Relatore
Descrizione
The AdS$_2$/CFT$_1$ correspondence plays a key role in the microscopical description of extremal black holes, AdS$_2$ being part of the geometry that appears in their near horizon limit in any dimension.
Another useful application of the AdS$_2$/CFT$_1$ correspondence is to the holographic description of superconformal line defects in higher dimensional CFTs. Geometrically, a sign that an AdS$_2$ solution may be describing a superconformal line defect is that it flows asymptotically locally to a higher dimensional AdS background, dual far from the defects to the higher dimensional CFT in which they are embedded.
I will present general results on the construction of AdS$_2$ solutions to Type II supergravity via U(1) and SL(2) T-dualities, paying special attention to the conditions for preservation of supersymmetry. I then exploit these to construct new classes of small ${\cal{N}} = 4$ solutions in Type II supergravity.
I also applied this procedure to two solutions in Type IIA Supergravity with $\mathbb{CP}^3$ along the internal space. These preserve ${\cal{N}}=(5,0)$ or ${\cal{N}}=(6,0)$ supersymmetry and realise the superconformal algebras $osp(5|2)$ and $osp(6|2)$. This results in four new classes of AdS$_2$ solutions, realising these superconformal algebras, hinting that a more general class AdS$_2 \times \mathbb{CP}^3 \times \Sigma$ may exist.
