• Holography
• Ads/CFT
• Skyrme Model

The Thesis is divided into four parts:

In the first part we'll introduce the historical background of strong interactions and the context in which the Gauge / Gravity duality arose.

In the second part we'll study in detail al the ingredients necessary to understand and explain the Maldacena's conjecture and the gauge gravity duality in general. We will begin giving the basics about string and supersymmetric string theory from the classical and the quantum point of view.Then we will approach the Large N expansion of Quantum Chromo Dynamics and we will review the different formulations concerning the Anti De Sitter space. After this we will acquire the Conformal Field Theory fundamentals such as conformal invariance and scale invariance from the classical and quantum point of view. At this point we will enter into the core of Maldacena conjecture, i.e. the AdS /CFT correspondence, showing how was realised in his original formulation as well as its Holographic interpretation. Then we will extend the Maldacena's Conjecture to finite temperature systems introducing firstly the Witten Background and then the Sakai Sugimoto Model.

In the third part we will introduce Topological Solitons basics. Firstly we will illustrate all the mathematical and physical tools such as Homotopy Groups, Chern Numbers, Derrick's Theorem needed to approach the huge variety of topological solitons that arise in quantum field theory .In this context we will approach only the most important ones such as Kinks, Vortices, Monopoles, Instantons, Sigma Model Lumps , Baby Skyrmions and Skyrmions in the ending. Instantons and Skyrmions will especially play a crucial role in the original part, which is the last one.

This is the truely original part. Here we will select, among an ensamble of possibilities, a quick procedure to extract the Sextic Term form the original Sakai Sugimoto Pion Expansion. This goal will be achieved considering the small 't Hooft coupling limit, instead of the large one ,providing the right context in which this may be done. We conjecture that the Sakai Sugimoto Instanton, in this limit, approaches the flat space. This conjecture will prove true, assuming an approximation on the equation of motion of the original Sakai Sugimoto Action which will be verifed a posteriori. Then, combining different ansatz's ,a new pion expansion will be provided and the solutions arising will be studied numerically, as well as the energy arising. It Will be shown that different energy terms will partecipate with a different weight to the total energy in the small lambda limit. More specifically we will show how the quartic term of the energy arising from the pion expansion. We will also provide a verification for this behaviour.