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In this thesis we study string compactifications on manifolds equipped with a $G$-structure, placing a special emphasis on the interplay between geometry and physics. We follow two complementary approaches. In the first part of the thesis…
We study the degenerating limits of superconformal theories for compactifications on singular K3 and Calabi-Yau threefolds. We find that in both cases the degeneration involves creating an Euclidean two-dimensional black hole coupled weakly…
Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the…
We consider brane gas models based on type II string theories and analyze the mass, the Ramond-Ramond charge and the charge on moduli fluctuations of branes wrapping over cycles of a compactified space in the four-dimensional Einstein…
Mirror symmetry, a three dimensional $\mathcal{N}=4$ IR duality, has been studied in detail for quiver gauge theories of the $ADE$-type (as well as their affine versions) with unitary gauge groups. The $A$-type quivers (also known as linear…
We study the twisted compactifications of five-dimensional Seiberg SCFTs, with $SU_\mathcal{M}(2)\times E_{N_f+1}$ flavor symmetry, on a generic Riemann surface that preserves four supercharges. The five-dimensional SCFTs are obtained from…
Duality groups of Abelian gauge theories on four manifolds and their reduction to two dimensions are considered. The duality groups include elements that relate different space-times in addition to relating different gauge-coupling…
We study (0,2) two-dimensional theories in type IIB configurations with D5 branes wrapping blow-up ${\bf{P}}^1$ cycles of deformed resolutions for $A_n$ singularities or in T-dual IIA configurations with suspended D4 branes. We consider…
Following the recent exploration of smooth heterotic compactifications with unitary bundles, orbifold compactifications in six dimensions can be shown to correspond in the blow-up to compactifications with U(1) gauge backgrounds. A powerful…
We consider six dimensional brane world models with a compact and a warped extra dimension with five dimensional branes. We find that such scenarios have many interesting features arising from both ADD and Randall-Sundrum -models. In…
Global aspects of Scherk-Schwarz dimensional reduction are discussed and it is shown that it can usually be viewed as arising from a compactification on the compact space obtained by identifying a (possibly non-compact) group manifold G…
Combining the effects of fluxes and gaugino condensation in heterotic supergravity, we use a ten-dimensional approach to find a new class of four-dimensional supersymmetric AdS compactifications on almost-Hermitian manifolds of SU(3)…
We investigate the ten dimensional origin of six dimensional F_4 variant supergravity with supersymmetric de Sitter background. We address first the issue of spontaneous compactification, showing that it consists of a warped…
T duality expresses the equivalence of a superstring theory compactified on a manifold K to another (possibly the same) superstring theory compactified on a dual manifold K'. The volumes of K and K' are inversely proportional. In this talk…
It is emphasized that compactified little string theories have compact moduli spaces of vacua, which globally probe compact string geometry. Compactifying various little string theories on T^3 leads to 3d theories with exact, quantum…
We study how to use smooth, compact toric varieties for supersymmetric $AdS_4$ flux compactifications using tools of SU(3) structures, similar to $CP3$ solution. A non-vanishing globally well defined complex 3-form plays a key role in such…
We study constrained generalized Killing spinors over the metric cone and cylinder of a (pseudo-)Riemannian manifold, developing a toolkit which can be used to investigate certain problems arising in supersymmetric flux compactifications of…
We demonstrate the presence of non-invertible symmetries in an infinite family of superconformal Argyres-Douglas theories. This class of theories arises from diagonal gauging of the flavor symmetry of a collection of multiple copies of…
The phase diagram for Dp-branes in M-theory compactified on $T^4$, $T^4/Z_2$, $T^5$, and $T^6$ is constructed. As for the lower-dimensional tori considered in our previous work (hep-th/9810224), the black brane phase at high entropy…
In the framework of heterotic M-theory compactified on a Calabi-Yau threefold 'times' an interval, the relation between geometry and four-flux is derived {\it beyond first order}. Besides the case with general flux which cannot be described…