Pure and Twisted Holography

Songyuan Li (1) , Jan Troost (1)

1 Champs, Gravitation et Cordes

We analyze a simple example of a holographically dual pair in which we topologically twist both theories. The holography is based on the two-dimensional N = 2 supersymmetric Liouville conformal field theory that defines a unitary bulk quantum supergravity theory in three-dimensional anti-de Sitter space. The supersymmetric version of three-dimensional Liouville quantum gravity allows for a topological twist on the boundary and in the bulk. We define the topological bulk supergravity theory in terms of twisted boundary conditions. We corroborate the duality by calculating the chiral configurations in the bulk supergravity theory and by quantizing the solution space. Moreover, we note that the boundary calculation of the structure constants of the chiral ring carries over to the bulk theory as well. We thus construct a topological AdS/CFT duality in which the bulk theory is independent of the boundary metric.

Mots clés: Conformal and W Symmetry; Gauge-gravity correspondence; Topological Field Theories; Extended Supersymmetry; field theory: conformal; dimension: 3; duality: holography; twist: topological; boundary condition: twist; solution: quantization; space: anti-de Sitter; supersymmetry: 2; dimension: 2; supergravity; Liouville; AdS/CFT correspondence; quantum gravity; chiral ring; unitarity; chiral

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Songyuan Li, Jan Troost. Pure and Twisted Holography. Journal of High Energy Physics, 2020, 03, pp.144. ⟨10.1007/JHEP03(2020)144⟩. ⟨hal-02392941⟩