Related papers: Orbifold Indices in Four Dimensions

Four-dimensional supergravity theories are reinterpreted in a 12-dimensional F-theory framework. The O(8) symmetry of N=8 supergravity is related to a reduction of F-theory on T_8, with the seventy scalars formally associated, by O(8)…

In classical field theory, the composite fibred manifolds Y -> Z -> X provides the adequate mathematical formulation of gauge models with broken symmetries, e.g., the gauge gravitation theory. This work is devoted to connections on…

Any oriented 4-dimensional real vector bundle is naturally a line bundle over a bundle of quaternion algebras. In this paper we give an account of modules over bundles of quaternion algebras, discussing Morita equivalence, characteristic…

Quaternionic tori are defined as quotients of the skew field $\mathbb{H}$ of quaternions by rank-4 lattices. Using slice regular functions, these tori are endowed with natural structures of quaternionic manifolds (in fact quaternionic…

The spine of a trisected 4-manifold is a singular 3-dimensional set from which the trisection itself can be reconstructed. 3-manifolds embedded in the trisected 4--manifold can often be isotoped to lie almost or entirely in the spine of the…

This thesis contains an introductory chapter on orbifolds. The following chapter explains the foundations of orientifolds. Chapters 4-7 present own research. In chapter 4 we quantize open strings with linear boundary conditions, as they…

We study N=1 dualities in four dimensional supersymmetric gauge theories in terms of wrapping D 6-branes around 3-cycles of Calabi-Yau threefolds in type IIA string theory. We generalize the recent work of geometrical realization for the…

D6-branes intersecting at angles allow for phenomenologically appealing constructions of four dimensional string theory vacua. While it is straightforward to obtain non-supersymmetric realizations of the standard model, supersymmetric and…

In this paper, we investigate topological aspects of indices of twisted geometric operators on manifolds equipped with fibered boundaries. We define $K$-groups relative to the pushforward for boundary fibration, and show that indices of…

An arbitrary surface mass density of gravitational lens can be decomposed into multipole components. We simulate the ray-tracing for the multipolar mass distribution of generalized SIS (Singular Isothermal Sphere) model, based on the…

In theories with $N=2$ supersymmetry on $R^{3,1}$, BPS bound states can decay across walls of marginal stability in the space of Coulomb branch parameters, leading to discontinuities in the BPS indices $\Omega(\gamma,u)$. We consider a…

Four dimensional N=1 supersymmetric gauge theories with unitary gauge groups and matter in the adjoint and fundamental representations give rise to a series of non-trivial fixed points with an ADE classification. Many of these models…

In analogy with the vector bundle theory we define universal and strongly universal Lefschetz fibrations over bounded surfaces. After giving a characterization of these fibrations we construct very special strongly universal Lefschetz…

4-dimensional optics is here introduced axiomatically as the space that supports a Universal wave equation which is applied to the postulated Higgs field. Self-guiding of this field is shown to produce all the modes necessary to provide…

Hypercubic groups in any dimension are defined and their conjugate classifications and representation theories are derived. Double group and spinor representation are introduced. A detailed calculation is carried out on the structures of…

Higher spin fields in four dimensions, and more generally conformal fields in arbitrary dimensions, can be described by spinning particle models with a gauged SO(N) extended supergravity on the worldline. We consider here the one-loop…

BPS states in N=4 supersymmetric SU(N) gauge theories in four dimensions can be represented as planar string networks with ends lying on D3-branes. We introduce several protected indices which capture information on the spectrum and various…

This is a summary of some of the basic facts about flat 2-orbifold groups, otherwise known as 2-dimensional crystallographic groups. We relate the geometric and topological presentations of these groups, and consider structures…

We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on $S^3 \times $ time. Our index receives contributions from states invariant under at least one supercharge and captures all…

We use brane configurations and SL(2,Z) symmetry of the type IIB string to construct mirror N=2 supersymmetric gauge theories in three dimensions. The mirror map exchanges Higgs and Coulomb branches, Fayet-Iliopoulos and mass parameters and…