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 [15], we first compute the one-loop partition functions, using the generalized eigenfunctions of the Dirac and Laplace operators 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 AdS4. We also note certain deviations from phases of these theories in flat space.
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Acknowledgments
Astha Kakkar acknowledges the support of Department of Science and Technology (DST), Ministry of Science and Technology, Government of India, for the DST INSPIRE Fellowship with the INSPIRE Fellowship Registration Number: IF180721. S.S. thanks the University Grants Commission (UGC), and DST, New Delhi, India, for providing special assistance and infrastructural support to the Department of Physics, Vidyasagar University, through the SAP and FIST program respectively.
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Kakkar, A., Sarkar, S. Phases of theories with fermions in AdS. J. High Energ. Phys. 2023, 9 (2023). https://doi.org/10.1007/JHEP06(2023)009
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DOI: https://doi.org/10.1007/JHEP06(2023)009