently been found. The S 3 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 A N 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.