Phases of theories with fermions in AdS

Abstract

We study the phases of Yukawa theories at weak coupling and the Gross-Neveu models in AdS spaces at zero and finite temperature. Following the method used in \cite{Kakkar:2022hub}, we first compute the one-loop partition functions, using the generalized eigenfunctions of the Laplacian on Euclidean AdS in the Poincaré coordinates. These functions satisfy desired periodicities under thermal identification. The method replicates results for partition functions known in the literature. We then study the phases of these field theories with fermions as regions in the corresponding parameter spaces at zero temperature. The phases and the corresponding phase boundaries are further identified as a function of the mass-squared of the scalar field and temperature for the Yukawa theories. While for the Gross-Neveu models, the changes in the phases as a function of the fermionic mass and the coupling constant at finite temperature are discussed. The Gross-Neveu-Yukawa model is studied for AdS${}_4$. We also note certain deviations from phases of these theories in flat space.

30+11 pages

References in corpus (6)

• Conformal field theories in anti-de Sitter space
• CFT in AdS and boundary RG flows
• Partition Functions, the Bekenstein Bound and Temperature Inversion in Anti-de Sitter Space and its Conformal Boundary
• Fermions in AdS and Gross-Neveu BCFT
• On partition functions and phases of scalars in AdS
• Snowmass White Paper: S-matrix Bootstrap

Cited by in corpus (2)

• Boundary criticality for the Gross-Neveu-Yukawa models
• Partition functions for $U(1)$ vectors and phases of scalar QED in AdS