Related papers: CP Symmetry and Symplectic Modular Invariance
Sixty years after the experimental discovery of CP violation in the quark sector, the existence of a similar CP violation in the lepton sector is still to be established. Actually, the structure of such a violation depends crucially on the…
We consider two dimensional $\mathcal{N}=(4,4)$ superconformal field theories in the moduli space of symmetric orbifolds of K3. We complete a classification of the discrete groups of symmetries of these models, conditional to a series of…
Within the framework of residual symmetry, two $\mathbb{Z}_2$ type associate $\mu\tau$ interchange symmetries robustly constrain the Dirac CP phase $\delta$ in a model independent way. Both of them predict simultaneous maximality of…
A brief heuristic explanation is given of recent work with Juergen Fuchs, Beatriz Gato-Rivera and Christoph Schweigert on the construction of modular invariant partition functions from Galois symmetry in conformal field theory. A…
We introduce a new approach of computing the automorphism group and the field of moduli of points $\p=[C]$ in the moduli space of hyperelliptic curves $\H_g$. Further, we show that for every moduli point $\p \in \H_g(L)$ such that the…
The deformation problem for pseudoholomorphic curves and related geometrical properties of the total moduli space of pseudoholomorphic curves are studied. A sufficient condition for the saddle point property of the total moduli space is…
We explore the implications of symmetries that remain unbroken at the self-dual point $\tau=i$ in modular invariant theories. Assuming that (a) the three generations of lepton doublets transform as an irreducible representation of a finite…
We analyze leptogenesis in a supersymmetric triplet seesaw scenario that explains the observed neutrino masses, adopting a phenomenological approach where the decay branching ratios of the triplets and the amount of CP--violation in its…
I study the weak basis CP-violating invariants in supersymmetric models, in particular those which cannot be expressed in terms of the Jarlskog--type invariants, and find basis--independent conditions for CP conservation. With an example of…
In this work, we have analyzed a neutrino model within the distinct framework of modular forms with degree, $ g>1 $ . This offers a more generalized scenario of modular forms which is popularly known as Siegel modular forms. We explore the…
For a prime number p, we construct a generating set for the ring of invariants for the p+1 dimensional indecomposable modular representation of a cyclic group of order p^2. We then use the constructed invariants to describe the…
Scalar triplet extensions of the Standard Model provide an interesting playground for the explanation of neutrino mass suppression through the type-II seesaw mechanism. Propelled by the possible connections with leptonic CP violation, we…
We make cohomological computations related to the moduli space of genus three curves with symplectic level two structure by means of counting points over finite fields. In particular, we determine the cohomology groups of the quartic locus…
We give a new characterization of symplectic surfaces in CP^2 via bridge trisections. Specifically, a minimal genus surface in CP^2 is smoothly isotopic to a symplectic surface if and only if it is smoothly isotopic to a surface in…
We show that elliptic curves with complex multiplication (CM) naturally emerge in the spectral geometry of Hermitian one-matrix models in the two-cut phase. Focusing on a symmetric quartic potential, we derive the corresponding genus-one…
We discuss the CP properties of the potential in the general Two-Higgs-Doublet Model (THDM). This is done in a concise way using real gauge invariant functions built from the scalar products of the doublet fields. The space of these…
The coupled angular momenta are a family of completely integrable systems that depend on three parameters and have a compact phase space. They correspond to the classical version of the coupling of two quantum angular momenta and they…
Let G be a split semi-simple algebraic group over Q. Let S be a decorated surface, that is a topological oriented surface with a finite set of marked points on the boundary, considered modulo isotopy. We introduce a moduli space D(G,S) and…
We derive the potential modular symmetries of heterotic string theory. For a toroidal compactification with Wilson line modulus, we obtain the Siegel modular group $\mathrm{Sp}(4,\mathbb{Z})$ that includes the modular symmetries…
We explore the geometrical origin of CP and the spontaneous CP violation in Calabi-Yau compactifications. We find that the CP symmetry is identified with an outer automorphism of the symplectic modular group in the large complex structure…