Given the huge size of the generic four-dimens-ional scalar potentials arising from the type II supergravities based on toroidal orientifolds, it is even hard to analytically solve the extremization conditions, and therefore the previous studies have been mainly focused on taking some numerical approaches. In this work, using the so-called we demonstrate that the scalar potential and the extremization conditions can be simplified to a great extent, leading to the possibility of performing an analytic exploration of the flux landscape. In this regard, we consider the isotropic case of a type IIB model based on the standard $${\mathbb T}^6/({\mathbb Z}_2 \times {\mathbb Z}_2)$$ orientifold having the three-form fluxes $$F_3/H_3$$ and the non-geometric -flux. This model results in around 300 terms in the scalar potential which depend on 6 moduli/axionic fields and 14 flux parameters. Considering that the axionic flux polynomials can take either zero or non-zero values results in the need of analyzing $$2^{14}=16{,}384$$ candidate configurations, and we find that more than 16,200 of those result in No-Go scenarios for Minkowskian/de-Sitter vacua. Based on our systematic exploration of non-tachyonic flux vacua, we present a detailed classification of such No-Go scenarios as well as the leftover “undecided” configurations for which we could not conclude about the presence/absence of the stable Minkowskian/de-Sitter vacua.

Iran

Shehu AbdusSalam

China

Xin Gao

Greece

George Leontaris

India

Pramod Shukla

Systematic exploration of the non-geometric flux landscape

In the context of four-dimensional $$ \mathcal{N} $$ = 1 type IIB superstring compactifications, the U-dual completion of the holomorphic flux superpotential leads to four S-dual pairs of fluxes, namely ( ) ( ) ( ′ ′) and ( ′ ′). It has been observed that the scalar potentials induced by such generalized superpotentials typically have an enormous amount of terms, making it hard to study any phenomenological aspects such as moduli stabilization. In this regard, we present a set of generic master formulae which not only formulate the scalar potential in a compact way but also enable one to the various scalar potential pieces by simply knowing a set of topological data of the compactifying Calabi Yau and its mirror threefold. We demonstrate the applicability of our master formulae by the scalar potentials for five explicit models, and using a set of combinations we show that 76276 terms arising from the flux superpotential in a 𝕋 (ℤ ℤ )-based model can be equivalently expressed by using 2816 terms, while 11212 terms arising from the flux superpotential in a Quintic-based model can be equivalently expressed by 668 terms! We argue that the master formulae presented in this work can be useful in an analytic exploration of the rich landscape of the non-geometric flux vacua.

Sayan Biswas

Reading-off the non-geometric scalar potentials with U-dual fluxes

We present a global embedding of the fiber inflation model in a perturbative large volume scenario (LVS) in which the inflationary potential is induced via a combination of string-loop corrections and higher derivative <math><mrow><msup><mrow><mi>F</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></math> effects. The minimal fiber inflation model developed in the standard LVS generically faces some strong bounds on the inflaton field range arising from the Kähler cone constraints, which subsequently creates a challenge for realizing the cosmological observables while consistently respecting the underlying supergravity approximations. The main attractive feature of this proposal is to naturally alleviate this issue by embedding fiber inflation in perturbative LVS.

Swagata Bera

Dibya Chakraborty

George K. Leontaris

Global embedding of fiber inflation in a perturbative large volume scenario

In this paper, we perform a systematic and analytical exploration of de Sitter conditions in type IIA compactifications with (non-)geometric fluxes along with the standard NS-NS and RR p-form fluxes. Exploiting the fact that the F-term scalar potential can be written as a bilinear form, we start by studying the most generic case. We find four conditions that the scalar fields and fluxes must satisfy to achieve de Sitter vacua. Particularizing to different configurations, we recover and extend previous results in the literature. We then impose an Ansatz in which the F-terms are proportional to the respective Kähler derivatives. In this set-up we are able to derive additional constraints and to classify the possible dS no-go scenarios in terms of eight axionic fluxes. Individually considering that any of these fluxes can be vanishing or non-vanishing leads to a total of 256 flux configurations. We find that 227 of these 256 possibilities result in a dS no-go scenario. The remaining 29 flux configurations, a priori, do not lead to dS no-go cases and would deserve further investigation.

Netherlands

David Prieto

Israel

Joan Quirant

On the limitations of non-geometric fluxes to realize dS vacua

We present a symplectic formulation of the <math><mi>N</mi><mo>=</mo><mn>1</mn></math> four-dimensional type IIB scalar potential arising from a flux superpotential which has four <math><mi>S</mi></math>-dual pairs of fluxes demanded by the <math><mi>U</mi></math>-dual completion arguments. Our symplectic formulation presents a very compact and concise way of expressing the generic scalar potential in just a few terms via using a set of symplectic identities along with the so-called “axionic-flux” combinations. We demonstrate the utility of our symplectic master formula by considering an underlying four-dimensional type IIB supergravity model based on a <math><mrow><msup><mrow><mi>T</mi></mrow><mrow><mn>6</mn></mrow></msup><mo>/</mo><mo>(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>×</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></math> orientifold, in which the scalar potential induced by the <math><mi>U</mi></math>-dual flux superpotential results in a total of 76 276 terms involving 128 flux parameters. Given that our symplectic formulation does not need the information about the metric of the internal background, it is applicable to the models beyond the toroidal compactifications such as to those which use orientifolds of the Calabi-Yau threefolds.

Symplectic formulation of the type IIB scalar potential with <math><mi>U</mi></math>-dual fluxes

We quantitatively estimate the leading higher derivative corrections to   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supergravity derived from IIB string compactifications and study how they may affect moduli stabilisation and LVS inflation models. Using the Kreuzer-Skarke database of 4D reflexive polytopes and their triangulated Calabi-Yau database, we present scanning results for a set of divisor topologies corresponding to threefolds with 1 ≤ h 1,1 ≤ 5. In particular, we find several geometries suitable to realise blow-up inflation, fibre inflation and poly-instantons inflation, together with a classification of the divisors topologies for which the leading higher derivative corrections to the inflationary potential vanish. In all other cases, we instead estimate numerically how these corrections modify the inflationary dynamics, finding that they do not destroy the predictions for the main cosmological observables.

Italy

Michele Cicoli

Matteo Licheri

Pellegrino Piantadosi

United Kingdom

Canada

Fernando Quevedo

Higher derivative corrections to string inflation

In the context of <math><mi>N</mi><mo>=</mo><mn>1</mn></math> four-dimensional type-IIB supergravity theories, the <math><mi>U</mi></math>-dual completion arguments suggest including four <math><mi>S</mi></math>-dual pairs of fluxes in the holomorphic superpotential, namely the so-called <math><mo>(</mo><mi>F</mi><mo>,</mo><mi>H</mi><mo>)</mo><mo>,</mo><mo>(</mo><mi>Q</mi><mo>,</mo><mi>P</mi><mo>)</mo><mo>,</mo><mo>(</mo><msup><mi>P</mi><mo>′</mo></msup><mo>,</mo><msup><mi>Q</mi><mo>′</mo></msup><mo>)</mo></math>, and <math><mo>(</mo><msup><mi>H</mi><mo>′</mo></msup><mo>,</mo><msup><mi>F</mi><mo>′</mo></msup><mo>)</mo></math>. These can generically induce cubic polynomials for the complex-structure moduli as well as the Kähler moduli in the flux superpotential. In this article, we explore the insights of the four-dimensional nongeometric scalar potential in the presence of such generalized <math><mi>U</mi></math>-dual fluxes by considering an explicit type-IIB toroidal compactification model based on an orientifold of <math><msup><mi>T</mi><mn>6</mn></msup><mo>/</mo><mo>(</mo><msub><mi>Z</mi><mn>2</mn></msub><mo>×</mo><msub><mi>Z</mi><mn>2</mn></msub><mo>)</mo></math> orbifold. First, we observe that the flux superpotential induces a huge scalar potential having a total of 76,276 terms involving 128 flux parameters and 14 real scalars. Subsequently, we invoke a new set of (the so-called) “axionic fluxes” comprising of combinations of the standard fluxes and the RR axions, and it turns out that these axionic fluxes can be very useful in rewriting the scalar potential in a relatively compact form. In this regard, using the metric of the compactifying toroidal sixfold, we present a new formulation of the effective scalar potential, which might be useful for understanding the higher-dimensional origin of the various pieces via the so-called “dimensional-oxidation” process. We also discuss the generalized Bianchi identities and the tadpole cancellation conditions, which can be important while seeking the physical anti–de Sitter/de Sitter vacua in such models.

Taxonomy of scalar potential with <math><mi>U</mi></math>-dual fluxes

In the context of type IIB superstring compactifications on K3-fibred (weak) Swiss-cheese Calabi Yau (CY) orientifolds, we consider the realisation of de Sitter vacua obtained through the introduction of an   <math> <mover> <mrow> <mi>D</mi> <mn>3</mn> </mrow> <mo>¯</mo> </mover> </math>  $$ \overline{D3} $$ -brane at the tip of a highly warped throat of Klebanov-Strassler type. Aiming to have a concrete global realisation, we perform a systematic search for the CY threefolds with 2 &lt; h 1,1 &lt; 5 arising from the Kreuzer-Skarke database, which satisfy the minimal requirements of being K3-fibred and suitable for moduli stabilisation within the LARGE Volume Scenario (LVS). In this context, after scanning the set of K3-fibred CY threefolds with a so-called diagonal del-Pezzo divisor needed for LVS, we realise that one of the main challenging requirements for having   <math> <mover> <mrow> <mi>D</mi> <mn>3</mn> </mrow> <mo>¯</mo> </mover> </math>  $$ \overline{D3} $$ -brane uplifting is to find a suitable orientifold involution which can simultaneously result in a sufficient large D3 tadpole charge along with the presence of suitable O3-planes. In our detailed analysis (limited to) using the CY threefolds with small h 1,1, we observe that these topological requirements rule out most of the CY geometries leading to only few possibly suitable candidates for the purpose of   <math> <mover> <mrow> <mi>D</mi> <mn>3</mn> </mrow> <mo>¯</mo> </mover> </math>  $$ \overline{D3} $$ -brane uplifting. Subsequently, we present a global model using one such explicit K3-fibred CY threefold with h 1,1 = 4 in which all the moduli can be consistently stabilised in a de Sitter minimum of the scalar potential.

Chiara Crinò

On K3-fibred LARGE Volume Scenario with de Sitter vacua from anti-D3-branes

We present a class of tachyon-free (stable) AdS as well as dS solutions in the context of type IIA orientifold compactifications. This model is based on a type IIA setting having geometric flux which, in addition, also includes the usual NS–NS three-form flux  $$\textrm{H}_3$$  <math> <msub> <mtext>H</mtext> <mn>3</mn> </msub> </math>   and the RR p-form fluxes  $$\textrm{F}_p$$  <math> <msub> <mtext>F</mtext> <mi>p</mi> </msub> </math>   for  $$p \in \{0, 2, 4, 6\}$$  <math> <mrow> <mi>p</mi> <mo>∈</mo> <mo>{</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>4</mn> <mo>,</mo> <mn>6</mn> <mo>}</mo> </mrow> </math>  . Although all the saxionic moduli are stabilized, there remains a combination of the RR axions which is flat, and the dS solution is realized through the D-term effects induced by the geometric fluxes, without which one can only have AdS solutions. Using flux scaling arguments we also discuss how to engineer a parametric control in these models, in the sense of realizing the respective AdS/dS solutions in large volume, weak string-coupling as well as large complex-structure regime. We also discuss open possibilities (e.g. about the unknown status on having the complete set of Bianchi identities) under which such tachyon-free dS solutions may or may not be viable.

On stable type IIA de-Sitter vacua with geometric flux

In this article we present a pheno-inspired classification for the divisor topologies of the favorable Calabi Yau (CY) threefolds with 1 ≤ h 1,1(CY) ≤ 5 arising from the four-dimensional reflexive polytopes of the Kreuzer-Skarke database. Based on some empirical observations we conjecture that the topologies of the so-called coordinate divisors can be classified into two categories: (i). χ  h  (D) ≥ 1 with Hodge numbers given by {h 0,0 = 1, h 1,0 = 0, h 2,0 = χ  h  (D) − 1, h 1,1 = χ(D) − 2χ  h  (D)} and (ii). χ  h  (D) ≤ 1 with Hodge numbers given by {h 0,0 = 1, h 1,0 = 1 −χ  h  (D), h 2,0 = 0, h 1,1 = χ(D) + 2 − 4χ  h  (D)}, where χ  h  (D) denotes the Arithmetic genus while χ(D) denotes the Euler characteristic of the divisor D. We present the Hodge numbers of around 140000 coordinate divisors corresponding to all the CY threefolds with 1 ≤ h 1,1(CY) ≤ 5 which corresponds to a total of nearly 16000 distinct CY geometries. Subsequently we argue that our conjecture can help in “bypassing” the need of cohomCalg for computing Hodge numbers of coordinate divisors, and hence can be significantly useful for studying the divisor topologies of CY threefolds with higher h 1,1 for which cohomCalg gets too slow and sometimes even breaks as well. We also demonstrate how these scanning results can be directly used for phenomenological model building, e.g. in estimating the D3-brane tadpole charge (under reflection involutions) which is a central ingredient for constructing explicit global models due to several different reasons/interests such as the de-Sitter uplifting through anti-D3 brane and (flat) flux vacua searches.