We study Motzkin paths of length $L$ with general weights on the edges and end points. We investigate the limit behavior of the initial and final segments of the random Motzkin path viewed as a pair of processes starting from each of the two end points as $L$ becomes large. We then study macroscopic limits of the resulting processes, where in two different regimes we obtain Markov processes that appeared in the description of the stationary measure for the KPZ equation on the half line and of conjectural stationary measure of the hypothetical KPZ fixed point on the half line. Our results rely on the behavior of the Al-Salam--Chihara polynomials in the neighbourhood of the upper end of their orthogonality interval and on the limiting properties of the $q$-Pochhammer and $q$-Gamma functions as $q\nearrow 1$.

It is commonly recognized that the primordial scalar spectral index $n_s$ is approximately $0.96-0.975$, depending on the dataset. However, this view is being completely altered by the early dark energy (EDE) resolutions of the Hubble tension, known as the most prominent tension the standard $\Lambda$CDM model is suffering from. In corresponding models with pre-recombination EDE, resolving the Hubble tension (i.e., achieving $H_0\sim 73$km/s/Mpc) must be accompanied by a shift of $n_s$ towards unity to maintain consistency with the cosmological data, which thus implies a scale invariant Harrison-Zel'dovich spectrum with $n_s=1$ $(|n_s-1|\simeq {\cal O}(0.001))$. In this work, we strengthen and reconfirm this result with the latest ground-based CMB data from ACT DR6 and SPT-3G D1, the precise measurements at high multipoles beyond the Planck angular resolution and sensitivity. Our work again highlights the importance of re-examining our understanding on the very early Universe within the broader context of cosmological tensions.

With the help of a given distance matrix of size $n$, we construct an infinite family of distances $d_p$ (where $p \geq 2$) on the the complex projective space $\mathbb{P}(\mathbb{C}^n)$, modelling the space of pure states of an $n$-dimensional quantum system. The construction can be seen as providing a natural way to isometrically embed any given finite metric space into the space of pure quantum states 'spanned' upon it. In order to show that the maps $d_p$ are indeed distance functions -- in particular, that they satisfy the triangle inequality -- we employ methods of analysis, multilinear algebra and convex geometry, obtaining a non-trivial convexity result in the process. The paper significantly extends earlier work, resolving an important question about the geometry of quantum state space imposed by the quantum Wasserstein distances and solidifying the foundation for applications of distances $d_p$ in quantum information science.

We present OSTRICH2, the latest evolution of the SMT solver OSTRICH for string constraints. OSTRICH2 supports a wide range of complex functions on strings and provides completeness guarantees for a substantial fragment of string constraints, including the straight-line fragment and the chain-free fragment. OSTRICH2 provides full support for the SMT-LIB theory of Unicode strings, extending the standard with several unique features not found in other solvers: among others, parsing of ECMAScript regular expressions (including look-around assertions and capture groups) and handling of user-defined string transducers. We empirically demonstrate that OSTRICH2 is competitive to other string solvers on SMT-COMP benchmarks.

We explore the role of color superconductivity in quarkyonic matter under the conditions of color and electric neutrality at $\beta$- and strong equilibrium, as relevant for neutron stars. By explicitly incorporating the color-superconducting pairing gap into the phenomenological model of a smooth transition from hadron to quark matter, we extend the known quarkyonic framework to include this essential aspect relevant at high densities. The momentum dependence of the pairing gap, motivated by the running of the QCD coupling and introduced similarly to chiral quark models with nonlocal interaction, is a novel element of the model that is crucial for enabling the simultaneous onset of all color-flavor quark states in the presence of color superconductivity. While asymptotically conformal behavior of the present model is ensured by construction, we demonstrate that reaching the conformal limit in agreement with the predictions of perturbative QCD is provided by the proper momentum dependence of the thickness of the hadron shell in momentum space. We employ the flexible meta-modeling approach to nuclear matter, analyzing the structure of the hadron shell in momentum space and focusing on the effects of color superconductivity in quarkyonic matter. Similar to the effects induced by the onset of the quarkyonic phase, color superconductivity leads to stiffening of the equation of state of the NS matter. This causes a significant impact on observable properties of neutron stars, which are analyzed and compared to recent astrophysical and theoretical constraints. We argue that the developed model of color-superconducting quarkyonic matter provides a new, consistent tool for studying the scenario of smooth quark-hadron transition in NSs.

We perform a physics-informed Bayesian analyses of the equation of state of hybrid neutron stars that incorporates color-flavor-locked quark matter modeled by a three-flavor non-local Nambu-Jona-Lasinio framework with vector repulsion and diquark pairing. Contrary to the model-agnostic Bayesian analyses our scheme allows for distinguishing between the scenarios of neutron stars with quark cores and without them. The used quark model realizes asymptotic conformality at high densities in accordance with perturbative QCD. The hadronic sector is described by the density-dependent relativistic functional DD2Y-T, which satisfies chiral effective field theory constraints and includes hyperonic degrees of freedom. We construct a large set of candidate hybrid EOSs by varying the vector and diquark couplings and apply a Maxwell construction for the quark-hadron phase transition. Observational constraints from recent NICER pulsar mass-radius measurements and tidal deformability from GW170817 are incorporated into the likelihood. Depending on whether the observational data from the black widow pulsar PSR J0952-0607 and the HESS J1731-347 object are included to the analysis or not, the posterior distribution favors vector and diquark couplings around $(\eta_V,\eta_D)\simeq (0.82,0.40)$ or $(\eta_V,\eta_D)\simeq (0.64,0.36)$, respectively. This corresponds to equations of state that support two-solar-mass neutron stars with superconformal speed of sound and relatively low onset densities for deconfinement. Our findings indicate that the most probable hybrid EOSs are statistically preferred over the purely hadronic baseline. The corresponding probabilities of agreeing with the observational data differ by one or two orders of magnitude depending on the data set used. This suggests that quark cores may exist in all observed neutron stars.

We investigate black hole superradiance evolution of the interacting multiple fields. We consider a model of two scalar fields interacting with a cubic coupling, and study the superradiant evolution of the cloud. We demonstrate that superradiance is typically suppressed when the superradiant field couples to another field, even with a very weak coupling strength. This implies that the constraints on dark particles derived from single-field analyses can be revised in the presence of interactions. Moreover, we find that the multi-field superradiant evolution and its corresponding observational signatures can be different across parameter spaces, which makes black hole superradiance an even more powerful probe of the dark sector in particle physics.

We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation ($U$) of a finite group ($G$), whenever $U \otimes U^c$ is simply reducible (with $U^c$ being the contragradient representation). Using the theory of group representations, we obtain the spectral decomposition of any such linear map. The eigenvalues and orthogonal projections arising in this decomposition are expressed entirely in terms of representation characteristics of the group $G$. This in turn yields necessary and sufficient conditions on the eigenvalues of any such linear map for it to be a quantum channel. We also obtain a wide class of quantum channels which are irreducibly covariant by construction. For two-dimensional irrreducible representations of the symmetric group $S(3)$, and the quaternion group $Q$, we also characterize quantum channels which are both irreducibly covariant and entanglement breaking.

It has been noted that with the pre-recombination early dark energy (EDE) resolution of Hubble tension, the preference of recent datasets for the evolving dark energy (DE) can be suppressed significantly. In this work, we clarify and reconfirm this result with DESI DR2 and the latest ACT DR6 and SPT-3G D1, the tightest small-scale CMB constraints up to date. In the $w_0w_a$CDM model with EDE, a quintessence-like component ($w_0+w_a\geq-1$) can be 1$\sigma$ consistent with Planck+ACT+SPT+DESI+Pantheon+SH0ES datasets, and $\Delta\chi^2\lesssim -14$ compared with $w_0w_a$CDM model without EDE. This reveals the possibility that when the potential resolutions of Hubble tension are considered, current accelerated expansion can attribute to a canonical evolving scalar field or cosmological constant, and again highlights the importance of re-examining the nature of DE within the broader context of cosmological tensions.

We derive a modified dispersion relation for massive particles within the frameworks of five-dimensional Kaluza-Klein theory and general relativity, taking into account strong gravitational effects. The resulting effective mass depends on the curvature of the underlying phase space. Notably, in regions with strong gravitational fields, the effective mass may become imaginary, implying the possibility of particle decay induced by spacetime curvature.

We investigate the thermodynamic properties of fermionic excitations in heavy-quark QCD on the lattice with Wilson fermions. The grand potential is calculated analytically in the hopping parameter expansion (HPE) on the basis of the cumulant expansion. Using the grand potential, we compute the quark number susceptibilities and their ratios up to next-to-leading order in the HPE. The ratio of fourth- to second-order susceptibilities is shown to be unity (nine) in the deconfined (confined) phase at the leading order. Excitation properties of baryonic and quark modes in each phase are also investigated utilizing the Boltzmann statistics. We obtain an analytic formula for the quark excitation energy in the deconfined phase, while that for baryonic excitations in the confined phase is decomposed into flavor multiplets.

The failure to calculate the vacuum energy is a central problem in theoretical physics. Presumably the problem arises from the insistent use of effective field theory reasoning in a context that is well beyond its intended scope. If one follows this path, one is led inevitably to statistical or anthropic reasoning for observations. It appears that a more palatable resolution of the vacuum energy problem requires some form of UV/IR feedback. In this paper we take the point of view that such feedback can be thought of as arising by defining a notion of quantum space-time. We reformulate the regularized computation of vacuum energy in such a way that it can be interpreted in terms of a sum over elementary phase space volumes, that we identify with a ground state degeneracy. This observation yields a precise notion of UV/IR feedback, while leaving a scale unfixed. Here we argue that holography can be thought to provide a key piece of information: we show that equating this microscopic ground state degeneracy with macroscopic gravitational entropy yields a prediction for the vacuum energy that can easily be consistent with observations. Essentially, the smallness of the vacuum energy is tied to the large size of the Universe. We discuss how within this scenario notions of effective field theory can go so wrong.

We develop a covariant differential-form framework to define scalar charges for stationary, asymptotically flat black holes in $4$--dimensional Einstein-scalar-Gauss-Bonnet gravity with a general scalar coupling function. Contracting the scalar field equation of motion with the horizon generator $k$ yields a non-closed-form scalar charge, revealing a bulk contribution encoded in a $3$--form, which measures the obstruction to its closedness. In the presence of shift-symmetry, this obstruction vanishes and the $2$--form scalar charge satisfies a Gauss law, depending solely on boundary data. Geometrically, this reproduces known topological results in the shift-symmetric limit. This framework allows us to analyze the role of the non-closed scalar charges in black hole thermodynamics through the Smarr formula for more general couplings and provide a covariant, charge-based interpretation of the spontaneous scalarization mechanism, showing how the behavior of the scalar charge and the bulk term capture the instability of scalar-free black holes and the emergence of scalar hair. Our results offer a unified geometric understanding of the role of scalar charges and the mechanism of spontaneous scalarization in Einstein-scalar-Gauss-Bonnet gravity.

Enhancing low-light images while maintaining natural colors is a challenging problem due to camera processing variations and limited access to photos with ground-truth lighting conditions. The latter is a crucial factor for supervised methods that achieve good results on paired datasets but do not handle out-of-domain data well. On the other hand, unsupervised methods, while able to generalize, often yield lower-quality enhancements. To fill this gap, we propose Dimma, a semi-supervised approach that aligns with any camera by utilizing a small set of image pairs to replicate scenes captured under extreme lighting conditions taken by that specific camera. We achieve that by introducing a convolutional mixture density network that generates distorted colors of the scene based on the illumination differences. Additionally, our approach enables accurate grading of the dimming factor, which provides a wide range of control and flexibility in adjusting the brightness levels during the low-light image enhancement process. To further improve the quality of our results, we introduce an architecture based on a conditional UNet. The lightness value provided by the user serves as the conditional input to generate images with the desired lightness. Our approach using only few image pairs achieves competitive results compared to fully supervised methods. Moreover, when trained on the full dataset, our model surpasses state-of-the-art methods in some metrics and closely approaches them in others.

We study the dual CFT description of the $d+1$-dimensional Reissner-Nordström-Anti de Sitter (RN-AdS$_{d+1}$) black hole in the large dimension (large $d$) limit, both for the extremal and nonextremal cases. The central charge of the dual CFT$_2$ (or chiral CFT$_1$) is calculated for the near horizon near extremal geometry which possess an AdS$_2$ structure. Besides, the $Q$-picture hidden conformal symmetry in the nonextremal background can be naturally obtained by a probe charged scalar field in the large $d$ limit, without the need to input the usual limits to probe the hidden conformal symmetry. Furthermore, an new dual CFT description of the nonextremal RN-AdS$_{d+1}$ black hole is found in the large $d$ limit and the duality is analyzed by comparing the entropies, the absorption cross sections and the retarded Green's functions obtained both from the gravity and the dual CFT sides.

This thesis contains of two parts: The first part is a pedagogical introduction into the field of bosonic SFT. After discussing some general properties we expect, Witten's open SFT and Zwiebach's closed SFT are presented in detail. This means we set up the action, explain the algebraical and geometrical structure and mention physical applications. In the open case we review the most important analytic solutions including the necessary operator technology whileas in the closed case we focus on quantization and the more elaborate construction of the vertices. The second part contains of reprints of papers completed within the PhD: 2301.13182, 2402.00308, 2410.16228 and 2411.15123.

The holographic entanglement entropy of an infinite strip subsystem on the asymptotic AdS boundary is used as a probe to study the thermodynamic instabilities of planar R-charged black holes (or their dual field theories). We focus on the single-charge AdS black holes in $D=5$, which correspond to spinning D3-branes with one non-vanishing angular momentum. Our results show that the holographic entanglement entropy indeed exhibits the thermodynamic instability associated with the divergence of the specific heat. When the width of the strip is large enough, the finite part of the holographic entanglement entropy as a function of the temperature resembles the thermal entropy, as is expected. As the width becomes smaller, however, the two entropies behave differently. In particular, there exists a critical value for the width of the strip, below which the finite part of the holographic entanglement entropy as a function of the temperature develops a self-intersection. We also find similar behavior in the single-charge black holes in $D=4$ and $7$.

The precise measurement of cosmic-ray antinuclei serves as an important means for identifying the nature of dark matter and other new astrophysical phenomena, and could be used with other cosmic-ray species to understand cosmic-ray production and propagation in the Galaxy. For instance, low-energy antideuterons would provide a "smoking gun" signature of dark matter annihilation or decay, essentially free of astrophysical background. Studies in recent years have emphasized that models for cosmic-ray antideuterons must be considered together with the abundant cosmic antiprotons and any potential observation of antihelium. Therefore, a second dedicated Antideuteron Workshop was organized at UCLA in March 2019, bringing together a community of theorists and experimentalists to review the status of current observations of cosmic-ray antinuclei, the theoretical work towards understanding these signatures, and the potential of upcoming measurements to illuminate ongoing controversies. This review aims to synthesize this recent work and present implications for the upcoming decade of antinuclei observations and searches. This includes discussion of a possible dark matter signature in the AMS-02 antiproton spectrum, the most recent limits from BESS Polar-II on the cosmic antideuteron flux, and reports of candidate antihelium events by AMS-02; recent collider and cosmic-ray measurements relevant for antinuclei production models; the state of cosmic-ray transport models in light of AMS-02 and Voyager data; and the prospects for upcoming experiments, such as GAPS. This provides a roadmap for progress on cosmic antinuclei signatures of dark matter in the coming years.

Core-collapse supernovae undergoing a first-order quantum chromodynamics (QCD) phase transition experience the collapse of the central proto-neutron star that leads to a second bounce. This event is accompanied by the release of a second neutrino burst. Unlike the first stellar core bounce neutrino burst which consists exclusively of electron neutrinos, the second burst is dominated by electron antineutrinos. Such a condition makes QCD supernovae an ideal site for the occurrence of fast neutrino flavor conversion (FFC), which can lead to rapid flavor equilibration and significantly impact the related neutrino signal. In this work, we perform a detailed analysis of the conditions for fast flavor instability (FFI) around and after the second neutrino burst in QCD phase transition supernova models launched from 25~$M_\odot$ and 40~$M_\odot$ progenitor models. We evaluate the relevant instability criteria and find two major phases of FFC. The first phase is closely associated with the collapse and the rapidly expanding shock wave, which is a direct consequence of the proto-neutron star collapse due to the phase transition. The second phase takes place a few milliseconds later when electron degeneracy is restored near the proto-neutron star surface. We also characterize the growth rate of FFI and estimate its impact on the evolution of the neutrino flavor content. The potential observational consequences on neutrino signals are evaluated by comparing a scenario assuming complete flavor equipartition with other scenarios without FFC. Finally, we investigate how FFC may influences $r$-process nucleosynthesis associated with QCD phase transition driven supernova explosions.