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 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.

scholarly journals Weak gravity bounds in asymptotic string compactifications

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Brice Bastian ◽  
Thomas W. Grimm ◽  
Damian van de Heisteeg
Keyword(s):  
Black Holes ◽  
Moduli Space ◽  
Mass Formula ◽  
Complex Structure ◽  
Mass Ratio ◽  
De Sitter ◽  
String Compactifications ◽  
Type Iib String Theory ◽  
Bps States ◽  
Weak Gravity

Abstract We study the charge-to-mass ratios of BPS states in four-dimensional $$ \mathcal{N} $$ N = 2 supergravities arising from Calabi-Yau threefold compactifications of Type IIB string theory. We present a formula for the asymptotic charge-to-mass ratio valid for all limits in complex structure moduli space. This is achieved by using the sl(2)-structure that emerges in any such limit as described by asymptotic Hodge theory. The asymptotic charge-to-mass formula applies for sl(2)-elementary states that couple to the graviphoton asymptotically. Using this formula, we determine the radii of the ellipsoid that forms the extremality region of electric BPS black holes, which provides us with a general asymptotic bound on the charge-to-mass ratio for these theories. Finally, we comment on how these bounds for the Weak Gravity Conjecture relate to their counterparts in the asymptotic de Sitter Conjecture and Swampland Distance Conjecture.

On Deformations of the Complex Structure on the Moduli Space of Spatial Polygons

2002 ◽  
Vol 45 (3) ◽  
pp. 417-421
Author(s):  
Yasuhiko Kamiyama ◽  
Shuichi Tsukuda
Keyword(s):  
Moduli Space ◽  
Tangent Bundle ◽  
Complex Structure ◽  
Fano Manifold ◽  
Complex Dimension ◽  
Holomorphic Sections

AbstractFor an integer n ≥ 3, let Mn be the moduli space of spatial polygons with n edges. We consider the case of odd n. Then Mn is a Fano manifold of complex dimension n − 3. Let ΘMn be the sheaf of germs of holomorphic sections of the tangent bundle TMn. In this paper, we prove Hq(Mn, ΘMn) = 0 for all q ≥ 0 and all odd n. In particular, we see that the moduli space of deformations of the complex structure on Mn consists of a point. Thus the complex structure on Mn is locally rigid.

scholarly journals Deformations of surface defect moduli spaces

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Andrew Neitzke ◽  
Ali Shehper
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Surface Defect ◽  
Complex Structure ◽  
Structure Deformation ◽  
Superconformal Surface

Abstract Given a 4d $$ \mathcal{N} $$ N = 2 superconformal theory with an $$ \mathcal{N} $$ N = (2, 2) superconformal surface defect, a marginal perturbation of the bulk theory induces a complex structure deformation of the defect moduli space. We describe a concrete way of computing this deformation using the bulk-defect OPE.

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.

scholarly journals A gravitino distance conjecture

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Alberto Castellano ◽  
Anamaría Font ◽  
Alvaro Herráez ◽  
Luis E. Ibáñez
Keyword(s):  
Moduli Space ◽  
Complex Structure ◽  
Hubble Constant ◽  
Low Energy ◽  
Hodge Structures ◽  
Supergravity Theory ◽  
Gravitino Mass ◽  
Mixed Hodge Structures ◽  
Range Of Values ◽  
Weak Gravity

Abstract We conjecture that in a consistent supergravity theory with non-vanishing gravitino mass, the limit m3/2 → 0 is at infinite distance. In particular one can write Mtower ~ $$ {m}_{3/2}^{\delta } $$ m 3 / 2 δ so that as the gravitino mass goes to zero, a tower of KK states as well as emergent strings becomes tensionless. This conjecture may be motivated from the Weak Gravity Conjecture as applied to strings and membranes and implies in turn the AdS Distance Conjecture. We test this proposal in classical 4d type IIA orientifold vacua in which one obtains a range of values $$ \frac{1}{3} $$ 1 3 ≤ δ ≤ 1. The parameter δ is related to the scale decoupling exponent in AdS vacua and to the α exponent in the Swampland Distance Conjecture for the type IIA complex structure. We present a general analysis of the gravitino mass in the limits of moduli space in terms of limiting Mixed Hodge Structures and study in some detail the case of two-moduli F-theory settings. Moreover, we obtain general lower bounds δ ≥$$ \frac{1}{3},\frac{1}{4} $$ 1 3 , 1 4 for Calabi-Yau threefolds and fourfolds, respectively. The conjecture has important phenomenological implications. In particular we argue that low-energy supersymmetry of order 1 TeV is only obtained if there is a tower of KK states at an intermediate scale, of order 108 GeV. One also has an upper bound for the Hubble constant upon inflation H ≲ $$ {m}_{3/2}^{\delta }{M}_{\mathrm{P}}^{\left(1-\delta \right)} $$ m 3 / 2 δ M P 1 − δ .

scholarly journals Higher Complex Structures

2019 ◽  
Author(s):  
Vladimir Fock ◽  
Alexander Thomas
Keyword(s):  
Moduli Space ◽  
Geometric Structure ◽  
Hilbert Scheme ◽  
Complex Structure ◽  
Teichmüller Space ◽  
Teichmuller Space ◽  
Complex Structures ◽  
Punctual Hilbert Scheme

Abstract We introduce and analyze a new geometric structure on topological surfaces generalizing the complex structure. To define this so-called higher complex structure, we use the punctual Hilbert scheme of the plane. The moduli space of higher complex structures is defined and is shown to be a generalization of the classical Teichmüller space. We give arguments for the conjectural isomorphism between the moduli space of higher complex structures and Hitchin’s component.

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.

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