2020/10/29 by Pietro Benetti Genolini, Matan Grinberg, Paul Richmond
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Classical mechanics #Cosmology and Gravitation Theories #Dual polyhedron #Duality (order theory) #Field (mathematics) #Field theory (psychology) #Gauged supergravity #Geometry #Gravitation #Legendre transformation #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Supergravity #Supersymmetry #Theoretical physics #Topological quantum field theory #hep-th
paper · pdf · doi:10.1007/jhep02(2021)156
published as JHEP 2021, 156 (2021) · 37 pages
arxiv created 2020/10/29 · openalex publication_date 2021/02/18 · arxiv updated 2022/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract We revisit the construction in four-dimensional gauged Spin(4) supergravity of the holographic duals to topologically twisted three-dimensional N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 field theories. Our focus in this paper is to highlight some subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion of finite counterterms and the necessity of a Legendre transformation to find the dual to the field theory generating functional. Studying the geometry of these supergravity solutions, we conclude that the gravitational free energy is indeed independent from the metric of the boundary, and it vanishes for any smooth solution.