Supersymmetry and complexified spectrum on Euclidean AdS2

Alfredo González Lezcano (Asia Pacific Center for Theoretical Physics, Postech, Pohang 37673, Korea) ; Augniva Ray (Asia Pacific Center for Theoretical Physics, Postech, Pohang 37673, Korea) ; Imtak Jeon (Asia Pacific Center for Theoretical Physics, Postech, Pohang 37673, Korea and Department of Physics, Postech, Pohang 37673, Korea)

Quantum study of supersymmetric theories on Euclidean two dimensional anti–de Sitter space (AdS2) is invalid if we use the standard normalizable functional basis due to its incompatibility with supersymmetry. We cure this problem by demonstrating that supersymmetry requires a complexified spectrum and constructing the supersymmetric basis for scalar and spinor fields. Our new basis is free of fermionic zero modes, delta-function normalizable with respect to a newly defined inner product, and compatible with the supersymmetric asymptotic boundary condition. We also explore the one-loop evaluation using this basis and show that it agrees with the standard nonsupersymmetric basis up to a global contribution arising from the fermion zero mode.

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      "title": "Supersymmetry and complexified spectrum on Euclidean <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>"
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      "value": "Quantum study of supersymmetric theories on Euclidean two dimensional anti\u2013de Sitter space (<math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>) is invalid if we use the standard normalizable functional basis due to its incompatibility with supersymmetry. We cure this problem by demonstrating that supersymmetry requires a complexified spectrum and constructing the supersymmetric basis for scalar and spinor fields. Our new basis is free of fermionic zero modes, delta-function normalizable with respect to a newly defined inner product, and compatible with the supersymmetric asymptotic boundary condition. We also explore the one-loop evaluation using this basis and show that it agrees with the standard nonsupersymmetric basis up to a global contribution arising from the fermion zero mode."
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Published on:
29 August 2023
Publisher:
APS
Published in:
Physical Review D , Volume 108 (2023)
Issue 4
DOI:
https://doi.org/10.1103/PhysRevD.108.045018
arXiv:
2305.12925
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: