Schwarzschild时空的共形超对称形变的超Poisson-Lie T-对偶/多重性分类
Classification of Conformal Supersymmetric Deformations of Schwarzschild Spacetime via Super Poisson-Lie T-duality/Plurality
- Azarbaijan Shahid Madani University（阿塞拜疆沙希德·马达尼大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过超Poisson-Lie T-对偶/多重性框架，研究Schwarzschild时空的共形超对称形变，推导四维弦背景的共形对偶链，并分类超引力背景几何。
AI中文摘要：
本文通过超Poisson-Lie T-对偶/多重性框架研究Schwarzschild时空的共形超对称形变。我们首先研究耦合了两个费米子场的Schwarzschild度规的σ模型中的超非阿贝尔T-对偶。这是通过用半阿贝尔Drinfeld超双代数描述原始四维几何及其对偶对应来实现的，这些超双代数由李超代数$({\C}^3 +{\A})$、${\C}^3 \oplus {\A}_{1,1}$和$(2{ \A}_{1,1}+2{ \A})^0$生成，并辅以两个旁观者场。我们强制原始模型和对偶模型的一圈β函数方程消失，以保证量子层面的紫外有限性；这一过程需要将膨胀子场与经典作用量中已有的度规和Kalb-Ramond场（B场）一起纳入。我们进一步研究了曲率不变量、奇点结构和超等距，并比较了所得的超几何，特别强调了它们的费米子部分和B场。从与$({\C}^3 +{\A})$和${\C}^3 \oplus {\A}_{1,1}$李超代数相关的半阿贝尔Drinfeld超双代数的分解出发，我们推导了四维弦背景的共形对偶/多重性链，其特征是耦合了两个费米子的Schwarzschild度规。我们的结果涵盖了一个有趣的超Poisson-Lie T-对偶σ模型谱，这些模型由具有两个玻色子和两个费米子生成元的李超代数描述。这些都是非平凡且有趣的超Poisson-Lie T-对偶模型实例，有助于实现对描述超引力背景的四维几何的一般分类。
英文摘要：
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 $({\C}^3 +{\A})$, ${\C}^3 \oplus {\A}_{1,1}$ 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 ${\C}^3 \oplus {\A}_{1,1}$ 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.
