Related papers: On Algorithmic Universality in F-theory Compactifi…
The most general geometrical scenario in which the brane-world program can be implemented is investigated. The basic requirement is that it should be consistent with the confinement of gauge interaction, the existence of quantum states and…
The strategy for assigning $Z_{4R}$ parity in the string compactification is presented. For the visible sector, an anti-SU(5) (flipped-SU(5)) grand unification (GUT) model with three families is used to reduce the number of representations…
Consistent coupling of effective field theories with a quantum theory of gravity appears to require bounds on the the rank of the gauge group and the amount of matter. We consider landscapes of field theories subject to such to boundedness…
We consider N=1 supersymmetric U(N), SO(N), and Sp(N) gauge theories, with two-index tensor matter and added tree-level superpotential, for general breaking patterns of the gauge group. By considering the string theory realization and…
The heterotic $E_8\times E_8$ string compactified on an orbifold $T^4/\IZ_N$ has gauge group $G\times G'$ with (massless) states in its twisted sectors which are charged under both gauge group factors. In the dual M-theory on…
We study four dimensional N=1 gauge theories that arise on the worldvolume of D3-branes probing complex cones over del Pezzo surfaces. Global symmetries of the gauge theories are made explicit by using a correspondence between bifundamental…
Quantum anomalies, determined by the Atiyah-Singer index theorem, place strong constraints on the space of quantum gravity theories in six dimensions with minimal supersymmetry. The conjecture of "string universality" states that all such…
Five-dimensional $\mathcal{N}=1$ theories with gauge group $U(N)$, $SU(N)$, $USp(2N)$ and $SO(N)$ are studied at large rank through localization on a large sphere. The phase diagram of theories with fundamental hypermultiplets is universal…
We give brief ideas on building gauge models in superstring theory, especially the four-dimensional models obtained from the compactification of F-theory. According to Vafa, we discuss the construction of F-theory to approach…
A fully realistic and systematic effective field theory model of a 3-brane universe is constructed. It consists of a six-dimensional gravitating spacetime, containing several, approximately parallel (3+1)-dimensional defects, or…
We formulate an extension of Maldacena's AdS/CFT conjectures to the case of branes located at singular points in the ambient transverse space. For singularities which occur at finite distance in the moduli space of M or F theory models with…
It has recently been proposed that gravity-localized compactifications can generate the required gauge hierarchy without the need for hierarchically large extra spacetime dimensions. In this paper, we show that gauge coupling unification…
We relate the existence problem of universal objects to the properties of corresponding enriched categories (lifts or expansions). In particular, extending earlier results, we prove that for every (possibly infinite) regular set F of finite…
The conjugacy problem for a finitely generated group $G$ is the two-variable problem of deciding for an arbitrary pair $(u,v)$ of elements of $G$, whether or not $u$ is conjugate to $v$ in $G$. We construct examples of finitely generated,…
We describe symmetry structure of a general singular theory (theory with constraints in the Hamiltonian formulation), and, in particular, we relate the structure of gauge transformations with the constraint structure. We show that any…
We propose a sequential topology on the space of sub-$\sigma$-algebras of a separable probability space $(\Omega,\mathcal{F},\mathbb{P})$ by linking conditional expectations on $L^{2}$ along sequences of sub-$\sigma$-algebras. The varying…
We study some geometrical and topological aspects of the generalised dimensional reduction of supergravities in D=11 and D=10 dimensions, which give rise to massive theories in lower dimensions. In these reductions, a global symmetry is…
We study seven-brane SU(5) GUT models of string phenomenology which can be consistently analyzed in a purely local framework. The requirement that gravity can decouple constrains the form of four-dimensional physics as well as the geometry…
It might seem that a choice of a time coordinate in Hamiltonian formulations of general relativity breaks the full four-dimensional diffeomorphism covariance of the theory. This is not the case. We construct explicitly the complete set of…
We develop a unified categorical framework for gauging both continuous and finite symmetries in arbitrary spacetime dimensions. Our construction applies to geometric categories i.e. categories internal to stacks. This generalizes the…