Group Theoretical Hidden Structure of Supergravity Theories in Higher Dimensions
L. Ravera
备注：
204 pages, 5 figures. Thesis discussed on February 8, 2018 for the Ph.D title achievement in Physics, carried out in the Politecnico di Torino Ph.D program in Physics (cycle 30th). It contains results and material already published in arXiv:1511.06245, arXiv:1606.07328, arXiv:1607.00373, arXiv:1609.05042, arXiv:1611.05812, arXiv:1701.04234, arXiv:1705.06251, arXiv:1801.08860
The purpose of my PhD thesis is to investigate different group theoretical and geometrical aspects of supergravity theories. To this aim, several research topics are explored: On one side, the construction of supergravity models in diverse space-time dimensions, including the study of boundary contributions, and the disclosure of the hidden gauge structure of these theories; on the other side, the analysis of the algebraic links among different superalgebras related to supergravity theories.
In the first three chapters, we give a general introduction and furnish the theoretical background necessary for a clearer understanding of the thesis. We then move to the original results of my PhD research activity: We start from the development of the so called $AdS$-Lorentz supergravity in $D=4$ by adopting the so called rheonomic approach and discuss on boundary contributions to the theory. Subsequently, we focus on the analysis of the hidden gauge structure of supersymmetric Free Differential Algebras. More precisely, we concentrate on the hidden superalgebras underlying $D=11$ and $D=7$ supergravities, exploring the symmetries hidden in the theories and the physical role of the nilpotent fermionic generators naturally appearing in the aforementioned superalgebras. After that, we move to the pure algebraic and group theoretical description of (super)algebras, focusing on new analytic formulations of the so called $S$-expansion method. The final chapter contains the summary of the results of my doctoral studies presented in the thesis and possible future developments. In the Appendices, we collect notation, useful formulas, and detailed calculations.
We report on recent developments regarding the supersymmetric Free Differential Algebra describing the vacuum structure of $D=11$ supergravity. We focus on the emergence of a hidden superalgebra underlying the theory, explaining the group-theoretical role played by the nilpotent fermionic generator naturally appearing for consistency of the construction. We also discuss the relation between this hidden superalgebra and other superalgebras of particular relevance in the context of supergravity and superstring, involving a fermionic generator with 32 components.
The ultrashort unitary (4,0) supermultiplet of 6d superconformal algebra OSp(8*|8) reduces to the CPT-self conjugate supermultiplet of 4d superconformal algebra SU(2,2|8) that represents the fields of maximal N=8 supergravity. The graviton in the (4,0) multiplet is described by a mixed tensor gauge field which can not be identified with the standard metric in 6d. Furthermore the (4,0) supermultiplet can be obtained as a double copy of (2,0) conformal supermultiplet whose interacting theories are non-Lagrangian. It had been suggested that an interacting non-metric (4,0) supergravity theory migh…
All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry
研究了强耦合超对称Yang-Mills理论中四个保护（半BPS）算子的关联函数.这些都是双重的树级超重力振幅上的AdS ${}_5\times$ S ${}_5$的各种球谐的五球。我们使用共形场论的方法，特别是最近获得的洛伦兹反演公式，分析这些自举。提取的$1/N^2$双迹反常维数证实了Aprile、Drummond、Heslop和Paul最近提出的一个简单模式。我们用一种出乎意料的十维共形对称来解释这种模式，这种对称似乎被树级超引力（或它的一个合适的子扇区）所享有。的对称性结合成一个单一的十维对象的所有球谐函数，并产生紧凑的表达式的任何半BPS相关器在每个循环顺序的领先的对数部分。
