arXiv subjects

Min-Seok Seo

Publications and source records attributed to Min-Seok Seo.

At least 19 recordsLinked to original sources

arXiv2026

Background instability of quintessence model in light of entropy and distance conjecture

We apply the covariant entropy bound argument supporting the de Sitter swampland conjecture to the quintessence model, to find out the condition for the background to be unstable. More concretely, the background is unstable when the matter entropy given by the species number of the effective field theory increases more rapidly than the geometrical entropy proportional to the apparent horizon area, since it contradicts the covariant entropy bound. The rapid increase in the matter entropy is proposed by the distance conjecture, which states that the time evolution of some scalar field along the geodesic in the field space brings about the descent of a tower of states from UV. From this, we find that for the quintessence model, the unstable background admits the event horizon of finite size, and the converse is also true when the string tower is taken into account. Here, the presence of the event horizon implies that the trans-Planckian modes can be classicalized, violating the trans-Planckian censorship bound. We also point out that the scale separation between the Kaluza-Klein mass scale and the Hubble parameter can be realized when the product between the increasing rates of the matter and the geometrical entropies is bounded from below, which is consistent with the AdS distance conjecture. Our study suggests that various swampland conjectures can be comprehensively understood in the language of the entropy.

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arXiv2026

Implication of dressed form of relational observable on von Neumann algebra

In quantum gravity, physically meaningful operator is required to be invariant under the diffeomorphisms. Such gauge invariant operator is typically given by the relational observable, the operator localized in relation to some background states. We point out that the relational observable can be comprehensively written in the form of the dressed operator. For the background having boundary where the diffeomorphisms are not gauged, we can use the gravitational Wilson line for dressing, then the relational observable is nonlocal. In contrast, when the background breaks some isometries, as can be found in quasi-de Sitter space, dressing can be local, which is a kind of Stückelberg mechanism. Since dressing resembles the outer automorphism in the von Neumann algebra, we may investigate the algebraic structure of the background by considering the dressed form of the relational observable. From this, we can understand that quasi-de Sitter space is described by the Type II$_\infty$ algebra where the trace diverges in the decoupling limit of gravity. It is different from the Type II$_1$ algebra of de Sitter space where the finite size of trace can be defined in the same limit. This shows that the isometry preserving and breaking backgrounds are quite different in the algebraic structure no matter how small the breaking effect is.

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arXiv2026

Local gauge invariant operator on isometry breaking background

Whereas local field operators play the crucial role in reconciling quantum mechanics and special relativity, they are not trivially compatible with the diffeomorphism invariance of gravity. In order to address this issue, we consider the background geometry which breaks the isometry spontaneously. Then the local gauge invariant operator can be constructed through the Stückelberg mechanism, where the fluctuation of the metric in the direction of the isometry breaking combines with that of matter whose classical solution breaks the isometry. This is equivalent to introducing the clock and the rod to promote the local field operators to the gauge invariant ones. A typical example is the curvature perturbation in quasi-de Sitter space arising from the spontaneous breaking of the timelike isometry. We also discuss the features of the local gauge invariant operator when the spacelike isometry is spontaneously broken. Meanwhile, even if the local gauge invariant operators exist, it does not guarantee the reliable construction of the gauge invariant operators on the local region like the island, which is regarded as an essential ingredient to resolve the black hole information paradox. This is because the fluctuation of the spacetime point is accumulated in time, which in fact also gives rise to eternal inflation in quasi-de Sitter space. In order to suppress the fluctuation at late time, the isometry must be strongly broken by the background. In the case of the evaporating black hole, it may be achieved by the transition to the higher dimensional black hole.

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arXiv2025

Bounds on complex structure moduli values for perturbative control

String compactification in the framework of the low energy effective supergravity requires the perturbative control in both the large volume and the weak coupling expansions. However, when the complex structure moduli couple to some lattice structure, the Sp$(2(h^{2,1}+1))$ symmetry of the tree level Kähler potential allows the correction to the Kähler potential to diverge in the large field limit of the complex structure moduli, resulting in the breakdown of the perturbative control. Here the lattice structure naturally appears in the presence of a tower of states like the Kaluza-Klein or the string modes, an essential ingredient of the distance conjecture. The similar situation can be found from the axio-dilaton contribution to the corrected Kähler potential, where the SL$(2, \mathbb{Z})$ symmetry as well as the coupling between the axio-dilaton and the lattice structure allow the correction to diverge in the weak coupling limit. In order to keep the perturbative control, the values of the complex structure moduli as well as the dilaton must have the upper bound, which is determined by the volume of the internal manifold and the string coupling constant, hence the Kaluza-Klein and the string mass scales. The form of the bounds are quite similar to that given by the distance conjecture, both prevents the descent of a tower of states.

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arXiv2025

Species scale associated with Weinberg operator and bound on Majorana neutrino mass

When states in a tower like the Kaluza-Klein or the string tower couple to another state through the irrelevant operators of the same type, their contributions to the loop corrections of the relevant or the marginal operators are not negligible, threatening the perturbativity. This can be avoided provided the cutoff scale is lower than the species scale associated with the irrelevant operator. We apply this to towers of states associated with the neutrino which couple to the Higgs through the Weinberg operator, the dimension-5 irrelevant operator generating the Majorana neutrino mass. Requiring the `Majorana species scale', the species scale associated with the Weinberg operator, to be below the gravitational species scale, one finds the lower bound on the Majorana neutrino mass determined by the species number. The Festina-Lente bound also gives the lower bound on the Majorana neutrino mass, but it is not so stringent. Meanwhile, even if the neutrino mass is of the Dirac type at the renormalizable level, the Majorana mass term still can be written in the effective field theory action so far as the Weinberg operator is not forbidden. Even if the Majorana neutrino mass is larger than the Dirac one, so far as there are sufficient degrees of freedom with mass smaller than the scale of the cosmological constant, the observation of the Majorana nature of the neutrino may not contradict to quantum gravity constraints which rules out the neutrino mass purely given by the Majorana type.

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arXiv2024

Axion species scale and axion weak gravity conjecture-like bound

As a cutoff scale of quantum gravity, the species scale can be defined by the scale at which the perturbativity of the non-renormalizable gravitational interaction begins to break down. Since it is determined by the number of species in the effective field theory, we can find the close connection to the distance conjecture, which predicts the lowering of the cutoff at the asymptotic limit of the moduli space caused by the descent of a tower of states from UV. Meanwhile, the same kind of the cutoff scale can be obtained from any non-renormalizable interaction, in particular the interaction between the axion and the gauge field through the $θF\wedge F$ term. Demanding this `axion species scale' not to exceed the gravitational species scale, we obtain the bound $(8π^2/g^2)f \lesssim M_{\rm Pl}$. This is quite similar to the axion weak gravity conjecture bound, but can be applied to any gauge as well as the string interactions which are relevant to towers of states. We also investigate the implications of the (axion) species scale and the axion weak gravity conjecture-like bound by considering the Peccei-Quinn charge reduction of black hole through the interaction between black hole and the string or wormhole.

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arXiv2024

Asymptotic behavior of saxion-axion system in stringy quintessence model

The late time behavior of the slow-roll parameter in the stringy quintessence model is studied when axion as well as saxion are allowed to move. Even though the potential is independent of the axion at tree level, the axion can move through its coupling to the saxion and the background geometry. Then the contributions of the axion kinetic energy to the slow-roll parameter and the vacuum energy density are not negligible when the slow-roll approximation does not hold. As the dimension of the field space is doubled, the fixed point at which the time variation of the slow-roll parameter vanishes is not always stable. It is found that the fixed point in the saxion-axion system is at most partially stable, in particular when the volume modulus and the axio-dilaton, the essential ingredients of the string compactification, are taken into account. It seems that as more saxion-axion pairs are considered, achieving the stability of the fixed point becomes difficult.

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arXiv2024

Asymptotic bound on slow-roll parameter in stringy quintessence model

We study the late time behavior of the scalar part of the volume modulus and the dilaton in stringy quintessence model, focusing on their contributions to the Hubble slow-roll parameter $ε$ which directly measures the deviation of the spacetime geometry from de Sitter space. When only one of the moduli is allowed to move, $ε$ converges to the stable fixed point at late time. The fixed point value is larger than $1$, thus the slow-roll cannot be realized. Moreover, if the decay rate of the quintessence potential is larger than some critical value, the positivity of the potential imposes that the stable fixed point value is just given by $3$, independent of the details of the moduli dynamics. Otherwise, the fixed point value coincides with the potential slow-roll parameter. When both the volume modulus and the dilaton roll down the potential simultaneously, we can find the relation between the contributions of two moduli to $ε$ satisfied at the fixed point. In this case, the fixed point value is not in general the simple sum of fixed point values in the single field case and cannot be larger than $3$.

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arXiv2024

Kaluza-Klein tower and bubble nucleation in six dimensional Einstein-Maxwell theory

We study the implication of the distance and the cobordism conjecture on the 6-dimensional Einstein-Maxwell theory compactified on $S^2$. In this toy model, the radion potential is stabilized by the conspiracy of the curvature of $S^2$ and the flux through $S^2$ parametrized by $f$, and uplifted by the positive 6-dimensional cosmological constant parametrized by $λ$. When $λ=0$, the radion is stabilized at the anti-de Sitter (AdS) vacuum, which cannot be interpolated to the Minkowski vacuum since the Kaluza-Klein (KK) tower descends from UV in the vanishing limit of the 4-dimensional cosmological constant. For nonzero $λ$ which realizes the metastable de Sitter (dS) vacuum, as well as the AdS and the Minkowski vacuum, such an obstruction can be found provided the combination $f^2λ$ is fixed and the limit $λ\to 0$ is taken. Moreover, the 6-dimensional Einstein-Maxwell theory allows the transition between vacua through the nucleation of the bubble. In this case, the values of the 4-dimensional cosmological constant inside and outside the bubble are different as $f$ is changed at the bubble wall, while $λ$ remains unchanged. Regarding the AdS vacuum with the vanishing curvature radius as the `nothing', we find that the transition from the metastable dS vacuum to the nothing is not prevented by the descent of the KK tower since $f^2λ$ is not fixed.

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arXiv2023

Bounds on tower mass scales in the presence of throats of different warping

In Type IIB flux compactification realizing the metastable de Sitter (dS) vacuum, the uplift potential can be generated by $\overline{\rm D3}$-branes at the tip of Klebanov-Strassler throat. Then the uplift potential obeys the scaling law with respect to the tower mass scale $m_{\rm sc}$, which can be the Kaluza-Klein (KK) mass scale associated with the throat containing $\overline{\rm D3}$-branes or the bulk tower mass scales, depending on the warping of the throat. On the other hand, in the presence of another throat of stronger warping, the KK mass scale associated with this throat is lower than $m_{\rm sc}$. Nevertheless, the Higuchi bound and the condition that the tower mass scale is higher than the gravitino mass provide the upper bound on $m_{\rm sc}$ determined by the lowest tower mass scale (or gravitino mass). This bound also can be interpreted as the lower bound on the lowest tower mass scale determined by $m_{\rm sc}$. We investigate this bound in detail when the throat containing $\overline{\rm D3}$-branes is strongly and weakly warped, respectively.

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arXiv2023

Von Neumann algebra description of inflationary cosmology

We study the von Neumann algebra description of the inflationary quasi-de Sitter (dS) space. Unlike perfect dS space, quasi-dS space allows the nonzero energy flux across the horizon, which can be identified with the expectation value of the static time translation generator. Moreover, as a dS isometry associated with the static time translation is spontaneously broken, the fluctuation in time is accumulated, which induces the fluctuation in the energy flux. When the inflationary period is given by $(ε_H H)^{-1}$ where $ε_H$ is the slow-roll parameter measuring the increasing rate of the Hubble radius, both the energy flux and its fluctuation diverge in the $G \to 0$ limit. Taking the fluctuation in the energy flux and that in the observer's energy into account, we argue that the inflationary quasi-dS space is described by Type II$_\infty$ algebra. As the entropy is not bounded from above, this is different from Type II$_1$ description of perfect dS space in which the entropy is maximized by the maximal entanglement. We also show that our result is consistent with the observation that the von Neumann entropy for the density matrix reflecting the fluctuations above is interpreted as the generalized entropy.

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arXiv2023

(In)stability of de Sitter vacuum in light of distance conjecture and emergence proposal

The distance conjecture claims that as the modulus traverses along the trans-Planckian geodesic distance, the effective field theory becomes invalid by a descent of a tower of states from UV. Moreover, according to the recent emergence proposal, the kinetic term of the modulus is entirely generated by the wavefunction renormalization in which a tower of states are integrated out. Assuming these two conjectures, we explore the role of a tower of states coupled to the modulus in (in)stability of the de Sitter (dS) vacuum by studying the one-loop effective potential generated by a tower of states. We find that a fermionic tower of states makes the effective potential more or less consistent with the dS swampland conjecture : either the slope or the curvature of the potential is sizeable. In contrast, the effective potential generated by a bosonic tower of states seems to allow the stable dS vacuum. Therefore, in order to argue the instability of the dS vacuum, the additional ingredient like supersymmetry breaking needs to be taken into account.

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arXiv2023

Uplift and towers of states in warped throat

We investigate the connection between the distance conjecture and the uplift potential. For this purpose, we consider the concrete model, the warped deformed conifold embedded into Type IIB flux compactifications, with the uplift potential produced by $\overline{\rm D3}$-branes at the tip of the throat. Whereas the various mass scales associated with towers of states can be found, it turns out that the lightest tower mass scale satisfies the scaling behavior with respect to the uplift potential, which is meaningful provided the number of $\overline{\rm D3}$-branes is nonzero. This indicates that the effective theory becomes invalid in the vanishing limit of the uplift potential by the descent of an infinite tower of states from UV, as predicted in the distance conjecture. Since too large uplift potential is also problematic due to the runaway behavior of the moduli potential as well as the sizeable backreaction of $\overline{\rm D3}$-branes, the uplift potential is bounded from both above and below. In the simple model like the KKLT or the large volume scenario in which non-perturbative effect is dominatd by the single term, this bound can be rewritten as the bound on the size of the superpotential.

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arXiv2022

Information paradox and island in quasi-de Sitter space

Whereas a static observer in de Sitter (dS) space detects thermal radiation emitted by the horizon, the dS isometries impose that the radiation is in equilibrium with the background. This implies that for the static observer to find the information paradox, the background must be deformed to quasi-dS space in which the dS isometries are spontaneously broken. We study the condition that the information paradox arises in quasi-dS space with the monotonically increasing horizon size which is used to describe the inflationary cosmology. For this purpose, the dimensional reduction of three-dimensional dS space with thermal radiation modelled by the JT gravity coupled to CFT is considered. We argue that when the central charge monotonically increases in time, the information paradox arises but the conditions for the existence of the island become more restrictive. As the central charge can be interpreted as the number of degrees of freedom, the absence of the island in quasi-dS space supports the entropy argument for the dS swampland conjecture.

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arXiv2022

Black hole production, eternal inflation, and information in quasi-de Sitter space

When the slow-roll parameter $ε_H$ is smaller than $H^2/M_{\rm Pl}^2$, the quantum fluctuations of the inflaton after the horizon crossing are large enough to realize eternal inflation. Whereas they do not generate a sufficient amount of density fluctuation of the inflaton to produce the black hole in quasi-de Sitter space, they can also generate the sizeable density fluctuation of the radiation when the number of degrees of freedom increases rapidly in time, as predicted by the distance conjecture. We argue that the condition that the density fluctuation of the radiation is not large enough to produce the black hole until the end of inflation is equivalent to the no eternal inflation condition. When the radiation emitted by the horizon does not produce the black hole, even if the number of degrees of freedom increases in time, the information paradox does not arise for $ε_H$ larger than $10^{-7} (H^2/ M_{\rm Pl}^2)$ and time scale shorter than $10^4 (M_{\rm Pl}/H^2)$. Regardless of the presence of the information paradox, a static observer cannot retrieve a sufficient amount of information, which is consistent with the complementarity.

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arXiv2022

Implication of the swampland distance conjecture on the Cohen-Kaplan-Nelson bound in de Sitter space

The Cohen-Kaplan-Nelson (CKN) bound formulates the condition that black hole is not produced by the low energy effective field theory dynamics. In de Sitter space it also constrains the maximal size of the matter distribution to be smaller than the cosmological horizon determined by black hole. On the other hand, the swampland distance conjecture (SDC) predicts that de Sitter space becomes unstable by the descent of the low energy degrees of freedom from UV. This results in the rapid increase in the energy inside the cosmological horizon, the distribution of which can be constrained by the CKN bound. We study the CKN bound in de Sitter space in detail and point out that when compared with the slow-roll in the inflation, the bound on the slow-roll parameter which forbids the eternal inflation is obtained.

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arXiv2022

Brane/flux annihilation in double-throat system

We study the brane/flux annihilation in the double-throat system in which the corresponding cycles of two throats are homologically equivalent. When we put $\overline{\rm D3}$-branes at only one of throat tips, two throats are no longer identical. Then the brane/flux annihilation can be interpreted as the process for reducing the difference between two throat geometries through the transition to the supersymmetric vacuum. To see this, we describe the changes in the amounts of the NSNS 3-form flux supporting the B-cycle contained in two throat regions during the brane/flux annihilation. We also compare our analysis with the recently proposed thraxion scenario, which also describes the inequivalence of two throats caused by the different NSNS 3-form flux distributions in two throat regions.

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arXiv2022

Festina-Lente Bound on Higgs Vacuum Structure and Inflation

The recently suggested Festina-Lente (FL) bound provides a lower bound on the masses of ${\rm U(1)}$ charged particles in terms of the positive vacuum energy. Since the charged particle masses in the Standard Model (SM) are generated by the Higgs mechanism, the FL bound provides a testbed of consistent Higgs potentials in the current dark energy-dominated universe as well as during inflation. We study the implications of the FL bound on the UV behavior of the Higgs potential for a miniscule vacuum energy, as in the current universe. We also present values of the Hubble parameter and the Higgs vacuum expectation value allowed by the FL bound during inflation, which implies that the Higgs cannot stay at the electroweak scale during this epoch.

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