scholarly journals Gopakumar-Vafa hierarchies in winding inflation and uplifts

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Federico Carta ◽  
Alessandro Mininno ◽  
Nicole Righi ◽  
Alexander Westphal
Keyword(s):  
Complete Intersection ◽  
Complex Structure ◽  
Scalar Potential ◽  
Vacuum Expectation ◽  
Side Product ◽  
Total Degree ◽  
De Sitter ◽  
Picard Number ◽  
Expectation Values ◽  
Combined Mechanism

Abstract We propose a combined mechanism to realize both winding inflation and de Sitter uplifts. We realize the necessary structure of competing terms in the scalar potential not via tuning the vacuum expectation values of the complex structure moduli, but by a hierarchy of the Gopakumar-Vafa invariants of the underlying Calabi-Yau threefold. To show that Calabi-Yau threefolds with the prescribed hierarchy actually exist, we explicitly create a database of all the genus 0 Gopakumar-Vafa invariants up to total degree 10 for all the complete intersection Calabi-Yau’s up to Picard number 9. As a side product, we also identify all the redundancies present in the CICY list, up to Picard number 13. Both databases can be accessed at this link (https://www.desy.de/∼westphal/GV_CICY_webpage/GVInvariants.html).

scholarly journals ON GEOMETRICAL INTERPRETATION OF NON-ABELIAN FLAT DIRECTION CONSTRAINTS

2008 ◽  
Vol 23 (22) ◽  
pp. 3461-3492 ◽  
Author(s):  
G. B. CLEAVER ◽  
D. V. NANOPOULOS ◽  
J. T. PERKINS ◽  
J. W. WALKER
Keyword(s):  
Scalar Potential ◽  
String Model ◽  
Vacuum Expectation ◽  
Vacuum State ◽  
Effective Field ◽  
Geometrical Interpretation ◽  
Expectation Values ◽  
Brane Model ◽  
Yield Information ◽  
Comprehensive Classification

In order to produce a low-energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called flat directions, leaving the F- and D-terms of the scalar potential to be zero. The situation becomes particularly interesting when one attempts to realize such directions while assigning vacuum expectation values to fields transforming under non-Abelian representations of the gauge group. Since the expectation value is now shared among multiple components of a field, satisfaction of flatness becomes an inherently geometrical problem in the group space. Furthermore, the possibility emerges that a single seemingly dangerous F-term might experience a self-cancellation among its components. The hope exists that the geometric language can provide an intuitive and immediate recognition of when the D and F conditions are simultaneously compatible, as well as a powerful tool for their comprehensive classification. This is the avenue explored in this paper, and applied to the cases of SU (2) and SO (2N), relevant respectively to previous attempts at reproducing the MSSM and the flipped SU (5) GUT. Geometrical interpretation of non-Abelian flat directions finds application to M-theory through the recent conjecture of equivalence between D-term strings and wrapped D-branes of Type II theory.1 Knowledge of the geometry of the flat direction "landscape" of a D-term string model could yield information about the dual brane model. It is hoped that the techniques encountered will be of benefit in extending the viability of the quasirealistic phenomenologies already developed.

scholarly journals Analysis of scalar and fermion quantum field theory on anti-de Sitter spacetime

2018 ◽  
Vol 27 (11) ◽  
pp. 1843014 ◽  
Author(s):  
Victor E. Ambruş ◽  
Carl Kent ◽  
Elizabeth Winstanley
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Vacuum Expectation ◽  
Dirac Fermion ◽  
De Sitter ◽  
Expectation Values ◽  
Sitter Spacetime ◽  
Fermion Fields ◽  
Spacetime Curvature ◽  
Ads Spacetime

We study vacuum and thermal expectation values of quantum scalar and Dirac fermion fields on anti-de Sitter (adS) spacetime. AdS spacetime is maximally symmetric and this enables expressions for the scalar and fermion vacuum Feynman Green’s functions to be derived in closed form. We employ Hadamard renormalization to find the vacuum expectation values (v.e.v.s). The thermal Feynman Green’s functions are constructed from the vacuum Feynman Green’s functions using the imaginary time periodicity/anti-periodicity property for scalars/fermions. Focusing on massless fields with either conformal or minimal coupling to the spacetime curvature (these two cases being the same for fermions) we compute the differences between the thermal expectation values and v.e.v.s. We compare the resulting energy densities, pressures and pressure deviators with the corresponding classical quantities calculated using relativistic kinetic theory.

scholarly journals QUANTUM EFFECTS IN HIGHER-DIMENSIONAL COSMOLOGICAL MODELS

2012 ◽  
Vol 18 ◽  
pp. 164-173 ◽  
Author(s):  
ARAM A. SAHARIAN
Keyword(s):  
Vacuum Energy ◽  
Vacuum Expectation ◽  
Vacuum Energy Density ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Expectation Values ◽  
Sitter Spacetime ◽  
Higher Dimensional ◽  
Spatial Dimensions ◽  
Robin Boundary

Vacuum energy density and stresses are investigated for a scalar field in de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions and in anti-de Sitter spacetime with two parallel branes. On the branes the field obeys the Robin boundary conditions. The behavior of the vacuum expectation values is discussed in various asymptotic regions of the parameters. Applications are given to Randall-Sundrum type braneworlds.

scholarly journals Nondecoupling in multi-Higgs doublet models

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Francisco Faro ◽  
Jorge C. Romão ◽  
João P. Silva
Keyword(s):  
Scalar Potential ◽  
Vacuum Expectation ◽  
Higgs Doublet ◽  
Expectation Values ◽  
Special Cases

Abstract We consider models with any number of Higgs doublets and study the conditions for decoupling. We show that, under very general circumstances, all the quadratic coefficients of the scalar potential must be present, except in special cases, which include terms related to directions of vanishing vacuum expectation values. We give a few examples. Moreover, we show that the decoupling of all charged scalars implies the decoupling of all extra neutral scalars and vanishing $$\mathcal {CP}$$CP violation in scalar-pseudoscalar mixing.

scholarly journals CASIMIR EFFECT IN TOROIDALLY COMPACTIFIED DE SITTER SPACETIME

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1813-1820 ◽  
Author(s):  
A. A. SAHARIAN
Keyword(s):  
Casimir Effect ◽  
Coupling Parameter ◽  
Vacuum Expectation ◽  
Vacuum Energy Density ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Expectation Values ◽  
Sitter Spacetime ◽  
Spatial Dimensions ◽  
Late Stages

Vacuum energy density and stresses are investigated for a scalar field with general curvature coupling parameter in (D + 1)-dimensional de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions. The corresponding expectation values are presented in the form of the sum of the vacuum expectation values in uncompactified dS spacetime and the part induced by the non-trivial topology. In the early stages of the cosmological evolution the topological parts dominate. In this limit the behavior of the Casimir densities does not depend on the curvature coupling parameter and coincides with that for a conformally coupled massless field. At late stages of the cosmological expansion the expectation values are dominated by the part corresponding to uncompactified dS spacetime. The vanishing of the topological parts is monotonic or oscillatory in dependence of the mass and the curvature coupling parameter of the field.

scholarly journals WIGHTMAN FUNCTIONS IN DE SITTER AND ANTI-DE SITTER SPACETIMES IN THE PRESENCE OF COSMIC STRINGS

2012 ◽  
Vol 18 ◽  
pp. 115-124
Author(s):  
EUGÊNIO R. BEZERRA DE MELLO
Keyword(s):  
Scalar Field ◽  
Cosmic String ◽  
Topological Defect ◽  
Cosmic Strings ◽  
Vacuum Expectation ◽  
De Sitter ◽  
Expectation Values ◽  
Proper Distance ◽  
Wightman Functions

In this paper we evaluate the Wightman functions associated with a massive quantum scalar field in de Sitter and anti-de Sitter spacetimes in the presence of a cosmic string. Having these functions we calculate the corresponding renormalized vacuum expectation values of the field squared and present the behavior of the contributions induced by the cosmic string as function of the proper distance to it for different values of the parameter which codify the presence of this linear topological defect.

scholarly journals Systematics of type IIA moduli stabilisation

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Fernando Marchesano ◽  
David Prieto ◽  
Joan Quirant ◽  
Pramod Shukla
Keyword(s):  
Scalar Potential ◽  
Systematic Search ◽  
Stability Criteria ◽  
De Sitter ◽  
Large Subset

Abstract We analyse the flux-induced scalar potential for type IIA orientifolds in the presence of p-form, geometric and non-geometric fluxes. Just like in the Calabi-Yau case, the potential presents a bilinear structure, with a factorised dependence on axions and saxions. This feature allows one to perform a systematic search for vacua, which we implement for the case of geometric backgrounds. Guided by stability criteria, we consider configurations with a particular on-shell F-term pattern, and show that no de Sitter extrema are allowed for them. We classify branches of supersymmetric and non-supersymmetric vacua, and argue that the latter are perturbatively stable for a large subset of them. Our solutions reproduce and generalise previous results in the literature, obtained either from the 4d or 10d viewpoint.

scholarly journals Winding uplifts and the challenges of weak and strong SUSY breaking in AdS

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Arthur Hebecker ◽  
Sascha Leonhardt
Keyword(s):  
Complex Structure ◽  
Susy Breaking ◽  
Technical Level ◽  
De Sitter ◽  
Large Complex ◽  
Breaking Scale ◽  
Large Complex Structure

Abstract We discuss the problem of metastable SUSY breaking in the landscape. While this is clearly crucial for the various de Sitter proposals, it is also interesting to consider the SUSY breaking challenge in the AdS context. For example, it could be that a stronger form of the non-SUSY AdS conjecture holds: it would forbid even metastable non-SUSY AdS in cases where the SUSY-breaking scale is parametrically above/below the AdS scale. At the technical level, the present paper proposes to break SUSY using the multi-cosine-shaped axion potentials which arise if a long winding trajectory of a ‘complex-structure axion’ appears in the large-complex-structure limit of a Calabi-Yau orientifold. This has been studied in the context of ‘Winding Inflation’, but the potential for SUSY breaking has not been fully explored. We discuss the application to uplifting LVS vacua, point out the challenges which one faces in the KKLT context, and consider the possibility of violating the non-SUSY AdS conjecture in the type-IIA setting of DGKT.

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.

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