arXiv subjects

David H. Wu

Publications and source records attributed to David H. Wu.

11 recordsLinked to original sources

arXiv2026

On BPS Branes

We study supersymmetric BPS branes (BPS-B) in supergravity theories. Some of these states are anticipated by BPS black-brane (BPS-BB) solutions of supergravity. In particular, we define and distinguish the cone generated by BPS branes from the subcone of charges that admit BPS black-brane attractor solutions in the infrared limit of the supergravity effective field theory. We denote these cones by $C_{\rm BPS-B}$ and $C_{\rm BPS-BB}$, respectively. We conjecture that, in any supersymmetric theory of quantum gravity, every integrally charged state lying in $C_{\rm BPS-BB}$ is realized by a BPS state in the spectrum. Furthermore, we conjecture and present evidence that when $C_{\rm BPS-B}$ is moduli independent, it can be determined as the cone dual to the $C_{\rm BPS-BB}$ under the electric-magnetic pairing.

hep-th↗

arXiv2026

Evolving Dark Sector and the Dark Dimension Scenario

String theory naturally leads to the expectation that dark energy is not stable, and may be evolving as captured by the Swampland de Sitter conjectures. Moreover, motivated by the distance conjecture, a unification of dark sector has been proposed, where the smallness of dark energy leads to one extra dimension of micron size with dark matter being the Kaluza--Klein graviton excitations in this extra dimension. We consider the natural possibility that the radius of the dark dimension varies as the energy decreases, leading to the variation of the dark matter mass. This correlates the variation of the dark energy with the variation of the dark matter mass as they depend on the variations of a scalar field $ϕ$ controlling the radius of the extra dimension. A simple realization of this idea for small range of $ϕ$ is adequately captured by choosing a potential which is locally of the form $V=V_0\ {\rm exp}(-cϕ)$ and dark matter mass $m_{\rm DM}=m_0\ {\rm exp}(-c' ϕ)$ as was proposed in Agrawal et al. (2019). We find excellent agreement with recent experimental data from DESI DR2 combined with SN measurements (from DES, Union3 or Pantheon+) and reproduces the same significance as CPL parametrization with the added benefit of providing a natural explanation for the apparent phantom behavior ($w<-1$) reported by DESI and DES based on a physical model. DESI and SN datasets independently favor non-zero values of $c'$ and $c$, respectively, both lying within the expected $\mathcal{O}(1)$ range suggested by the Swampland criteria. Moreover, our best fit value $c'\simeq 0.05 \pm 0.01$ is remarkably consistent with the experimental upper bound of $c'\lesssim 0.2$ demanded by the lack of detection of fifth force in the dark sector.

astro-ph.CO↗

arXiv2026

Holes in Calabi-Yau Effective Cones

Motivated by their role in non-perturbative potentials in string theory, we study divisors in effective cones of Calabi-Yau threefolds. We give examples of geometries for which some divisor classes in the effective cone are not themselves effective: i.e., they have no global sections. We call these non-holomorphic divisor classes "holes," and characterize their behavior in an ensemble of toric hypersurface Calabi-Yau threefolds. We prove some necessary and sufficient conditions for the existence of holes, show consequences of holes that follow from the minimal model program, and demonstrate that a class of holes come in semigroups (with this class conjectured to constitute all holes). Furthermore, we provide moduli-dependent bounds on the volumes of four-cycles representing holes.

hep-th↗

arXiv2026

E-Strings and Four-Manifolds

We investigate the physics of the E-string theory and its compactifications as well as their applications to four-dimensional topology. In particular, we compute the partition function of the topologically twisted theory on $M_4\times T^2$, where $M_4$ is a four-manifold. In a range of examples, we verify that this partition function, as a $q$-series, 1) has integral coefficients, 2) is modular, and 3) can be lifted to a topological modular form. Remarkably, the E-string theory "knows" about various subtle aspects of the world of smooth 4-manifolds, as the (topological) modularity of the partition function is contingent on a collection of properties of 4-manifolds and their Seiberg-Witten invariants, including, notably, the simple-type conjecture. Furthermore, both theoretical and empirical evidences indicate that this partition function defines a genuine smooth invariant, even when $b_2^+\le 1$. Therefore, the E-string theory may offer powerful new tools for exploring regions in the geography of 4-manifolds that have been inaccessible to existing invariants obtained from gauge theory and quantum field theory.

hep-th↗

arXiv2024

The Tale of Three Scales: the Planck, the Species, and the Black Hole Scales

Quantum gravity (QG) has a natural cutoff given by the Planck scale $M_{\rm pl}$. However, it is known that the EFT of gravity can break down at a lower scale, the species scale $Λ_s\lesssim M_{\rm pl}$, if there are light species of particles. Here we point out that there is a third scale $Λ_{\rm BH}\lesssim Λ_s\lesssim M_{\rm pl}$, which marks the inverse length (or the temperature) of the smallest black hole where the EFT gives a correct description of its entropy and free energy. This latter scale is hard to detect from the viewpoint of EFT as it represents a phase transition to a state with lower free energy. We illustrate this using examples drawn from consistent QG landscape. In particular $Λ_{\rm BH}$ gets related to Gregory--Laflamme transition in the decompactification limits of quantum gravity and to the Horowitz--Polchinski solution in the light perturbative string limits. We propose the existence of $Λ_{\rm BH}$ marking the temperature at which neutral black holes undergo a phase transition, as a new Swampland condition for all consistent quantum theories of gravity. In the asymptotic regimes of field space $Λ_{\rm BH}$ is close to the mass scale of the lightest tower but deviates from it as we move inwards in the moduli space.

hep-th↗

arXiv2024

Species Scale in Diverse Dimensions

In a quantum theory of gravity, the species scale $Λ_s$ can be defined as the scale at which corrections to the Einstein action become important or alternatively as codifying the "number of light degrees of freedom", due to the fact that $Λ_s^{-1}$ is the smallest size black hole described by the EFT involving only the Einstein term. In this paper, we check the validity of this picture in diverse dimensions and with different amounts of supersymmetry and verify the expected behavior of the species scale at the boundary of the moduli space. This also leads to the evaluation of the species scale in the interior of the moduli space as well as to the computation of the diameter of the moduli space. We also find evidence that the species scale satisfies the bound $\big|{\nabla Λ_s \over Λ_s} \big|^2\leq {1\over d-2}$ all over moduli space including the interior.

hep-th↗

arXiv2023

Bounds on Field Range for Slowly Varying Positive Potentials

In the context of quantum gravitational systems, we place bounds on regions in field space with slowly varying positive potentials. Using the fact that $V<Λ_s^2$, where $Λ_s(ϕ)$ is the species scale, and the emergent string conjecture, we show this places a bound on the maximum diameter of such regions in field space: $Δϕ\leq a \log(1/V) +b$ in Planck units, where $a\leq \sqrt{(d-1)(d-2)}$, and $b$ is an $\mathcal{O}(1)$ number and expected to be negative. The coefficient of the logarithmic term has previously been derived using TCC, providing further confirmation. For type II string flux compactifications on Calabi--Yau threefolds, using the recent results on the moduli dependence of the species scale, we can check the above relation and determine the constant $b$, which we verify is $\mathcal{O}(1)$ and negative in all the examples we studied.

hep-th↗

arXiv2022

Moduli-dependent Species Scale

The counting of the number of light modes in a gravitational theory is captured by the notion of the `species scale', which serves as an effective UV cutoff below the Planck scale. We propose to define a moduli-dependent species scale in the context of 4d, ${\cal N}=2$ theories, using the one loop topological free energy $F_1$, which we relate to a gravitational version of the $a$-function. This leads to $Λ_{\rm sp}\sim 1/\sqrt{F_1}$ from which we recover the expected scaling of the species scale in various corners of the moduli space. Moreover by minimizing $F_1$ we define the center of the moduli space (the `desert point') as a point where the species scale is maximal. At this point the number of light degrees of freedom is minimized.

hep-th↗

arXiv2021

Approximating the two-mode two-photon Rabi model

The Rabi model describes the simplest nontrivial interaction between a few-level system and a bosonic mode, featuring in multiple seemingly unrelated systems of importance to quantum science and technology. While exact expressions for the energies of this model and its few-mode extensions have been obtained, they involve roots of transcendental functions and are thus cumbersome and unintuitive. Utilizing the symmetric generalized rotating wave approximation (S-GRWA), we develop a family of approximations to the energies of the two-mode two-photon Rabi model. The simplest elements of the family are analytically tractable, providing good approximations in regimes of interest such as ultra- and deep-strong coupling. Higher-order approximate energies can be used if more accuracy is required.

quant-ph↗

arXiv2021

Statistical description of coalescing magnetic islands via magnetic reconnection

The physical picture of interacting magnetic islands provides a useful paradigm for certain plasma dynamics in a variety of physical environments, such as the solar corona, the heliosheath, and the Earth's magnetosphere. In this work, we derive an island kinetic equation to describe the evolution of the island distribution function (in area and in flux of islands) subject to a collisional integral designed to account for the role of magnetic reconnection during island mergers. This equation is used to study the inverse transfer of magnetic energy through the coalescence of magnetic islands in 2D. We solve our island kinetic equation numerically for three different types of initial distribution: delta-distribution, Gaussian and power-law distribution. The time evolution of several key quantities is found to agree well with our analytical predictions: magnetic energy decays as $\tilde t^{-1}$, the number of islands decreases as $\tilde t^{-1}$, and the averaged area of islands grows as $\tilde t$, where $\tilde t$ is the time normalized to the characteristic reconnection time scale of islands. General properties of the distribution function and the magnetic energy spectrum are also studied.

physics.plasm-ph↗

arXiv2020

Resurgent Analysis of SU(2) Chern-Simons Partition Function on Brieskorn Spheres $Σ(2,3,6n+5)$

$\hat{Z}$-invariants, which can reconstruct the analytic continuation of the SU(2) Chern-Simons partition functions via Borel resummation, were discovered by GPV and have been conjectured to be a new homological invariant of 3-manifolds which can shed light onto the superconformal and topologically twisted index of 3d $\mathcal{N}=2$ theories proposed by GPPV. In particular, the resurgent analysis of $\hat{Z}$ has been fruitful in discovering analytic properties of the WRT invariants. The resurgent analysis of these $\hat{Z}$-invariants has been performed for the cases of $Σ(2,3,5),\ Σ(2,3,7)$ by GMP, $Σ(2,5,7)$ by Chun, and, more recently, some additional Seifert manifolds by Chung and Kucharski, independently. In this paper, we extend and generalize the resurgent analysis of $\hat{Z}$ on a family of Brieskorn homology spheres $Σ(2,3,6n+5)$ where $n\in\mathbb{Z}_+$ and $6n+5$ is a prime. By deriving $\hat{Z}$ for $Σ(2,3,6n+5)$ according to GPPV and Hikami, we provide a formula where one can quickly compute the non-perturbative contributions to the full analytic continuation of SU(2) Chern-Simons partition function.

hep-th↗