Space(time) oddity: dualities, holography and branes

In this Thesis, we study (several) aspects of three and five dimensional non-supersymmetric gauge theories. Using non-perturbative techniques, such as known strong-weak coupling dualities and holography, we present new results concerning their dynamics and phase diagrams. The thesis is divided into six Chapters. In the first Chapter, we start reviewing some general aspects of non-supersymmetric three dimensional theories, focusing on the dynamics of gauge theory both in the absence and in presence of Chern-Simons terms. We then focus on known dualities among three dimensional theories, such as particle-vortex and bosonization duality. Thanks to these tools, we discuss what is known about the phase diagram of QCD3, namely the three dimensional analog of four dimensional quantum chromodynamics, for various ranges of its parameters. In Chapter two, we introduce the basics of holography, starting by reviewing the AdS/CFT correspondence. We then generalize the discussion to the case of non-conformal field theories, with particular emphasis on the description of confining theories. Finally, we review the holographic construction of four dimensional and three dimensional gauge theories, and, focusing on the latter case, we construct the gravity dual of QCD3. In Chapter three, we show new results regarding the phase diagram of QCD3 in presence of flavor-breaking mass deformation. The corresponding theory, namely QCD3 with two sets of flavors, is studied in detail, thanks to the conjectured infrared dualities characterizing gauge theories with matter in three dimensions, namely boson-fermion dualities. In particular, the low-energy phase diagram is charted, and its consistency gives additional support to the conjectured phase diagram of QCD3. Moreover, new non-perturbative phases are observed, together with peculiar phase transitions among them, which are novel to QCD3 with two flavors. In Chapter four, we study the phase diagram of large N QCD3 through its holographic dual. This novel study shows perfect agreement with the field theory analysis, giving a simple explanation of the observed peculiarity of its phase diagram, together with an holographic evidence of the validity of boson-fermion dualities. In Chapter five, we review the main aspects of five dimensional theories. Firstly, we focus on general properties of supersymmetric gauge theories, their BPS spectrum, and their moduli spaces of vacua. Then, we study their non-perturbative dynamics using string constructions, both in type I’ and in type IIB string theory. The latter type of construction, known as the pq-web or brane web construction, gives us the possibility of studying in detail many non-perturbative phenomena characterizing these theories and their superconformal ultraviolet fixed points, such as global symmetry enhancement and continuation past infinite coupling.