Classification of Conformal Supersymmetric Deformations of Schwarzschild Spacetime via Super Poisson-Lie T-duality/Plurality
Abstract
This paper investigates conformal supersymmetric deformations of Schwarzschild spacetime through the framework of super Poisson-Lie T-duality/plurality. We first study super non-Abelian T-duality in σ-models featuring a Schwarzschild metric coupled to two fermionic fields. This is realized by describing the original four-dimensional geometry and its dual counterpart via semi-Abelian Drinfeld superdoubles generated by the Lie superalgebras (C3 +A), C3 ⊕ A1,1 and (2 A1,1+2 A)0, supplemented by two spectator fields. We enforce the vanishing of one-loop beta-function equations for both original and dual models to guarantee UV finiteness at quantum level; this procedure necessitates the inclusion of the dilaton field alongside the metric and the Kalb-Ramond field (B-field) already present in the classical action. We further study the curvature invariants, singularity structure, and superisometries, and compare the resulting supergeometries, with particular emphasis on their fermionic parts and B-fields. Starting from the decompositions of semi-Abelian Drinfeld superdoubles associated with the (C3 +A) and C3 ⊕ A1,1 Lie superalgebras, we derive the conformal duality/plurality chains for four-dimensional string backgrounds, characterized by a Schwarzschild metric coupled to two fermions. Our results span an interesting spectrum of super Poisson-Lie T-dual σ-models described by Lie superalgebras with two bosonic and two fermionic generators. These are all non-trivial and interesting examples of super Poisson-Lie T-dual models which help in the intent of providing a general classification of four-dimensional geometries describing supergravity backgrounds.
Related
- Mapping Schwarzschild Spacetime: From Kruskal to Diamond and Golden Representations
- Local tests of Schwarzschild-Bertotti-Robinson spacetime
- Analytic Electromagnetic Effective Source for Geodesic Orbit in Schwarzschild Spacetime
- Thermal Casimir Effect in A Schwarzschild-like Wormhole Spacetime
- Dynamical evolution of quantum mutual information in Schwarzschild spacetime
BibTeX
@misc{eghbali2026classification,
title = {{Classification of Conformal Supersymmetric Deformations of Schwarzschild Spacetime via Super Poisson-Lie T-duality/Plurality}},
author = {Ali Eghbali and Meysam Hosseinpour-Sadid and Adel Rezaei-Aghdam},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30426},
eprint = {2609.30426},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30426},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classification of Conformal Supersymmetric Deformations of Schwarzschild Spacetime via Super Poisson-Lie T-duality/Plurality
AU - Ali Eghbali
AU - Meysam Hosseinpour-Sadid
AU - Adel Rezaei-Aghdam
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30426
UR - https://arxiv.org/abs/2609.30426
AB - This paper investigates conformal supersymmetric deformations of Schwarzschild spacetime through the framework of super Poisson-Lie T-duality/plurality. We first study super non-Abelian T-duality in σ-models featuring a Schwarzschild metric coupled to two fermionic fields. This is realized by describing the original four-dimensional geometry and its dual counterpart via semi-Abelian Drinfeld superdoubles generated by the Lie superalgebras (C^3 +A), C^3 ⊕ A_1,1 and (2 A_1,1+2 A)^0, supplemented by two spectator fields. We enforce the vanishing of one-loop beta-function equations for both original and dual models to guarantee UV finiteness at quantum level; this procedure necessitates the inclusion of the dilaton field alongside the metric and the Kalb-Ramond field (B-field) already present in the classical action. We further study the curvature invariants, singularity structure, and superisometries, and compare the resulting supergeometries, with particular emphasis on their fermionic parts and B-fields. Starting from the decompositions of semi-Abelian Drinfeld superdoubles associated with the (C^3 +A) and C^3 ⊕ A_1,1 Lie superalgebras, we derive the conformal duality/plurality chains for four-dimensional string backgrounds, characterized by a Schwarzschild metric coupled to two fermions. Our results span an interesting spectrum of super Poisson-Lie T-dual σ-models described by Lie superalgebras with two bosonic and two fermionic generators. These are all non-trivial and interesting examples of super Poisson-Lie T-dual models which help in the intent of providing a general classification of four-dimensional geometries describing supergravity backgrounds.
ER -