scholarly journals Landscape of modular symmetric flavor models

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Keiya Ishiguro ◽  
Tatsuo Kobayashi ◽  
Hajime Otsuka
Keyword(s):  
Fixed Point ◽  
Flux Compactifications ◽  
Strong Correlation ◽  
Complex Structure ◽  
Fundamental Region ◽  
Moduli Stabilization ◽  
Flavor Symmetries ◽  
Flavor Structure ◽  
String Landscape

Abstract We study the moduli stabilization from the viewpoint of modular flavor symmetries. We systematically analyze stabilized moduli values in possible configurations of flux compactifications, investigating probabilities of moduli values and showing which moduli values are favorable from our moduli stabilization. Then, we examine their implications on modular symmetric flavor models. It is found that distributions of complex structure modulus τ determining the flavor structure are clustered at a fixed point with the residual ℤ3 symmetry in the SL(2, ℤ) fundamental region. Also, they are clustered at other specific points such as intersecting points between |τ|2 = k/2 and Re τ = 0,±1/4,±1/2, although their probabilities are less than the ℤ3 fixed point. In general, CP-breaking vacua in the complex structure modulus are statistically disfavored in the string landscape. Among CP-breaking vacua, the values Re τ = ±1/4 are most favorable in particular when the axio-dilaton S is stabilized at Re S = ±1/4. That shows a strong correlation between CP phases originated from string moduli.

Rational Integer Invariants of Regular Cyclic Actions

2004 ◽  
Vol 47 (1) ◽  
pp. 60-72 ◽  
Author(s):  
Robert D. Little
Keyword(s):  
Fixed Point ◽  
Normal Bundle ◽  
Complex Structure ◽  
Rational Integer ◽  
Fixed Point Set ◽  
Cyclic Action ◽  
Point Set ◽  
Smooth Map

AbstractLet g : M2n → M2n be a smooth map of period m ≥ 2 which preserves orientation. Suppose that the cyclic action defined by g is regular and that the normal bundle of the fixed point set F has a g-equivariant complex structure. Let F ⋔ F be the transverse self-intersection of F with itself. If the g-signature Sign(g, M) is a rational integer and n < ϕ(m), then there exists a choice of orientations such that Sign(g, M) = Sign F = Sign(F ⋔ F).

scholarly journals G 4 flux, algebraic cycles and complex structure moduli stabilization

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
A. P. Braun ◽  
R. Valandro
Keyword(s):  
Moduli Space ◽  
Complex Structure ◽  
Algebraic Cycles ◽  
Specific Point ◽  
Moduli Stabilization ◽  
Fermat Point

Abstract We construct G4 fluxes that stabilize all of the 426 complex structure moduli of the sextic Calabi-Yau fourfold at the Fermat point. Studying flux stabilization usually requires solving Picard-Fuchs equations, which becomes unfeasible for models with many moduli. Here, we instead start by considering a specific point in the complex structure moduli space, and look for a flux that fixes us there. We show how to construct such fluxes by using algebraic cycles and analyze flat directions. This is discussed in detail for the sextic Calabi-Yau fourfold at the Fermat point, and we observe that there appears to be tension between M2-tadpole cancellation and the requirement of stabilizing all moduli. Finally, we apply our results to show that even though symmetric fluxes allow to automatically solve several F-term equations, they typically lead to flat directions.

scholarly journals Heterotic complex structure moduli stabilization for elliptically fibered Calabi-Yau manifolds

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Wei Cui ◽  
Mohsen Karkheiran
Keyword(s):  
Spectral Data ◽  
Moduli Space ◽  
Vector Bundles ◽  
Complex Structure ◽  
Algebraic Cycles ◽  
Higgs Bundle ◽  
Moduli Stabilization ◽  
Atiyah Class ◽  
Dual Complex ◽  
Calabi Yau Manifolds

Abstract Holomorphicity of vector bundles can stabilize complex structure moduli of a Calabi-Yau threefold in N = 1 supersymmetric heterotic compactifications. In principle, the Atiyah class determines the stabilized moduli. In this paper, we study how this mechanism works in the context of elliptically fibered Calabi-Yau manifolds where the complex structure moduli space contains two kinds of moduli, those from the base and those from the fibration. Defining the bundle with spectral data, we find three types of situations when bundles’ holomorphicity depends on algebraic cycles exist only for special loci in the complex structure moduli, which allows us to stabilize both of these two moduli. We present concrete examples for each type and develop practical tools to analyze the stabilized moduli. Finally, by checking the holomorphicity of the four-flux and/or local Higgs bundle data in F-theory, we briefly study the dual complex structure moduli stabilization scenarios.

scholarly journals Universal axion backreaction in flux compactifications

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Thomas W. Grimm ◽  
Chongchuo Li
Keyword(s):  
Flux Compactifications ◽  
Complex Structure ◽  
Boundary Structure ◽  
Type Ii ◽  
Newton Polygons ◽  
String Compactifications ◽  
Axion Field ◽  
Field Excursion ◽  
Scalar Potentials ◽  
Puiseux Expansions

Abstract We study the backreaction effect of a large axion field excursion on the saxion partner residing in the same $$ \mathcal{N} $$ N = 1 multiplet. Such configurations are relevant in attempts to realize axion monodromy inflation in string compactifications. We work in the complex structure moduli sector of Calabi-Yau fourfold compactifications of F-theory with four-form fluxes, which covers many of the known Type II orientifold flux compactifications. Noting that axions can only arise near the boundary of the moduli space, the powerful results of asymptotic Hodge theory provide an ideal set of tools to draw general conclusions without the need to focus on specific geometric examples. We find that the boundary structure engraves a remarkable pattern in all possible scalar potentials generated by background fluxes. By studying the Newton polygons of the extremization conditions of all allowed scalar potentials and realizing the backreaction effects as Puiseux expansions, we find that this pattern forces a universal backreaction behavior of the large axion field on its saxion partner.

scholarly journals The tadpole problem

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Iosif Bena ◽  
Johan Blåbäck ◽  
Mariana Graña ◽  
Severin Lüst
Keyword(s):  
Moduli Space ◽  
Complex Structure ◽  
De Sitter ◽  
Generic Point ◽  
Cancellation Condition ◽  
Moduli Stabilization ◽  
Induced Charge ◽  
De Sitter Vacua ◽  
Breaking Scale ◽  
Rule Out

Abstract We examine the mechanism of moduli stabilization by fluxes in the limit of a large number of moduli. We conjecture that one cannot stabilize all complex-structure moduli in F-theory at a generic point in moduli space (away from singularities) by fluxes that satisfy the bound imposed by the tadpole cancellation condition. More precisely, while the tadpole bound in the limit of a large number of complex-structure moduli goes like 1/4 of the number of moduli, we conjecture that the amount of charge induced by fluxes stabilizing all moduli grows faster than this, and is therefore larger than the allowed amount. Our conjecture is supported by two examples: K3 × K3 compactifications, where by using evolutionary algorithms we find that moduli stabilization needs fluxes whose induced charge is 44% of the number of moduli, and Type IIB compactifications on $$ \mathbbm{CP} $$ CP 3, where the induced charge of the fluxes needed to stabilize the D7-brane moduli is also 44% of the number of these moduli. Proving our conjecture would rule out de Sitter vacua obtained via antibrane uplift in long warped throats with a hierarchically small supersymmetry breaking scale, which require a large tadpole.

Moduli stabilization and flavor structure in 5D SUGRA with multi moduli

2008 ◽  
Author(s):  
Hiroyuki Abe ◽  
Yutaka Sakamura ◽  
Pyungwon Ko ◽  
Deog Ki Hong
Keyword(s):  
Moduli Stabilization ◽  
Flavor Structure

scholarly journals TARGET SPACE DUALITY AND MODULI STABILIZATION IN STRING GAS COSMOLOGY

2007 ◽  
Vol 22 (01) ◽  
pp. 165-179 ◽  
Author(s):  
AUTTAKIT CHATRABHUTI
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Moduli Space ◽  
Target Space ◽  
Moduli Stabilization ◽  
String Gas Cosmology ◽  
The Stability

Motivated by string gas cosmology, we investigate the stability of moduli fields coming from compactifications of string gas on torus with background flux. It was previously claimed that moduli are stabilized only at a single fixed-point in moduli space, a self-dual point of T-duality with vanishing flux. Here, we show that there exist other stable fixed-points on moduli space with nonvanishing flux. We also discuss the more general target space dualities associated with these fixed-points.

scholarly journals On D-brane dynamics and moduli stabilization

2017 ◽  
Vol 32 (29) ◽  
pp. 1750150
Author(s):  
Noriaki Kitazawa
Keyword(s):  
String Theory ◽  
Fixed Points ◽  
Supersymmetry Breaking ◽  
Compact Space ◽  
Complex Structure ◽  
Simultaneous Presence ◽  
Moduli Stabilization ◽  
Type Iib String Theory ◽  
The Stability ◽  
Repulsive Forces

We discuss the effect of the dynamics of D-branes on moduli stabilization in type IIB string theory compactifications, with reference to a concrete toy model of [Formula: see text] orientifold compactification with fractional D3-branes and anti-D3-branes at orbifold fixed points. The resulting attractive forces between anti-D3-branes and D3-branes, together with the repulsive forces between anti-D3-branes and O3-planes, can affect the stability of the compact space. There are no complex structure moduli in [Formula: see text] orientifold, which should thus capture some generic features of more general settings where all complex structure moduli are stabilized by three-form fluxes. The simultaneous presence of branes and anti-branes brings along the breaking of supersymmetry. Non-BPS combinations of this type are typical of “brane supersymmetry breaking” and are a necessary ingredient in the KKLT scenario for stabilizing the remaining Kähler moduli. The conclusion of our analysis is that, while mutual D-brane interactions sometimes help Kähler moduli stabilization, this is not always the case.

scholarly journals The eclectic flavor symmetry of the ℤ2 orbifold

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Alexander Baur ◽  
Moritz Kade ◽  
Hans Peter Nilles ◽  
Saúl Ramos-Sánchez ◽  
Patrick K. S. Vaudrevange
Keyword(s):  
String Theory ◽  
Moduli Space ◽  
Particle Physics ◽  
Mirror Symmetry ◽  
Modular Group ◽  
Complex Structure ◽  
Flavor Symmetry ◽  
Two Dimensional ◽  
Flavor Symmetries

Abstract Modular symmetries naturally combine with traditional flavor symmetries and $$ \mathcal{CP} $$ CP , giving rise to the so-called eclectic flavor symmetry. We apply this scheme to the two-dimensional ℤ2 orbifold, which is equipped with two modular symmetries SL(2, ℤ)T and SL(2, ℤ)U associated with two moduli: the Kähler modulus T and the complex structure modulus U. The resulting finite modular group is ((S3× S3) ⋊ ℤ4) × ℤ2 including mirror symmetry (that exchanges T and U) and a generalized $$ \mathcal{CP} $$ CP -transformation. Together with the traditional flavor symmetry (D8× D8)/ℤ2, this leads to a huge eclectic flavor group with 4608 elements. At specific regions in moduli space we observe enhanced unified flavor symmetries with as many as 1152 elements for the tetrahedral shaped orbifold and $$ \left\langle T\right\rangle =\left\langle U\right\rangle =\exp \left(\frac{\pi \mathrm{i}}{3}\right) $$ T = U = exp π i 3 . This rich eclectic structure implies interesting (modular) flavor groups for particle physics models derived form string theory.

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