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We study two-dimensional conformal field theories generated from a ``symplectic fermion'' - a free two-component fermion field of spin one - and construct the maximal local supersymmetric conformal field theory generated from it. This…
The heterotic $SU(3)$ system, also known as the Hull--Strominger system, arises from compactifications of heterotic string theory to six dimensions. This paper investigates the local structure of the moduli space of solutions to this system…
We consider topologically twisted $\mathcal{N}=2$, $SU(2)$ gauge theory with a massive adjoint hypermultiplet on a smooth, compact four-manifold $X$. A consistent formulation requires coupling the theory to a ${\rm Spin}^c$ structure, which…
We study a topological obstruction of a very stringy nature concerned with deforming the target space of an $N=2$ non-linear \sm. This target space has a singularity which may be smoothed away according to the conventional rules of geometry…
We demonstrate that type II string theory compactified on a singular Calabi-Yau manifold is related to $c=1$ string theory compactified at the self-dual radius. We establish this result in two ways. First we show that complex structure…
We investigate some classical aspects of fundamental strings via numerical experiments. In particular, we study the thermodynamics of a string network within a toroidal universe, as a function of string energy density and space…
The condition of having an $N=1$ spacetime supersymmetry for heterotic string leads to 4 distinct possibilities for compactifications namely compactifications down to 6,4,3 and 2 dimensions. Compactifications to 6 and 4 dimensions have been…
Considering SO(32) heterotic string theory compactified on a torus of dimension 4 and less, stability of non-supersymmetric states is studied. A non-supersymmetric state with robust stability is constructed, and its exact stability is…
We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncom- mutative space where the noncommutativity is induced by a shift of the dynamical variables with generators of SL(2;R) in a unitary irreducible…
Three-manifolds can be obtained through surgery of framed links in $S^3$. We study the meaning of surgery procedures in the context of topological strings. We obtain U(N) three-manifold invariants from U(N) framed link invariants in…
We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau…
We present solutions of the holomorphic anomaly equations for compact two-parameter Calabi-Yau manifolds which are hypersurfaces in weighted projective space. In particular we focus on K3-fibrations where due to heterotic type II duality…
We study topological string theory on elliptically fibered Calabi-Yau threefolds using mirror symmetry. We compute higher genus topological string amplitudes and express these in terms of polynomials of functions constructed from the…
We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their relation with refined topological strings. Our results generalize the familiar connections between local topological strings and matrix models leading to An measure,…
We provide a new class of exactly solvable superconformal field theories that corresponds to type II compactification on manifolds with exceptional holonomies. We combine N=1 Liouville field and N=1 coset models and construct modular…
In the present thesis I studied the phenomenology arising from a class of string models called sequestered compactifications, which were born with the aim of getting low-energy SUSY from strings. This is not an easy task if combined with…
S-folds are generalizations of orientifolds in type IIB string theory, such that the geometric identifications are accompanied by non-trivial S-duality transformations. They were recently used by Garcia-Etxebarria and Regalado to provide…
We study various composites of global solitons consisting of domain walls, strings, and monopoles in linear $O(N)$ models with $N=2$ and $3$. Spontaneous symmetry breaking (SSB) of the $O(N)$ symmetry down to $O(N-1)$ results in the vacuum…
We investigate the arguably simplest $SU(2)$-invariant wave functions capable of accounting for spin-liquid behavior, expressed in terms of nearest-neighbor valence-bond states on the square lattice and characterized by different…
This work investigates cosmic topological defects in gauge theories, focusing on models with an $SU(N)$ gauge group coupled with a single flavor, explored through a holographic framework. At low energies, the effective theory is described…