Holographic RG flows and boundary conditions in a 3D gauged supergravity

Ksenia Arkhipova; Lev Astrakhantsev; Nihat Sadik Deger; Anastasia A. Golubtsova; Kirill Gubarev; Edvard T. Musaev

doi:10.1140/epjc/s10052-024-12932-1

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 560
https://doi.org/10.1140/epjc/s10052-024-12932-1

Regular Article – Theoretical Physics

Holographic RG flows and boundary conditions in a 3D gauged supergravity

Ksenia Arkhipova¹, Lev Astrakhantsev², Nihat Sadik Deger³, Anastasia A. Golubtsova¹^,4, Kirill Gubarev² and Edvard T. Musaev²^,5^f

¹ Bogoliubov Laboratory of Theoretical Physics, JINR, Joliot-Curie str. 6, 141980, Dubna, Russia
² Moscow Institute of Physics and Technology, Institutskii per. 9, 141700, Dolgoprudny, Russia
³ Department of Mathematics, Bogazici University, Bebek, 34342, Istanbul, Turkey
⁴ Steklov Mathematical Institute, Russian Academy of Sciences, 119991, Moscow, Russia
⁵ Institute for Theoretical and Mathematical Physics, MSU, 119991, Moscow, Russia

^f musaev.et@phystech.edu

Received: 29 February 2024
Accepted: 20 May 2024
Published online: 4 June 2024

Abstract

In this work we focus on the study of RG flows of conformal field theories that are holographically dual to Poincaré domain wall solutions in $D = 3$ $$D=3$$ , $N = (2, 0)$ $\mathcal {N}=(2,0)$ gauged supergravity coupled to a sigma model with target space $SU (1, 1) / U (1) = H^{2}$ $\textrm{SU}(1, 1)/\textrm{U}(1) = \mathbb {H}^2$ . This theory is truncated to a subsector where the vector field and phase of the scalar field vanish and we consider different boundary conditions for the remaining real scalar field. The RG flows, which are mostly non-superysymmetric, are analyzed by treating the supergravity field equations as a dynamical system for the scalar field and its derivative with respect to the scale factor. Phase diagrams are constructed for different values of the parameter $a^{2}$ $$a^2$$ , which is related to the curvature of the scalar manifold. The behavior of solutions near the boundary is used to determine their type based on the expansion of the corresponding fake superpotential. By incorporating information on the boundary conditions, the obtained RG flows are interpreted using the holographic dictionary. Numerical solutions and plots of the fake superpotential are also provided.

© The Author(s) 2024

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