Related papers: The Vacuum Moduli Space of the Minimal Supersymmet…

Vacuum structure of a quantum field theory is a crucial property. In theories with extended symmetries, such as supersymmetric gauge theories, the vacuum is typically a continuous manifold, called the vacuum moduli space, parametrized by…

We give necessary conditions on complete embedded \cmc surfaces with three or four ends subject to reflection symmetries. The respective submoduli spaces are two-dimensional varieties in the moduli spaces of general \cmc surfaces. We…

We analyze the moduli space of the low-energy limit of 3-dimensional N=3 Maxwell-Chern-Simons theories described by circular quiver diagrams, as for 4-dimensional elliptic models. We define the theories by using D3-NS5-(k,1)5-brane systems…

A consistent theoretical description of physics at high energies requires an assessment of vacuum stability in either the Standard Model or any extension of it. Especially supersymmetric extensions allow for several vacua and the choice of…

The moduli space of K3 surfaces $X$ with a purely non-symplectic automorphism $\sigma$ of order $n\geq 2$ is one dimensional exactly when $\varphi(n)=8$ or $10$. In this paper we classify and give explicit equations for the very general…

Let $k$ be an algebraically closed field and let $b$ and $n$ be integers with $n\geq 3$ and $1\leq b \leq n-1.$ Consider the moduli space $X$ of hypersurfaces in $\mathbb{P}^n_k$ of fixed degree $l$ whose singular locus is at least…

We study the moduli space of discrete, faithful, type-preserving representations of the modular group $\mathbf{PSL}(2,\mathbb{Z})$ into $\mathbf{PU}(3,1)$. The entire moduli space $\mathcal{M}$ is a union of…

The minimal supersymmetric standard model (MSSM) is extended by including an additional pair of constrained Higgs doublet superfields through which the electroweak symmetry is nonlinearly realized. The superpotential couplings of this…

The scalar potential of the Minimal Supersymmetric Standard Model (MSSM) admits the existence of vacua with non-vanishing expectation values of electrically and color charged fields. If such minima are deep enough, the physical electroweak…

Let $M_1$ be the moduli space of the KSBA stable surfaces $X$ of geometric genus $p_g(X)=1$ realizing the minimal possible volume $K_X^2=\frac1{143}$. We show that its reduced part $M_{1,\rm red}$ is a $10$-dimensional projective variety…

We consider very constrained versions of the minimal supersymmetric extension of the Standard Model (VCMSSMs) which, in addition to constraining the scalar masses m_0 and gaugino masses m_{1/2} to be universal at some input scale, impose…

The cosmological moduli problem (CMP) comes in three parts: 1. potential violation of BBN constraints from late decaying moduli fields, 2. the moduli-induced gravitino problem wherein gravitinos are overproduced and 3. the moduli-induced…

We propose a new next-to-minimal supersymmetric standard model (NMSSM) which is on a six-dimensional spacetime compactified on a $T^2/Z_3$ orbifold. In this model, three gauge singlet fields $N, S_1$ and $S_2$ in addition to the minimal…

This article introduces a universal moduli space for the set whose archetypal element is a pair that consists of a metric and second fundamental form from a compact, oriented, positive genus minimal surface in some hyperbolic 3-manifold.…

Let $\mathcal{F}_1(n,m)$ be the space of ordered m-tuples of pairwise distinct points in $\partial \mathbf{H}_{\mathbb{H}}^n$ up to its isometry group $PSp(n,1)$. It is a real $2m^2-6m+5-\sum^{m-n-1}_{i=1}{m-2 \choose n-1+i}$ dimensional…

We analyze a scalar potential of the minimal supersymmetric standard model (MSSM) with neutrino mass operators along Unbounded-From-Below (UFB) and Color and/or Charged Breaking (CCB) directions. We show necessary conditions to avoid the…

In this thesis, we study moduli in compactifications of ten-dimensional heterotic supergravity. We consider supersymmetric compactifications to four-dimensional maximally symmetric space, commonly referred to as the Strominger system. The…

In this article, we study the topology and bifurcations of the moduli space $\mathcal{M}_3$ of cubic Newton maps. It's a subspace of the moduli space of cubic rational maps, carrying the Riemann orbifold structure $(\mathbb{\widehat{C}},…

We present a novel class of theories where supersymmetry is only preserved in a partial (non-isolated) sector. The supersymmetric sector consists of CFT bound-states that can coexist with fundamental states which do not respect…

This article studies moduli spaces of Bridgeland semistable objects in the Kuznetsov component of a cubic fourfold that don't admit a symplectic resolution, i.e., moduli spaces of objects with non-primitve Mukai vector v=mv_0 that is not of…