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SCFTs in six dimensions are interrelated by networks of RG flows. Compactifying such models on a Riemann surface with flux for the $6d$ global symmetry, one can obtain a wide variety of theories in four dimensions. These four dimensional…
M(atrix) theory compactified on an orbifold ${\bf T}_9/{\bf Z}_2$ is studied. Via zero-brane parton scattering we find that each of the $2^9 = 512$ orbifold fixed points carry $-1/32$ units of zero-brane charge. The anomalous flux is…
In M(atrix) theory, there exist membranes and longitudinal 5-branes (L5-branes) as extended objects. Transverse components of these brane solutions are known to be described by fuzzy CP^k (k=1,2), where k=1 and k=2 correspond to spherical…
In this paper we show that the number of all 1/2-BPS branes in string theory compactified on a torus can be derived by universal wrapping rules whose formulation we present. These rules even apply to branes in less than ten dimensions whose…
We study the conditions an arbitrary flux configuration must fulfill in order to construct a 4d space-time of the type $AdS_2\times S^2$ from a type IIB supergravity flux compactification in which NS-NS fluxes are included. We present a…
We study M and F theory compactifications on Calabi-Yau four-folds in the presence of non-trivial background flux. The geometry is warped and belongs to the class of p-brane metrics. We solve for the explicit warp factor in the orbifold…
We discuss issues concerning M(atrix) theory compactifications on curved spaces. We argue from the form of the graviton propagator on curved space that excited string states do not decouple from the annulus D0-brane $v^4$ amplitude, unlike…
The main topic of this thesis are flux compactifications. Firstly, we study dimensional reductions of type II and eleven-dimensional supergravities using exceptional generalised geometry. We start by presenting the needed mathematical…
We study the $T^2$ compactification of a class of 6d $\mathcal{N}{=}(1,0)$ theories that is Higgsable to $\mathcal{N}{=}(2,0)$ theories. We show that the resulting 4d $\mathcal{N}{=}2$ theory at the origin of the Coulomb branch and the…
Using F-theory/heterotic duality, we describe a framework for analyzing non-geometric T2-fibered heterotic compactifications to six- and four-dimensions. Our results suggest that among T2-fibered heterotic string vacua, the non-geometric…
In the light of the duality between physics in the bulk of anti-de Sitter space and a conformal field theory on the boundary, we review the M2, D3 and M5 branes and how their near-horizon geometry yields the compactification of D=11…
We investigate a particle physics model in a six-dimensional spacetime, where two extra dimensions form a torus. Particles with Standard Model charges are confined by interactions with a scalar field to four four-dimensional branes, two…
Compactification of type IIB theory on torus, in the presence of fluxes, is considered. The reduced effective action is expressed in manifestly S-duality invariant form. Cosmological solutions of the model are discussed in several cases in…
It was shown by Connes, Douglas, Schwarz[1] that one can compactify M(atrix) theory on noncommutative torus. We prove that compactifications on Morita equivalent tori are physically equivalent. This statement can be considered as a…
We consider four dimensional N=1 supersymmetric Type I compactifications on toroidal orbifolds T^6/G. In particular, we focus on the Type I vacua which are perturbative from the orientifold viewpoint, that is, on the compactifications with…
We consider the tensor theory on coincident E8 5-branes compactified on a three torus. Using string theory, we predict that there must be distinct components in the moduli space of this theory.We argue that new superconformal field theories…
We study a decoupling limit of M-theory where the three-form gauge potential becomes critical. This limit leads to nonrelativistic M-theory coupled to a non-Lorentzian spacetime geometry. Nonrelativistic M-theory is U-dual to M-theory in…
In tropical geometry, one studies algebraic curves using combinatorial techniques via the tropicalization procedure. The tropicalization depends on a map to an algebraic torus and the combinatorial methods are most useful when the…
We show that global properties of gauge groups can be understood as geometric properties in M-theory. Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with $A_{N-1}$ gauge algebra and different…
Following a recent suggestion by Randall and Sundrum, we consider string compactification scenarios in which a compact slice of AdS-space arises as a subspace of the compactification manifold. A specific example is provided by the type II…