arXiv subjects

Seung-Joo Lee

Publications and source records attributed to Seung-Joo Lee.

At least 19 recordsLinked to original sources

arXiv2026

Calabi-Yau Metrics with Full Moduli Dependence

Recent advances in numerical and machine-learning methods have enabled highly accurate constructions of Ricci-flat metrics on compact Calabi-Yau three-folds. For phenomenological applications it is crucial to understand how these metrics vary across moduli space. In this work, we construct approximate analytic expressions for Ricci-flat Calabi-Yau metrics with explicit complex-structure and Kähler moduli dependence by combining machine-learned numerical data with symbolic regression. Our approach is based on an explicit Ansatz for the Kähler potential with moduli-dependent coefficients. Fitting this Ansatz to numerical data and applying symbolic regression allows us to reconstruct analytic formulae for these coefficients, thereby obtaining approximate Ricci-flat metrics with explicit moduli dependence. We apply the construction to a one-parameter family of bi-cubic three-folds in $\mathbb{P}^2 \times \mathbb{P}^2$, achieving percent-level agreement with the underlying numerical data.

hep-th↗

arXiv2026

CIPro Package: Complete Intersections in Products of Projective Spaces and Line Bundles

CIPro is a Mathematica package for constructing and analyzing complete intersections in products of projective spaces and line bundles over such varieties. It computes properties of complete intersections, such as Chern classes, Hilbert series, GV invariants and symmetries, as well as properties of line bundles on complete intersections, including their cohomology groups. The package also consolidates a number of data sets available in the literature into a single system, including the lists of complete intersection Calabi-Yau three- and four-folds. This short tutorial introduces the package, provides a brief discussion of some of the mathematical background underlying its computations, and gives a series of examples to illustrate its use. These tools are of utility for many computations in string compactifications, especially for Calabi-Yau geometries appearing in Heterotic and Type II constructions. Many tools apply beyond the Calabi-Yau context, including for example, almost Fano bases in F-theory.

hep-th↗

arXiv2025

Explicit Bounds on the Spectrum of 6d N=(1,0) Supergravity

We propose a novel strategy to derive explicit and uniform upper bounds on the particle spectrum of six-dimensional gravitational theories with minimal supersymmetry, focusing initially on the tensor sector. The strategy is motivated by considerations of F-theory compactifications on elliptic Calabi-Yau 3-folds. However, it admits a clear bottom-up interpretation and is thus applicable to general supergravity theories modulo certain physical conjectures. At the heart of the strategy are two key structures, most natural in birational geometry: one concerns the singularity of the natural pairs on the base manifolds, and the other, the fibration generically exhibited by the bases. Put physically, the former structure keeps the effective theories from decompactifying and the latter ensures the (generic) presence of a heterotic string. We sketch our bounding strategy and present, for an illustration, the explicit bounds thereby derived on the tensor spectrum, with the technical details relegated to a companion paper [1].

hep-th↗

arXiv2025

A Picard rank bound for base surfaces of elliptic Calabi-Yau 3-folds

We compute an explicit rank bound on the Picard group of the compact surfaces, which can serve as the base of an elliptic Calabi-Yau variety with canonical singularities. To bound the Picard rank from above, we develop a novel strategy in birational geometry, motivated in part by the physics of six-dimensional vacua of F-theory as discussed in a companion paper [1] to this one. The derivation of the concrete bound illustrates the strategy and clarifies the origin of the boundedness.

hep-th↗

arXiv2025

Approximate Ricci-flat Metrics for Calabi-Yau Manifolds

We outline a method to determine analytic Kähler potentials with associated approximately Ricci-flat Kähler metrics on Calabi-Yau manifolds. Key ingredients are numerically calculating Ricci-flat Kähler potentials via machine learning techniques and fitting the numerical results to Donaldson's Ansatz. We apply this method to the Dwork family of quintic hypersurfaces in $\mathbb{P}^4$ and an analogous one-parameter family of bi-cubic CY hypersurfaces in $\mathbb{P}^2\times\mathbb{P}^2$. In each case, a relatively simple analytic expression is obtained for the approximately Ricci-flat Kähler potentials, including the explicit dependence on the complex structure parameter. We find that these Kähler potentials only depend on the modulus of the complex structure parameter.

hep-th↗

arXiv2025

Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics

We interpret infinite-distance limits in the complex structure moduli space of F-theory compactifications to six dimensions in the light of general ideas in quantum gravity. The limits we focus on arise from non-minimal singularities in the elliptic fiber over curves in a Hirzebruch surface base, which do not admit a crepant resolution. Such degenerations take place along infinite directions in the non-perturbative brane moduli space in F-theory. A blow-up procedure, detailed generally in Part I of this project, gives rise to an internal space consisting of a union of log Calabi-Yau threefolds glued together along their boundaries. We geometrically classify the resulting configurations for genus-zero single infinite-distance limits. Special emphasis is put on the structure of singular fibers in codimension zero and one. As our main result, we interpret the central fiber of these degenerations as endpoints of a decompactification limit with six-dimensional defects. The conclusions rely on an adiabatic limit to gain information on the asymptotically massless states from the structure of vanishing cycles. We also compare our analysis to the heterotic dual description where available. Our findings are in agreement with general expectations from quantum gravity and provide further evidence for the Emergent String Conjecture.

hep-th↗

arXiv2025

Non-minimal Elliptic Threefolds at Infinite Distance I: Log Calabi-Yau Resolutions

We study infinite-distance limits in the complex structure moduli space of elliptic Calabi-Yau threefolds. In F-theory compactifications to six dimensions, such limits include infinite-distance trajectories in the non-perturbative open string moduli space. The limits are described as degenerations of elliptic threefolds whose central elements exhibit non-minimal elliptic fibers, in the Kodaira sense, over curves on the base. We show how these non-crepant singularities can be removed by a systematic sequence of blow-ups of the base, leading to a union of log Calabi-Yau spaces glued together along their boundaries. We identify criteria for the blow-ups to give rise to open chains or more complicated trees of components and analyse the blow-up geometry. While our results are general and applicable to all non-minimal degenerations of Calabi-Yau threefolds in codimension one, we exemplify them in particular for elliptic threefolds over Hirzebruch surface base spaces. We also explain how to extract the gauge algebra for F-theory probing such reducible asymptotic geometries. This analysis is the basis for a detailed F-theory interpretation of the associated infinite-distance limits that will be provided in a companion paper.

hep-th↗

arXiv2022

Geometric Bounds on the 1-Form Gauge Sector

We classify the allowed structures of the discrete 1-form gauge sector in six-dimensional supergravity theories realized as F-theory compactifications. This provides upper bounds on the 1-form gauge factors $\mathbb{Z}_m$ and in particular demands each cyclic factor to obey $m\leq 6$. Our bounds correspond to the universal geometric constraints on the torsion subgroup of the Mordell-Weil group of elliptic Calabi-Yau three-folds. For any F-theory vacua with at least one tensor multiplet, we derive the constraints from the $\mathbb{P}^1$ fibration structure of the base two-fold and identify their physical origin in terms of the worldsheet symmetry of the associated effective heterotic string. The bounds are also extended to the F-theory vacua with no tensor multiplets via a specific deformation of the theory followed by a small instanton transition, along which the 1-form gauge sector is not reduced. We envision that our geometric bounds can be promoted to a swampland constraint on any six-dimensional gravitational theories with minimal supersymmetry and also extend them to four-dimensional F-theory vacua.

hep-th↗

arXiv2022

Holomorphic Anomalies, Fourfolds and Fluxes

We investigate holomorphic anomalies of partition functions underlying string compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic fourfolds the partition functions have an alternative interpretation as elliptic genera of N=1 supersymmetric string theories in four dimensions, or as generating functions for relative Gromov-Witten invariants of fourfolds with fluxes. We derive the holomorphic anomaly equations by starting from the BCOV formalism of topological strings, and translating them into geometrical terms. The result can be recast into modular and elliptic anomaly equations. As a new feature, as compared to threefolds, we find an extra contribution which is given by a gravitational descendant invariant. This leads to linear terms in the anomaly equations, which support an algebra of derivatives mapping between partition functions of the various flux sectors. These geometric features are mirrored by certain properties of quasi-Jacobi forms. We also offer an interpretation of the physics from the viewpoint of the worldsheet theory.

hep-th↗

arXiv2022

Emergent Strings from Infinite Distance Limits

As a refinement of the Swampland Distance Conjecture, we propose that a quantum gravitational theory in an infinite distance limit of its moduli space either decompactifies, or reduces to an asymptotically tensionless, weakly coupled string theory. We support our claim by classifying, as special cases, the behaviour of M-Theory and Type IIA string theory compactifications on Calabi-Yau three-folds at infinite distances in Kahler moduli space. The analysis comprises three parts: We first classify the possible infinite distance limits in the classical Kahler moduli space of a Calabi-Yau three-fold. Each such limit at finite volume is characterized by a universal fibration structure, for which the generic fiber shrinking in the limit is either an elliptic curve, a K3 surface, or an Abelian surface. In the second part we focus on M-Theory and investigate the nature of the towers of asymptotically massless states that arise from branes wrapped on the shrinking fibers. Depending on which of the three classes of fibrations are considered, we obtain decompactification to F-Theory, or a theory with a unique asymptotically tensionless, weakly coupled heterotic or Type II string, respectively. The latter probes a dual D-manifold which is in general non-geometric. In addition to the intrinsic string excitations, towers of states from M2-branes along non-contractible curves become light and correspond to further wrapping and winding modes of the tensionless heterotic or Type II string. In the third part of the analysis, we consider Type IIA string theory on Calabi-Yau three-folds and show that quantum effects obstruct taking finite volume infinite distance limits in the Kahler moduli space. The only possible infinite distance limit which is not a decompactification limit involves K3-fibrations with string scale fiber volume and gives rise to an emergent tensionless heterotic string.

hep-th↗

arXiv2022

Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions

We investigate the interplay between the enumerative geometry of Calabi-Yau fourfolds with fluxes and the modularity of elliptic genera in four-dimensional string theories. We argue that certain contributions to the elliptic genus are given by derivatives of modular or quasi-modular forms, which encode BPS invariants of Calabi-Yau or non-Calabi-Yau threefolds that are embedded in the given fourfold. As a result, the elliptic genus is only a quasi-Jacobi form, rather than a modular or quasi-modular one in the usual sense. This manifests itself as a holomorphic anomaly of the spectral flow symmetry, and in an elliptic holomorphic anomaly equation that maps between different flux sectors. We support our general considerations by a detailed study of examples, including non-critical strings in four dimensions. For the critical heterotic string, we explain how anomaly cancellation is restored due to the properties of the derivative sector. Essentially, while the modular sector of the elliptic genus takes care of anomaly cancellation involving the universal B-field, the quasi-Jacobi one accounts for additional B-fields that can be present. Thus once again, diverse mathematical ingredients, namely here the algebraic geometry of fourfolds, relative Gromow-Witten theory pertaining to flux backgrounds, and the modular properties of (quasi-)Jacobi forms, conspire in an intriguing manner precisely as required by stringy consistency.

hep-th↗

arXiv2021

On Towers of Light States at Infinite Distance

Upon investigating asymptotic regimes of the F-theory moduli space, we verify that a tower of light states arises as predicted by the Distance Conjecture. Specifically, we provide a geometric classification of the infinite distance limits and comprehensively analyze the light states of the associated effective theories. We thereby find for every infinite distance limit that the effective theory either reduces to a weakly-coupled (dual) string theory or decompactifies to a higher-dimensional theory. This is in full agreement with the Emergent String Conjecture, which clarifies the physical nature of the light particle tower either as the excitation modes of an emergent weakly-coupled string or as the Kaluza-Klein modes associated with a decompactification of the spacetime. The results reported encompass both the Kähler and the complex structure limits of F-theory, respectively, in $4$ and $8$ dimensions, and hence are indicative of the overarching microscopic origins of the light towers.

hep-th↗

arXiv2021

Physics of Infinite Complex Structure Limits in eight Dimensions

We investigate infinite distance limits in the complex structure moduli space of F-theory compactified on K3 to eight dimensions. While this is among the simplest possible arenas to test ideas about the Swampland Distance Conjecture, it is nevertheless non-trivial enough to improve our understanding of the physics for these limiting geometries, including phenomena of emergence. It also provides a perspective on infinite distance limits from the viewpoint of open strings. The paper has two quite independent themes. In the main part we show that all degenerations of elliptic K3 surfaces at infinite distance as analysed in a companion paper can be interpreted as (partial) decompactification or emergent string limits in F-theory, in agreement with the Emergent String Conjecture. We present a unified geometric picture of the possible towers of states that can become light and illustrate our general claims via the connection between Kulikov models of degenerating K3 surfaces and the dual heterotic string. As an application we classify the possible maximal non-abelian Lie algebras and their Kac-Moody and loop extensions that can arise in the infinite distance limits. In the second part we discuss the infinite distance behaviour of certain exact quartic gauge couplings. We encounter a tension with the hypothesis that effective couplings should be fully generated by integrating out massive states. We show that by appropriately renormalizing the string coupling, at least partial emergence can be achieved.

hep-th↗

arXiv2021

Elliptic K3 Surfaces at Infinite Complex Structure and their Refined Kulikov models

Motivated by the Swampland Distance and the Emergent String Conjecture of Quantum Gravity, we analyse the infinite distance degenerations in the complex structure moduli space of elliptic K3 surfaces. All complex degenerations of K3 surfaces are known to be classified according to their associated Kulikov models of Type I (finite distance), Type II or Type III (infinite distance). For elliptic K3 surfaces, we characterise the underlying Weierstrass models in detail. Similarly to the known two classes of Type II Kulikov models for elliptic K3 surfaces we find that the Weierstrass models of the more elusive Type III Kulikov models can be brought into two canonical forms. We furthermore show that all infinite distance limits are related to degenerations of Weierstrass models with non-minimal singularities in codimension one or to models with degenerating generic fibers as in the Sen limit. We explicitly work out the general structure of blowups and base changes required to remove the non-minimal singularities. These results form the basis for a classification of the infinite distance limits of elliptic K3 surfaces as probed by F-theory in a companion paper. The Type III limits, in particular, are (partial) decompactification limits as signalled by an emergent affine enhancement of the symmetry algebra.

hep-th↗

arXiv2021

Quantum Corrections in 4d N=1 Infinite Distance Limits and the Weak Gravity Conjecture

We study quantum corrections in four-dimensional theories with $N=1$ supersymmetry in the context of Quantum Gravity Conjectures. According to the Emergent String Conjecture, infinite distance limits in quantum gravity either lead to decompactification of the theory or result in a weakly coupled string theory. We verify this conjecture in the framework of $N=1$ supersymmetric F-theory compactifications to four dimensions including perturbative $α'$ as well as non-perturbative corrections. After proving uniqueness of the emergent critical string at the classical level, we show that quantum corrections obstruct precisely those limits in which the scale of the emergent critical string would lie parametrically below the Kaluza-Klein scale. Limits in which the tension of the asymptotically tensionless string sits at the Kaluza-Klein scale, by contrast, are not obstructed. In the second part of the paper we study the effect of quantum corrections for the Weak Gravity Conjecture away from the strict weak coupling limit. We propose that gauge threshold corrections and mass renormalisation effects modify the super-extremality bound in four dimensions. For the infinite distance limits in F-theory the classical super-extremality bound is generically satisfied by a sublattice of states in the tower of excitations of an emergent heterotic string. By matching the F-theory $α'$ corrections to gauge threshold corrections of the dual heterotic theory we predict how the masses of this tower must be renormalised in order for the Weak Gravity Conjecture to hold at the quantum level.

hep-th↗

arXiv2020

Machine Learning String Standard Models

We study machine learning of phenomenologically relevant properties of string compactifications, which arise in the context of heterotic line bundle models. Both supervised and unsupervised learning are considered. We find that, for a fixed compactification manifold, relatively small neural networks are capable of distinguishing consistent line bundle models with the correct gauge group and the correct chiral asymmetry from random models without these properties. The same distinction can also be achieved in the context of unsupervised learning, using an auto-encoder. Learning non-topological properties, specifically the number of Higgs multiplets, turns out to be more difficult, but is possible using sizeable networks and feature-enhanced data sets.

hep-th↗

arXiv2019

Swampland Bounds on the Abelian Gauge Sector

We derive bounds on the number of abelian gauge group factors in six-dimensional gravitational theories with minimal supersymmetry and in their F-theoretic realisations. These bounds follow by requiring consistency of certain BPS strings in the spectrum of the theory, as recently proposed in the literature. Under certain assumptions this approach constrains the number of abelian gauge group factors in six-dimensional supergravity theories with at least one tensor multiplet to be $N \leq 20$ (or $N \leq 22$ in absence of charged matter). For any geometric F-theory realisation with at least one tensor multiplet we establish the bound $N \leq 16$ by demanding unitarity of a heterotic solitonic string which exists even in absence of a perturbative heterotic dual. This result extends to four-dimensional F-theory vacua on any blowup of a rational fibration. Our findings lead to universal bounds on the rank of the Mordell-Weil group of elliptically fibered Calabi-Yau threefolds.

hep-th↗

arXiv2019

Distinguishing Elliptic Fibrations with AI

We use the latest techniques in machine-learning to study whether from the landscape of Calabi-Yau manifolds one can distinguish elliptically fibred ones. Using the dataset of complete intersections in products of projective spaces (CICY3 and CICY4, totalling about a million manifolds) as a concrete playground, we find that a relatively simple neural network with forward-feeding multi-layers can very efficiently distinguish the elliptic fibrations, much more so than using the traditional methods of manipulating the defining equations. We cross-check with control cases to ensure that the AI is not randomly guessing and is indeed identifying an inherent structure. Our result should prove useful in F-theory and string model building as well as in pure algebraic geometry.

hep-th↗