arXiv subjects

Pramod Shukla

Publications and source records attributed to Pramod Shukla.

At least 19 recordsLinked to original sources

arXiv2026

Tetra-quadric CY Threefold and Assisted Fibre Inflation

In the context of type IIB superstring compactification, we demonstrate the assisted fibre inflation proposal for a four-field model realized using the orientifold of a tetra-quadric Calabi-Yau (CY) threefold. This CY threefold has an underlying permutation symmetry $S_4$ and belongs to both the list of CY threefolds, namely the Kreuzer-Skarke (KS) database as well as the Complete Intersection Calabi-Yau (CICY) database. After fixing the overall volume modulus of the CY threefold using the framework of perturbative large volume scenario, there are three K\"ahler moduli which remain flat and assist in driving fibre inflation via sub-leading corrections. In a particular benchmark model, we show that the effective inflaton shift of around $5.7$ M$_p$, as needed for driving fibre inflation, can be successfully shared by three inflaton moduli which need to be individually shifted by nearly $2.2$ M$_p$ only ! The main motivation for the work is to show that the effective large field excursions of the inflaton field is possible without the need of pushing the individual volume moduli towards a large super-Planckian excursion or close to the boundary of the K\"ahler cone which may create various subsequent challenges for the effective field theory and supergravity approximations, especially in Swiss-Cheese based models of fibre inflation.

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arXiv2026

On Calabi-Yau Threefolds For Unified LVS Inflation

Fibre inflation, Poly-instanton inflation and (Loop) Blow-up inflation are among the most popular K\"ahler moduli based inflationary models realized in the standard LARGE volume scenarios (LVS). In this article, we present a unified framework in which all these three LVS inflationary models can be realized by using (different orientifolds of) a single Calabi-Yau (CY) threefold. In fact, the desired CY threefold needs to have a K3- or ${\mathbb T}^4$-fibration structure along with two diagonal del Pezzo divisors, and a so-called `Wilson' divisor which corresponds to a surface realized as a ${\mathbb P}^1$ fibration over ${\mathbb T}^2$s. For classification purpose, we perform a detailed scan of the CY geometries with $1 \leq h^{1,1}({\rm CY}) \leq 6$ that arise from the triangulation of the four-dimensional reflexive polytopes of the Kreuzer-Skarke database. In this regard, after scanning around 100,000 CY geometries and the corresponding topologies of around a million of toric divisors, we find two CY threefolds satisfying these requirements for $1 \leq h^{1,1}({\rm CY}) \leq 4$, while there are 14 and 45 candidate CY geometries for $h^{1,1}({\rm CY}) = 5$ and $h^{1,1}({\rm CY}) = 6$, respectively. We discuss the extended applications of such CY threefolds for cosmological model building in string theoretic frameworks.

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arXiv2026

Towards Systematics of Calabi-Yau Landscape for String Cosmology

In this review, we discuss the relevance and impact of studying Calabi-Yau threefolds in the context of global model building in string phenomenology. First, taking a phenomenologist-friendly approach, we review how the topologies of the various divisors and curves of the compactifying CY threefolds play a crucial role for generating the various ``suitable" classes of effective scalar potentials, within the framework of the popular moduli stabilization schemes such as KKLT and LVS. Subsequently, we discuss the impact of the specifics of the CY threefold geometries in the minimal LVS inflationary models such as fibre inflation, in particular, along the challenges such as the inflaton field-range bound. In this regard, we discuss a multi-field approach in which several fibre moduli assist to drive successful inflation having a sufficient number of efolds, without getting close to their individual K\"ahler cone boundaries.

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arXiv2026

On Global Embedding of Assisted Fibre Inflation

Fibre inflation is one of the most attractive models realized in the type IIB orientifold compactification. It is embedded in the framework of L(arge) V(olume) S(cenarios) using a class of compactifying Calabi-Yau (CY) threefolds having K3-fibration. The standard single-field fibre inflation is driven by a fibre modulus which needs to travel a trans-Planckian distance of the order of ${\cal O}(5-8)$M$_p$ in the effective moduli space. The global embedding attempts using concrete CY orientifold setups have shown that K\"ahler cone conditions can generically induce some significantly tight bounds on the inflaton range, especially in the presence of a Swiss-Cheese structure via an exceptional rigid divisor in the CY threefold. Such field range bounds usually obstruct the inflationary plateau, leading to insufficient number of efolds during the inflationary dynamics. In this context, we review our recent work about the possibility of assisting multiple fibre moduli such that the burden of traveling the required trans-Planckian distance could be shared by multiple fields, and successful inflation could be realized before hitting (or being too close to) their respective individual K\"ahler cone boundaries.

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arXiv2025

Assisted Fibre Inflation in Perturbative LVS

We propose a multi-field fibre inflation scenario in type IIB perturbative large volume compactifications, showing that the multi-field dynamics suppresses trans-Planckian displacements of the canonical inflaton. Considering a concrete K3-fibred Calabi-Yau (CY) threefold with $h^{1,1}({\rm CY})=3$ and having certain underlying symmetries, we show that the presence of multi-fibre moduli creates an assisted inflation scenario where multiple moduli collectively help in producing the cosmological observables consistent with the current experimental bounds. We further argue that individual field range excursions $(\Delta\phi_n)$ corresponding to each of the inflaton fields can be estimated as $\Delta\phi_n = \Delta\phi/\sqrt{n}$, where $\Delta\phi$ denotes the effective single-field inflaton range needed to generate the desired cosmological observables, and $n$ is the number of moduli assisting the multi-fibre inflation. We also present various numerical benchmark models consistently producing cosmological observables in light of the recent ACT experiments.

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arXiv2025

Perturbative LVS and Inflation: A Review of Volume Modulus and Fibre Scenarios

In type IIB superstring compactifications, incorporating log-loop corrections and higher-derivative ${(\alpha^\prime)}^3$-corrections can stabilize the overall volume of the compact internal space at exponentially large values. This mechanism forms the basis of the perturbative Large Volume Scenario (LVS). In this report, we briefly review two inflationary models realized within the perturbative LVS framework. The first one is the volume modulus inflation (also known as inflection point inflation) and the second one is popularly known as fibre inflation. Using an explict Calabi-Yau orientifold, some concrete global embeddings of both models are also discussed.

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arXiv2024

Systematic exploration of the non-geometric flux landscape

Given the huge size of the generic four-dimensional 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 {\it axionic flux polynomials} 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 $Q$-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 $2^{14}=16384$ candidate configurations, and we find that more than 16200 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.

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arXiv2024

On Formulating the Non-Geometric Scalar Potentials

In the context of four-dimensional type II supergravities, the successive application of various S/T-dualities leads to a generalized notion of fluxes, which includes certain (non-)geometric fluxes along with the standard RR and NS-NS p-form fluxes. These fluxes induce a diverse set of superpotential couplings leading to scalar potentials with a very rich structure, which may possibly result in a vast landscape of physical vacua. However such scalar potentials typically consist of a huge number of terms and in order to make any attempt for phenomenological model building with some analytic understanding/control it is necessary to formulate them in some compact and concise form. Along these lines we review various equivalent methods of deriving the same scalar potential through a set of master formulae, which may open up a new avenue for model building using non-geometric fluxes.

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arXiv2024

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

In the context of four-dimensional ${\cal N} = 1$ type IIB superstring compactifications, the U-dual completion of the holomorphic flux superpotential leads to four S-dual pairs of fluxes, namely $(F, H), (Q, P), (P', Q')$ and $(H', F')$. 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 {\it read-off} 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 {\it reading-off} the scalar potentials for five explicit models, and using a set of {\it axionic flux} combinations we show that 76276 terms arising from the flux superpotential in a ${\mathbb T}^6/({\mathbb Z}_2\times{\mathbb Z}_2)$-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.

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arXiv2024

Global Embedding of Fibre Inflation in Perturbative LVS

We present a global embedding of the Fibre inflation model in perturbative large volume scenario (LVS) in which the inflationary potential is induced via a combination of string-loop corrections and higher derivative F$^4$-effects. The minimal Fibre inflation model developed in the standard LVS generically faces some strong bounds on the inflaton field range arising from the K\"ahler cone constraints, which subsequently creates a challenge for realising 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 Fibre inflation in perturbative LVS.

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arXiv2024

Inflating in perturbative LVS: Global Embedding and Robustness

The perturbative LARGE volume scenario (LVS) is a promising moduli stabilisation scheme in which the overall volume modulus of the compactifying Calabi-Yau (CY) threefold is dynamically stabilised to exponentially large values via using only perturbative corrections. In this article, using an orientifold of a K3-fibred CY threefold, we present the global embedding of an inflationary model proposed in the framework of perturbative LVS, in which the overall volume modulus acts as the inflaton field rolling on a nearly flat potential induced by a combination of the ${\alpha^\prime}^3$-corrections and the so-called {\it log-loop} effects. Given that having a concrete global construction facilitates explicit expressions for a set of sub-leading corrections, as a next step, we present a detailed analysis investigating the robustness of the single-field inflationary model against such corrections, in particular those arising from the winding-type string loop corrections and the higher derivative F$^4$-corrections.

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arXiv2024

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

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 K\"ahler 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.

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arXiv2023

Seeking de-Sitter Vacua in the String Landscape

In this report, we present a concise review on the various moduli stabilisation schemes proposed in the context of type IIB superstring compactifications using Calabi-Yau orientifolds. We discuss the details of the known schemes by classifying them into two categories; the first one includes non-perturbative superpotential contributions leading to the well-known class of models like KKLT, Racetrack and LVS, while the second one includes only perturbative corrections arising from the series of $α^\prime$- and string-loop effects, leading to a new scheme - known as perturbative LVS. In addition, we motivate and briefly discuss about the global embedding requirements for all these moduli stabilisation schemes, and present some details for the perturbative LVS scheme by focusing on a concrete CY orientifold setting. In this context, the resulting 4D effective supergravity model indeed does not receive any non-pertubative superpotential effects due to the lack of necessary divisor topologies, and the Kähler moduli stabilisation is performed entirely by perturbative effects, leading to AdS minimum with exponentially large VEV for the overall volume of the internal CY manifold. It is further shown how this class of AdS solutions can be uplifted to de-Sitter solutions by using a couple of prescriptions such as $D$-term uplifting and the $T$-brane uplifting.

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arXiv2023

Higher Derivative Corrections to String Inflation

We quantitatively estimate the leading higher derivative corrections to ${\mathcal{N}}=1$ 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 $1 \leq h^{1,1} \leq 5$. 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 that they do not destroy the predictions for the main cosmological observables.

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arXiv2023

Symplectic formulation of the type IIB scalar potential with U-dual fluxes

We present a symplectic formulation of the $N =1$ four-dimensional type IIB scalar potential arising from a flux superpotential which has four S-dual pairs of fluxes demanded by the U-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 ${\mathbb T}^6/({\mathbb Z}_2 \times {\mathbb Z}_2)$ orientifold, in which the scalar potential induced by the U-dual flux superpotential results in a total of 76276 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.

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arXiv2023

Taxonomy of scalar potential with U-dual fluxes

In the context of $N =1$ four-dimensional type IIB supergravity theories, the U-dual completion arguments suggest to include four S-dual pairs of fluxes in the holomorphic superpotential, namely the so-called $(F, \, H), \, (Q, \, P), \, (P^\prime, Q^\prime)$ and $(H^\prime, \, F^\prime)$. These can generically induce cubic polynomials for the complex-structure moduli as well as the K\"ahler-moduli in the flux superpotential. In this article, we explore the insights of the four-dimensional non-geometric scalar potential in the presence of such generalized U-dual fluxes by considering an explicit type IIB toroidal compactification model based on an orientifold of ${\mathbb T}^6/({\mathbb Z}_2 \times {\mathbb Z}_2)$ orbifold. First, we observe that the flux superpotential induces a huge scalar potential having a total of 76276 terms involving 128 flux parameters and 14 real scalars. Subsequently, we invoke a new set of (the so-called) ``axionic fluxes" comprising 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 (AdS/dS) vacua in such models.

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arXiv2023

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

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 anti-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 $2 < h^{1,1} < 5$ 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 anti-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 anti-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.

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arXiv2023

Systematics of perturbatively flat flux vacua for CICYs

In this paper, we extend the analysis of scanning the perturbatively flat flux vacua (PFFV) for the type IIB orientifold compactifications on the mirror of the projective complete intersection Calabi-Yau (pCICY) 3-folds, which are realized as hypersurfaces in the product of complex projective spaces. We present the PFFV statistics for all the 36 pCICYs with $h^{1,1}=2$ and classify them into two categories of being K3-fibered model and non K3-fibered model. We find that all the K3-fibered models have a significantly large number of PFFV leading to physical vacua by fixing the axio-dilaton by non-perturbative effects, while only a couple of non K3-fibered models have such physical vacua. We have found that there are five pCICY $3$-folds with the suitable exchange symmetry leading to the so-called exponentially flat flux vacua (EFFV) which are protected against non-perturbative prepotential effects as well. Finally we explored the underlying exchange symmetries in the favorable dataset of 7820 pCICYs and have found that there are only 15 spaces which can result in EFFV configurations.

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