2012/07/17 by Justin R. David, Somyadip Thakur · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Brane cosmology #Consistency (knowledge bases) #Cosmology and Gravitation Theories #Discrete mathematics #Finite set #Function (biology) #Galaxies: Formation, Evolution, Phenomena #Geometry #Mathematical analysis #Mathematics #Physics #Point (geometry) #Quantum chromodynamics #Quantum mechanics #Statistical physics #Sum rule in quantum mechanics #Theoretical physics #hep-th
paper · pdf · doi:10.1007/jhep11(2012)038
41 pages
arxiv created 2012/07/17 · openalex publication_date 2012/11/01 · arxiv updated 2015/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Sum rules constraining the R-current spectral densities are derived holographically for the case of D3-branes, M2-branes and M5-branes all at finite chemical potentials. In each of the cases the sum rule relates a certain integral of the spectral density over the frequency to terms which depend both on long distance physics, hydrodynamics and short distance physics of the theory. The terms which which depend on the short distance physics result from the presence of certain chiral primaries in the OPE of two R-currents which are turned on at finite chemical potential. Since these sum rules contain information of the OPE they provide an alternate method to obtain the structure constants of the two R-currents and the chiral primary. As a consistency check we show that the 3 point function derived from the sum rule precisely matches with that obtained using Witten diagrams.