2014/12/30 by Sangmin Lee, Lee, Sangmin, Daisuke Yokoyama +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.1412.8703
39 pages, 21 figures; v2. references added, minor improvements
openalex publication_date 2014/12/30 · arxiv created 2015/01/22 · arxiv updated 2015/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the supersymmetric free energy of three dimensional Chern-Simons-matter theories holographically dual to AdS4 times toric Sasaki-Einstein seven-manifolds. In the large N limit, we argue that the square of the free energy can be written as a quartic polynomial of trial R-charges. The coefficients of the polynomial are determined geometrically from the toric diagrams. We present the coefficients of the quartic polynomial explicitly for generic toric diagrams with up to 6 vertices, and some particular diagrams with 8 vertices. Decomposing the trial R-charges into mesonic and baryonic variables, and eliminating the baryonic ones, we show that the quartic polynomial reproduces the inverse of the Martelli-Sparks-Yau volume function. On the gravity side, we explore the possibility of using the same quartic polynomial as the prepotential in the AdS gauged supergravity. Comparing Kaluza-Klein gravity and gauged supergravity descriptions, we find perfect agreement in the mesonic sector but some discrepancy in the baryonic sector.