arXiv subjects

Eran Palti

Publications and source records attributed to Eran Palti.

At least 19 recordsLinked to original sources

arXiv2026

On Type II$_0$ Loci in Moduli Space

We study type II$_0$ loci in the moduli space of type IIB string theory compactified on Calabi-Yau manifolds. We show that around these infinite distance singular loci the leading order behaviour of the gauge kinetic matrix, and of the prepotential, can always be written in the form of a threshold correction from integrating out a BPS state, but one with an effectively complex charge. In order to understand the physical meaning of this, we carefully identify the splitting in the effective supergravity between the graviphoton direction and matter vector multiplets. Within a specific two-parameter example of a Calabi-Yau, we use this to identify a strongly-coupled matter sector involving both light electric and light magnetic states. We propose that the leading gauge kinetic matrix arises as a threshold correction from integrating out this non-perturbative sector, and that the sector has an effective weakly-coupled infrared description in terms of the complex-charged state. The region in moduli space has a Heterotic string dual microscopic description. The light magnetic state in this description corresponds to a Kaluza-Klein monopole, which becomes lighter than the fundamental Heterotic string, leading to the non-perturbative sector. Assuming this picture is correct, it implies the existence of infrared emergent infinite distance loci in moduli spaces of quantum gravity.

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arXiv2025

On the K-point in moduli space

We study a class of infinite-distance loci, referred to as K-points, in one-parameter complex-structure moduli spaces of type IIB string theory compactified on Calabi-Yau manifolds. We show that around K-points the effective four-dimensional supergravity exhibits certain unusual properties. The two most prominent being that the leading order dependence of the prepotential on the gauge couplings is non-perturbative and that the leading gauge kinetic terms in the action vanish when evaluated on an anti self-dual graviphoton background. These properties are shared with the conifold locus in moduli space, rather than the large complex-structure locus. The conifold locus is well-known to arise from integrating out a charged BPS state, and so the similarities suggest that the K-point also arises from integrating out a BPS state. We develop such an interpretation, finding that it corresponds to a BPS state which is extremely light, whose mass in Planck units is doubly-exponentially small in the distance to the K-point. The state behaves as if it had complex charges, or as if it couples to the self-dual and anti self-dual parts of the graviphoton differently. Assuming such an integrating-out scenario is indeed the correct physics for the K-point, we discuss the implications for our understanding of infinite distances in moduli space and for the Swampland Distance Conjecture.

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arXiv2025

Metrics over multi-parameter AdS vacua

We study the notion of a distance between different AdS vacua of string theory. The distance is measured by a metric that is derived by taking an off-shell quadratic variation of the effective action, and evaluating it over families of vacua. We calculate this metric for increasingly complex families of vacua. We first consider the two-parameter families of solutions of type $\mathrm{AdS}_4 \times \mathbb{C}\mathrm{P}^3$. We find that the metric is flat and positive, and so yields a well-defined distance along any path in the space of solutions. We then consider solutions of type $\mathrm{AdS}_3 \times S^3 \times \mathrm{CY}_2$ which have two (non-compact) flux parameters as well as a moduli space. We find that the space of solutions factorises between directions which vary the AdS radius, and the moduli space. The metric over AdS variations is flat and positive, and the metric over the moduli space is the usual one. Finally, we consider solutions of type $\mathrm{AdS}_3 \times S^3 \times S^3 \times S^1$ which also have a further direction in the space of solutions that is compact. We find that the metric is flat only on non-compact directions in the space of solutions. Restricting to such directions, we evaluate the metric and find it is positive definite and therefore yields a well-defined distance along any path.

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arXiv2024

Notes on integrating out M2 branes

Integrating out supersymmetric M2 branes wrapped on two-cycles in Calabi-Yau manifolds is an important calculation: it allows the determination of, and in some ways defines, the free energy of topological strings. In these notes, based on a short course aimed at graduate students, we go through various aspects of this calculation in detail. The end result is a recently proposed new formula for the topological string free energy.

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arXiv2024

On Calabi-Yau manifolds at strong topological string coupling

It was recently shown that integrating out M2 states on Calabi-Yau manifolds captures non-perturbative topological string physics in the free energy. In this note, we show that the resulting expression manifests a certain duality symmetry: the free energy at strong string coupling is equal to the Calabi-Yau period at weak string coupling. The duality yields the appropriate prescription for completing the integrating out in the ultraviolet.

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arXiv2024

Emergent potentials and non-perturbative open topological strings

We show that integrating out M2 branes ending on M5 branes inside Calabi-Yau manifolds captures non-perturbative open topological string physics. The integrating out is performed using a contour integral in complexified Schwinger proper time. For the resolved conifold, this contour can be extended to include the zero pole, which we argue captures the ultraviolet completion of the integrating out and yields the tree-level polynomial terms in the free energy. This is a manifestation of the Emergence Proposal, and provides further evidence for it. Unlike the case of closed strings, where the emergent terms are kinetic terms in the action, for these open strings it is tree-level potential terms which are emergent. This provides a first quantitative example of the proposal that classical tree-level potentials in string theory emerge from integrating out co-dimension one states.

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arXiv2024

Non-perturbative topological string theory on compact Calabi-Yau manifolds from M-theory

We show that the full non-perturbative topological string free energy, in the holomorphic limit, follows simply from a target space integrating out calculation of M2 states. Qualitatively, this is the same as the calculation performed by Gopakumar and Vafa, but we find that the final expression must be modified due to a subtlety with poles induced by non-perturbative physics. Accounting for this modification leads to a Gopakumar-Vafa-like formula, which we propose as the exact formulation of the integrating out procedure. Evaluating the formula necessarily requires a contour integral in a complexified Schwinger proper time parameter. We show that this evaluation yields the full non-perturbative topological string free energy, and can be applied to a compact, or non-compact, Calabi-Yau threefold. The explicit formula presented holds as long as the two-cycles wrapped by the branes are rigid and smooth, but the methodology can be used to study also more general Calabi-Yau geometries.

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arXiv2024

A positive metric over DGKT vacua

We study the notion of a metric over the space of AdS solution in string theory, leading to an associated distance between them. Such a distance is the idea underlying the AdS distance conjecture. We utilise the previously developed prescription for extracting such a metric: taking an off-shell quadratic variation of the string theory effective action and then evaluating it over the space of on-shell solutions. It was shown that this prescription leads to a well-defined positive metric over M-theory Freund-Rubin vacua. In this work, we use the same prescription to calculate the metric over type IIA DGKT vacua. These are much more involved, they have multiple flux parameters and exhibit scale separation. While it remains an open question whether these vacua exist as fully localised solutions of string theory, they are well-defined within the four-dimensional effective theory, which is all that is required for the calculation. We find that they also have a positive metric over them. Interestingly, this metric turns out to be independent of the many flux parameters in the solution, similarly to what happens for metrics over scalar field spaces. This non-trivial flux cancellation, as well as results from explicit vacua, lead us to propose a Swampland condition: that the metric over the space of vacua in quantum gravity, as defined by the above prescription, is always positive.

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arXiv2024

Emergence in String Theory and Fermi Gases

The Emergence Proposal suggests that some Swampland criteria, in particular on large field distances, are a consequence of the emergent nature of dynamics for fields in the infrared. In the context of type II string theory compactified on Calabi-Yau manifolds, it proposes that the cubic tree-level piece of the genus-zero prepotential is emergent from integrating out massive non-perturbative states. For a certain special non-compact Calabi-Yau, the blown-up conifold, it is known that the full all-genus prepotential can be matched onto the Grand Canonical potential of a two-dimensional Fermi gas. We propose here that this should be understood in the context of emergence: the prepotential is induced by integrating out the Fermi gas degrees of freedom. To make contact with the Swampland we need dynamical gravity, so compact Calabi-Yau manifolds. We show that for specifically the cubic term, an integrating out calculation also works for compact cases. In particular, the exact cubic term coefficient can be recovered from integrating out a Fermi gas for any compact Calabi-Yau that is an elliptic fibration over a reflexive toric base. We also propose a general map, for any one-parameter Calabi-Yau, between the Grand Canonical potential of the ultraviolet non-perturbative system and the period. In particular, this map leads to an emergent cubic term in the genus-zero prepotential for any such one-parameter model.

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arXiv2023

On the particle picture of Emergence

The Emergence Proposal is the idea that all kinetic terms for fields in quantum gravity are emergent in the infrared from integrating out towers of states. It predicts that in a supersymmetric string theory context, the tree-level prepotential terms can be recovered precisely by integrating out a tower of non-perturbative states. In this note we present a new perspective, and associated quantitative evidence, for this proposal. We argue that the tree-level kinetic terms arise from integrating out the ultraviolet physics of each of the states in the tower. This ultraviolet physics is associated to extended objects, and cannot be captured by a standard particle Schwinger integral. Instead, we argue that it should be captured by a Schwinger-like integral where the proper time is analytically continued, and a contour is taken around the origin. This maps to certain integral representations for the moduli space periods, and indeed one recovers the tree-level prepotential exactly. This interpretation suggests that the ultraviolet physics which gives the leading contribution to the prepotential is localised on point intersections of the extended objects. We also argue that over special loci in moduli space there can exist a particle picture of the states, and an associated simple particle Schwinger integral, which leads to the full tree-level prepotential. These are loci with special degenerations, such as the singular limit of the resolved conifold.

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arXiv2023

Regge growth of isolated massive spin-2 particles and the Swampland

We consider an effective theory with a single massive spin-2 particle and a gap to the cutoff. We couple the spin-2 particle to gravity, and to other lower-spin fields, and study the growth of scattering amplitudes of the particle in the Regge regime: where $s$ is much larger than $t$ and also any mass scales in the effective theory, but still much lower than the cutoff scale of the theory and therefore any further massive spin-2 particles. We include in the effective theory all possible operators, with an arbitrary, but finite, number of derivatives. We prove that the scattering amplitude grows strictly faster than $s^2$ in any such theory. Such fast growth goes against expected bounds on Regge growth. We therefore find further evidence for the Swampland spin-2 conjecture: that a theory with an isolated massive spin-2 particle, coupled to gravity, is in the Swampland.

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arXiv2023

Towards AdS Distances in String Theory

The AdS Distance Conjecture proposes to assign a notion of distance between AdS vacua in quantum gravity. We perform some initial developments of this idea. We first propose more sharply how to define a metric on conformal variations of AdS through the action. This metric is negative, making the distance ill-defined, a property relating to the famous conformal factor problem of quantum gravity. However, in string theory, variations of the AdS conformal factor are accompanied by variations of the internal dimensions and of the background flux. We propose an $\textit{action metric}$, which accounts for all of these variations simultaneously. Accounting for the variations of the overall volume of the internal dimensions can flip the sign of the action metric making it positive. This positivity is related to the absence of scale separation between the internal and external dimensions: the negative external conformal contribution must be sub-dominant to the positive internal contribution. We then focus specifically on the families of solutions of eleven-dimensional supergravity on AdS$_4 \times S^7$ and AdS$_7 \times S^4$. For these, there is only a single further additional contribution to the action metric coming from variations of the Freund-Rubin flux. This contribution is subtle to implement, and the unique prescription we find requires singling out the radial direction of AdS as special. Adding the flux contribution yields an overall total action metric which becomes positive for both the AdS$_4$ and AdS$_7$ families of solutions. The final result is therefore a procedure which yields a well-defined distance for these families of solutions.

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arXiv2023

Goldstone Bosons and Convexity

We study the spectrum of scalar charged operators in Conformal Field Theories (CFTs) with a $U(1)$ global symmetry. The charged operators are dual, by the state-operator correspondence, to homogenous charged states on the sphere. Such states can break the $U(1)$ symmetry, and we define what we call the large $f$ regime in the CFT as one where the symmetry breaking scale is much higher than the scale of the CFT sphere. In such a regime, there is (an approximate) Goldstone boson associated to the breaking. We show that consistency of the Goldstone boson physics implies that the spectrum of states, and therefore of operators, must be convex in charge. More precisely, we show that any family of operators of different charges, which are lowest dimension of their charge, and which additionally share the same realisation of the Goldstone boson in terms of the degrees of freedom of the CFT, must be convex.

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arXiv2022

Self-Binding Energies in AdS

The Positive Binding Conjecture is a proposed formulation of the Weak Gravity Conjecture appropriate to Anti de-Sitter (AdS) space. It proposes that in a consistent gravitational theory, with a $U(1)$ gauge symmetry, there must exist a charged particle with non-negative self-binding energy. In order to formulate this as a constraint on a given effective theory, we calculate the self-binding energy for a charged particle in AdS$_4$ and AdS$_5$. In particular, we allow it to couple to an additional scalar field of arbitrary mass. Unlike the flat-space case, even when the scalar field is massive it contributes significantly to the binding energy, and therefore is an essential component of the conjecture. In AdS$_5$, we give analytic expressions for the self-binding energy for the cases when the scalar field is massless and when it saturates the Breitenlohner-Freedman (BF) bound, and in AdS$_4$ when it is massless. We show that the massless case reproduces the flat-space expressions in the large AdS radius limit, and that both analytic cases lead to vanishing total self-binding energy for BPS particles in example supersymmetric models. For other masses of the scalar we give numerical expressions for its contribution to the self-binding energy.

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arXiv2022

Convexity of Charged Operators in CFTs with Multiple Abelian Symmetries

Motivated by the Weak Gravity Conjecture in the context of holography in AdS, it has been proposed that operators charged under global symmetries in CFTs, in three dimensions or higher, should satisfy certain convexity properties on their spectrum. A key element of this proposal is the charge at which convexity must appear, which was proposed to never be parametrically large. In this paper, we develop this constraint in the context of multiple Abelian global symmetries. We propose the statement that the convex directions in the multi-dimensional charge space should generate a sub-lattice of the total lattice of charged operators, such that the index of this sub-lattice cannot be made parametrically large. In the special case of two-dimensional CFTs, the index can be made parametrically large, which we prove by an explicit example. However, we also prove that in two dimensions there always exist convex directions generating a sub-lattice with an index bounded by the current levels of the global symmetry. Therefore, in two dimensions, the conjecture should be slightly modified to account for the current levels, and then it can be proven. In more than two dimensions, we show that the index of the sub-lattice generated by marginally convex charge vectors associated to BPS operators only, can be made parametrically large. However, we do not find evidence for parametric delay in convexity once all operators are considered.

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arXiv2021

On supersymmetric AdS$_4$ orientifold vacua

In this work we study ten-dimensional solutions to type IIA string theory of the form AdS$_4$ x $X_6$ which contain orientifold planes and preserve N=1 supersymmetry. In particular, we consider solutions which exhibit some key features of the four-dimensional DGKT proposal for compactifications on Calabi-Yau manifolds with fluxes, and in this sense may be considered their ten-dimensional uplifts. We focus on the supersymmetry equations and Bianchi identities, and find solutions to these that are valid at the two-derivative level and at first order in an expansion parameter which is related to the AdS cosmological constant. This family of solutions is such that the background metric is deformed from the Ricci-flat one to one exhibiting SU(3)xSU(3)-structure, and dilaton gradients and warp factors are induced.

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arXiv2021

On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture

The Weak Gravity Conjecture is typically stated as a bound on the mass-to-charge ratio of a particle in the theory. Alternatively, it has been proposed that its natural formulation is in terms of the existence of a particle which is self-repulsive under all long-range forces. We propose a closely related, but distinct, formulation, which is that it should correspond to a particle with non-negative self-binding energy. This formulation is particularly interesting in anti-de Sitter space, because it has a simple conformal field theory (CFT) dual formulation: let $Δ(q)$ be the dimension of the lowest-dimension operator with charge $q$ under some global $U(1)$ symmetry, then $Δ(q)$ must be a convex function of $q$. This formulation avoids any reference to holographic dual forces or even to locality in spacetime, and so we make a wild leap, and conjecture that such convexity of the spectrum of charges holds for any (unitary) conformal field theory, not just those that have weakly coupled and weakly curved duals. This Charge Convexity Conjecture, and its natural generalization to larger global symmetry groups, can be tested in various examples where anomalous dimensions can be computed, by perturbation theory, $1/N$ expansions and semi-classical methods. In all examples that we tested we find that the conjecture holds. We do not yet understand from the CFT point of view why this is true.

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arXiv2021

Stability of BPS States and Weak Coupling Limits

We study the stability and spectrum of BPS states in ${\cal N}=2$ supergravity. We find evidence, and prove for a large class of cases, that BPS stability exhibits a certain filtration which is partially independent of the value of the gauge couplings. Specifically, for any perturbative value of any gauge coupling $g \ll 1$, a BPS state can only decay to some constituents if those constituents do not become infinitely heavier than it in the vanishing coupling limit $g \rightarrow 0$. This stability filtration can be mathematically formulated in terms of the monodromy weight filtration of the limiting mixed Hodge structure associated to the vanishing coupling limit. We study various implications of the result for the Swampland program which aims to understand such weak-coupling limits, specifically regarding the nature and presence of an infinite tower of light charged BPS states.

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