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