本文研究了N=4和N=8的三维规范超引力中的$AdS_3$超对称真空，其中标量流形分别为非半单Chern-Simons规范$SO(4)\ltimes {\bf R}^6$和$(SO(4)\ltimes {\bf R}^6)^2$，即$(\frac{SO(4,4)}{SO(4)\times SO(4)})^2$和$\frac{SO(8,8)}{SO(8)\times SO(8)}$.这些理论又等价于SO（4）和耦合到超引力的$SO(4)\times SO(4)$杨-米尔斯理论。对于N=4的情形，我们研究了具有相同超对称性的紫外和红外$AdS_3$真空之间的重整化群流：在（3，1）超对称的情形下，我们可以找到解析解，而在（2，0）超对称的情形下，我们给出了数值解.在这两种情况下，流都是v. e. v.流，即它们由对偶$SCFT_2$中相关算子的期望值驱动。这些提供了在测量的超重力框架内两个$AdS_3$真空之间的v. e. v.流的例子。
英文摘要：
We study $AdS_3$ supersymmetric vacua in N=4 and N=8, three dimensional gauged supergravities, with scalar manifolds $(\frac{SO(4,4)}{SO(4)\times SO(4)})^2$ and $\frac{SO(8,8)}{SO(8)\times SO(8)}$, non-semisimple Chern-Simons gaugings $SO(4)\ltimes {\bf R}^6$ and $(SO(4)\ltimes {\bf R}^6)^2$, respectively. These are in turn equivalent to SO(4) and $SO(4)\times SO(4)$ Yang-Mills theories coupled to supergravity. For the N=4 case, we study renormalization group flows between UV and IR $AdS_3$ vacua with the same amount of supersymmetry: in one case, with (3,1) supersymmetry, we can find an analytic solution whereas in another, with (2,0) supersymmetry, we give a numerical solution. In both cases, the flows turn out to be v.e.v. flows, i.e. they are driven by the expectation value of a relevant operator in the dual $SCFT_2$. These provide examples of v.e.v. flows between two $AdS_3$ vacua within a gauged supergravity framework.
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Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova（帕多瓦大学伽利略·伽利莱物理与天文系）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Université Libre de Bruxelles (ULB)（布鲁塞尔自由大学）；International Solvay Institutes（国际索尔维研究所）
In an ungauged supergravity theory, the presence of a \emph{scalar potential} is allowed only for the minimal $\N=1$ case. In extended supergravities, a non-trivial scalar potential can be introduced without explicitly breaking supersymmetry only through the so-called \emph{gauging procedure}. The latter consists in promoting a suitable global symmetry group to local symmetry to be gauged by the vector fields of the theory. Gauged supergravities provide a valuable approach to the study of superstring flux-compactifications and the construction of phenomenologically viable, string-inspired mode…
We study supersymmetric $AdS_4$ black holes in matter-coupled $N=3$ and $N=4$ gauged supergravities in four dimensions. In $N=3$ theory, we consider $N=3$ gauged supergravity coupled to three vector multiplets and $SO(3)\times SO(3)$ gauge group. The resulting gauged supergravity admits two $N=3$ supersymmetric $AdS_4$ vacua with $SO(3)\times SO(3)$ and $SO(3)$ symmetries. We find an $AdS_2\times H^2$ solution with $SO(2)\times SO(2)$ symmetry and an analytic solution interpolating between this geometry and the $SO(3)\times SO(3)$ symmetric $AdS_4$ vacuum. For $N=4$ gauged supergravity coupled…
This thesis is focused on supersymmetric objects in gauged supergravities and their interpretation in string theory. Three particular theories are considered and analyzed: matter-coupled $d=4, 5$ abelian gauged supergravities with 8 supercharges and minimal $d=7$ gauged supergravity with 16 supercharges. Respectively in the $d=4$ and $d=5$ cases, the BPS first-order flows of static extremal black holes and black strings are studied using the Hamilton-Jacobi formalism. The attractor mechanism is formulated for the case of couplings to hypermultiplets and two exact BPS black hole solutions are d…
