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Eun Kyung Park

Publications and source records attributed to Eun Kyung Park.

9 recordsLinked to original sources
arXiv2023

Accelerating internal dimensions and nonzero positive cosmological constant

We present a new scenario for the moduli stabilization with a very small but nonzero positive cosmological constant $λ$. In this scenario the complex structure moduli are still stabilized by the three-form fluxes as in the usual flux compactifications, but the K$\ddot{\rm a}$hler modulus is not fixed by the KKLT scenario. In our case the scale factor (or the K$\ddot{\rm a}$hler modulus) of the internal dimensions is basically allowed to change with time. But at the supergravity level it is fixed by a set of dynamical (plus constraint) equations defined on the 4D spacetime, not by the nonperturbative corrections of KKLT. Also at the supergravity level it is shown that $λ$ is fine-tuned to zero, $λ=0$, by the same set of 4D equations. This result changes once we admit $α^{\prime}$-corrections of the string theory. The fine-tuning $λ=0$ changes into $λ= \frac{2}{3} Q$, where $Q$ is a constant representing quantum corrections of the brane and 6D action defined on the internal dimensions and its value is determined by the $α^{\prime}$-corrections. It is also shown that this nonzero $λ$ must be positive and at the same time the internal dimensions must evolve with time almost at the same rate as the external dimensions in the case of nonzero $λ$.

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arXiv2019

A torsion-free background solution of the string theory

We find a background solution of the string theory which has a special property distinguished from the usual background solutions. This background solution does not produce the NS-NS two-form fields under T-duality and therefore the background vacua described by this solution essentially do not involve NS-NS type branes in their configurations, unlikely to the case of the ordinary Calabi-Yau ansatz. As a result the non-linear $σ$-models, whose target space metrics are given by these T-dual partners, can both be torsion-free.

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arXiv2015

Towards the core of the cosmological constant problem

We apply a new self-tuning mechanism to the well-known Kachru-Kallosh-Linde-Trivedi (KKLT) model to address the cosmological constant problem. In this mechanism the cosmological constant $λ$ contains a supersymmetry breaking term ${\mathcal E}_{\rm SB}$ besides the usual scalar potential ${\mathcal V}_{\rm scalar}$ of the $N=1$ supergravity, which is distinguished from the usual theories where $λ$ is directly identified with ${\mathcal V}_{\rm scalar}$ alone. Also in this mechanism, whether $λ$ vanishes or not is basically determined by the tensor structure of the scalar potential density, not by the zero or nonzero values of the scalar potential itself. As a result of this application we find that the natural scenario for the vanishing $λ$ of the present universe is to take one of the AdS (rather than dS) vacua of KKLT as the background vacuum of our present universe. This AdS vacuum scenario has more nice properties as compared with dS vacua of the usual flux compctifications. The background vacuum is stable both classically and quantum mechanically (no tunneling instabilities), and the value $λ=0$ is also stable against quantum corrections because in this scenario the perturbative corrections of ${\mathcal V}_{\rm scalar}$ and quantum fluctuations $δ_Q {\hat I}_{\rm brane}^{(NS)} + δ_Q {\hat I}_{\rm brane}^{(R)}$ on the branes are all gauged away by an automatic cancelation between ${\mathcal V}_{\rm scalar} + δ_Q {\hat I}_{\rm brane}^{(NS)} + δ_Q {\hat I}_{\rm brane}^{(R)}$ and ${\mathcal E}_{\rm SB}$.

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arXiv2013

Remark on Calabi-Yau vacua of the string theory and the cosmological constant problem

We propose, based on the viewpoint that our three-dimensional space is a stack of BPS D3-branes located at the conifold singularity of the Calabi-Yau three-fold, a new mechanism to address the cosmological constant problem in the framework of the conventional compactifications where the $n$-form fluxes including NS-NS three-form are all turned off. In this mechanism the four-dimensional cosmological constant $λ$ appears as two types, NS-NS type and R-R type, of vacuum energies on the brane plus supersymmetry breaking term, which constitute a brane action density ${\hat I}_{\rm brane}$, and sum of these three terms of ${\hat I}_{\rm brane}$ are forced to vanish by field equations so that $λ$ adjusts itself to zero as a result. Also in this mechanism the $d=4$ supersymmetry is broken in the brane region, while still maintaining $λ=0$. The supersymmetry breaking occurs as a result of the gauge symmetry breaking of the R-R four-form arising at the quantum level. We generalize the above mechanism to the case of the flux compactifications where the fluxes are all turned on to stabilize the moduli. In the generalized theory $λ$ appears as ${\hat I}_{\rm brane}$ plus the scalar potential ${\mathcal V}_{\rm scalar}$ for the moduli, in contrast to the case of the ordinary flux compactifications where $λ$ is simply given by ${\mathcal V}_{\rm scalar}$. Also in this theory any nonzero ${\mathcal V}_{\rm scalar}$ arising from perturbative or nonperturbative corrections is gauged away by the gauge arbitrariness of ${\hat I}_{\rm brane}$ and the condition $λ=0$. So $λ$ is again expressed only as a brane action density as before, or it simply vanishes by the cancelation between ${\hat I}_{\rm brane}$ and ${\mathcal V}_{\rm scalar}$.

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arXiv2010

NS-branes in 5d brane world models

We study codimension-1 brane solutions of the 5d brane world models compactified on $S_1 / \mathbb{Z}_2$. In string theoretical setup they suggest that the background branes located at orbifold fixed points should be NS-branes (in the five dimensional sense), rather than D-branes. Indeed, the existence of the background NS-branes is indispensable to obtain flat geometry $M_4 \times S_1 / \mathbb{Z}_2$ where $M_4$ represents the 4d Minkowski spacetime, and without these branes the 5d metric becomes singular everywhere. This result is very reminiscent of the $(p+3)$d effective string theory \cite{1} where the NS-NS type $p$-brane is indispensable to obtain a flat geometry $R_2$ or $R_2 /\mathbb{Z}_n$ on the transverse dimensions. Without this NS-NS type $p$-brane the 2d transverse space becomes a pin-shaped singular space. The correspondence between these two theories leads us to a conjecture that the whole flat backgrounds of the string theory inherently invovle the NS-branes implicitly in their ansatz, and hence the true background $p$-branes immanent in our spacetime may be NS-branes, instead of D-branes. We argue that this result can have a significant consequence in the context of the cosmological constant problem.

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arXiv2009

A comment on $p$-branes of ($p+3$)$\rm{d}$ string theory

We argue that in ($p+3$)d string theory the existence of NS-NS type $p$-brane with negative tension is essential to obtain background geometry $R_2$ or $R_2 / Z_n$ on the transverse dimensions, and the usual codimension-2 brane solutions with these background geometries already contain the negative tension NS-brane implicity in their ansatz. Such an argument leads us, in the context of brane world scenarios, to a conjecture that true background $p$-brane immanent in our spacetime may perhaps be NS-NS type brane, rather than D-brane.

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arXiv2007

A self-tuning mechanism in (3+p)d gravity-scalar theory

We present a new type of self-tuning mechanism for ($3+p$)d brane world models in the framework of gravity-scalar theory. This new type of self-tuning mechanism exhibits a remarkable feature. In the limit $g_s \to 0$, $g_s$ being the string coupling, the geometry of bulk spacetime remains virtually unchanged by an introduction of the Standard Model(SM)-brane, and consequently it is virtually unaffected by quantum fluctuations of SM fields with support on the SM-brane. Such a feature can be obtained by introducing Neveu-Schwarz(NS)-brane as a background brane on which our SM-brane is to be set. Indeed, field equations naturally suggest the existence of the background NS-brane. Among the given such models, of the most interest is the case with $Λ=0$, where $Λ$ represents the bulk cosmological constant. This model contains a pair of coincident branes (of the SM- and the NS-branes), one of which is a codimension-2 brane placed at the origin of 2d transverse space ($\equiv Σ_2$), another a codimension-1 brane placed at the edge of $Σ_2$. These two branes are (anti) T-duals of each other, and one of them may be identified as our SM-brane plus the background NS-brane. In the presence of the background NS-brane (and in the absence of $Λ$), the 2d transverse space $Σ_2$ becomes an orbifold $R_2 /Z_n$ with an appropriate deficit angle. But this is only possible if the ($3+p$)d Planck scale $M_{3+p}$ and the string scale $M_s$($\equiv 1/\sqrt{α^{\prime}}$) are of the same order, which accords with the hierarchy assumption \cite{1,2,3} that the electroweak scale $m_{EW}$ is the only short distance scale existing in nature.

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arXiv2003

Homotopy Structure of 5d Vacua

It is shown that flat zero-energy solutions (vacua) of the 5d Kaluza-Klein theory admit a non-trivial homotopy structure generated by certain Kaluza-Klein excitations. These vacua consist of an infinite set of homotopically different spacetimes denoted by $\mathcal{M}^{(n)}_5$, among which $\mathcal{M}^{(0)}_5$ and $\mathcal{M}^{(1)}_5$ are especially identified as $M_{4} \times S^{1}$ and $M_5$, the ground states of the 5d Kaluza-Klein theory and the 5d general relativity, respectively (where $M_k$ represents the $k$-dimensional Minkowski space).

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