arXiv subjects

Zhijin Li

Publications and source records attributed to Zhijin Li.

At least 19 recordsLinked to original sources

arXiv2026

The Environmental Effects on Inspiraling Binary Black Hole Systems in the Centers of the LMC and M31

Binary black hole (BBH) systems residing in the centers of galaxies evolve within complex astrophysical environments. These environments, comprising dark matter (DM) halos and baryonic accretion disks, can significantly alter the orbital dynamics of the binaries and their resulting gravitational wave (GW) emission. In this study, we investigate the dynamical evolution and GW waveforms of BBH systems embedded in the centers of the Large Magellanic Cloud (LMC) and the Andromeda Galaxy (M31). We construct a comprehensive analytical framework that jointly incorporates GW radiation reaction, DM spike effects (including dynamical friction and accretion, derived from the Navarro-Frenk-White profile), and accretion disk perturbations. Using this framework, we track the long-term evolution of the binary's semi-latus rectum $p$ and orbital eccentricity $e$. Our simulations reveal that the coexistence of a DM spike and an accretion disk significantly accelerates the inspiral process compared to pure DM or vacuum scenarios. Crucially, to assess the observability of these environmental effects, we calculate the Signal-to-Noise Ratio (SNR) and waveform Mismatch for future Pulsar Timing Arrays (PTAs). Our analysis demonstrates that these systems can achieve robust detectability thresholds ($\text{SNR} \ge 8$) within specific parameter spaces. Furthermore, the substantial Mismatch (reaching $\sim 0.7$ over a 20-year observation in the LMC scenario) indicates that the phase deviations induced by these environmental effects are highly distinguishable from vacuum templates. These findings predict the prospect of using future GW detections to probe complex galactic environments.

astro-ph.HE↗

arXiv2026

Central charges $C_J$ and $C_T$ in QED$_d$-GNY model and scalar QED$_d$

We compute the leading-order $1/N$ corrections to the central charges $C_J$ and $C_T$ in the conformal QED$_d$-Gross-Neveu-Yukawa (GNY) model and the scalar QED$_d$ in $d$ dimensions. The scaling dimensions of the lowest adjoint bilinear scalars are obtained to order $O(1/N)$ for general $d$. In $d=3$, the $U(1)$ Abelian gauge theory possesses a topological $U(1)$ global symmetry, and we evaluate the central charge $C_J^{\text{top}}$ of the topological symmetry current to subleading order in the $1/N$ expansion. Our interest in these theories is primarily motivated by their potential connection to the $SO(5)$ symmetric deconfined quantum critical point (DQCP). We compare the large $N$ results for the central charges $C_J$ and $C_T$ with the conformal data of the $SO(5)$ DQCP obtained from fuzzy sphere and conformal bootstrap. The large $N$ predictions of the QED$_3$-GNY model are found to be in reasonable agreement with the nonperturbative estimates for the $SO(5)$ DQCP.

hep-th↗

arXiv2026

Bootstrap Cone of the Multicritical Deconfined Quantum Critical Point

The deconfined quantum critical point (DQCP) provides a prominent example of the unconventional phase transitions beyond the Landau-Ginzburg-Wilson paradigm and its nature has been controversial for decades. The DQCP has been extensively studied and the results lead to two opposite scenarios with pseudo-criticality or multicriticality. The pseudo-criticality is a prevailing scenario of DQCP which interprets the approximately scale invariant numerical results with the walking behavior near complex fixed points. In contrast, the multicriticality scenario conjectures the DQCP is a unitary fixed point with a relevant $SO(5)$ singlet scalar. In this work we provide substantial evidence for the multicriticality scenario using conformal bootstrap. We start with the observation that the large scale Quantum Monte Carlo (QMC) results nearly saturate the bootstrap bounds. After imposing suitable sparseness condition the bootstrap bound forms a sharp cone in the three-dimensional parameter space. The bootstrap cone is close to the QMC data. We use the navigator algorithm to locate the apex of the cone and extract the extremal solutions. We find striking consistencies between the bootstrap solutions and the fuzzy sphere data of DQCP, including the coefficients in the operator product expansions (OPEs) and the higher spectrum! The bootstrap cone unifies the QMC and the fuzzy sphere data into a unitary conformal field theory with a relevant $SO(5)$ singlet scalar, thus strongly supporting the multicriticality scenario of DQCP. The agreement between the conformal bootstrap, QMC and fuzzy sphere results is a surprise towards solving DQCP and decoding the profound phase diagram of the two-dimensional quantum magnets.

hep-th↗

arXiv2025

Conformal 3-point correlators in momentum space, method of subgraphs and the $1/N$ expansion

Conformal 3-point correlators of conserved currents play important roles in numerous directions. These correlators are fixed by conformal symmetry up to a few parameters, which are known only at leading order in perturbative expansions. The major challenges come from the multi-loop Feynman integrals with three external momenta. In this work, we employ the method of subgraphs to compute the subleading order corrections to the conformal current 3-point correlators in the large $N$ expansion. We show that the method of subgraphs generates diagrammatic expansions for the conformal 3-point correlators, and that it is closely related to the operator product expansions in momentum space. We verify the subgraph expansions of conserved current 3-point correlators using exact results in 3D. We demonstrate that multi-loop 3-point Feynman integrals can be significantly simplified by taking the subgraph expansions. Due to constraints from conformal symmetry, it suffices to keep only the first few terms in the subgraph expansions to completely fix the subleading order corrections. We apply this method to compute the $1/N$ corrections to current correlators $\langle JJJ\rangle$ in the critical $O(N)$ vector model and the Gross-Neveu-Yukawa model. We also compute the $1/N$ corrections to the coefficients in the current-current-scalar correlators $\langle JJσ_{T}\rangle$ and $\langle JJσ\rangle$ in the critical $O(N)$ vector model. We compare the perturbative results with the bootstrap data and discuss their application to conductivity near the quantum critical point.

hep-th↗

arXiv2025

Detectability of dark matter density distribution via gravitational waves from binary black holes in the Galactic center

The fundamental nature of dark matter (DM) remains unknown, with significant uncertainties in its density profile. DM environments surrounding massive binary black holes (BBHs) modify their orbital dynamics, thereby altering gravitational wave (GW) emissions. For BBH systems at the Galactic Center, dynamical friction induced by DM spikes could produce detectable deviations in GW spectra, potentially observable by future space-based detectors. To address the uncertainties in the Galactic Center's DM profile, we systematically examine two scenarios: the generalized Navarro-Frenk-White (gNFW) profile and its post-spike modification. We investigate the evolutionary effects of DM dynamical friction and accretion on the eccentricity and semi-latus rectum of secondary black holes (BHs) in elliptical orbits. By constructing orbital models with varying initial eccentricities across the mass-semi-latus rectum parameter space and utilizing 30 years of simulated pulsar timing array data from the Square Kilometer Array (SKA), we identify detectable parameter regimes of DM effects and employ these GW observational signatures to constrain different DM density profiles. Our analysis reveals that among gNFW profiles ($γ=2,1.5,1,0.5$), only $γ=2$ produces significant detectable signatures. The formation of DM spikes further enhances these observable waveform deviations for all gNFW slopes.

astro-ph.HE↗

arXiv2024

Conformality loss and short-range crossover in long-range conformal field theories

We study the conformality loss of theories with long-range interactions. We consider the $O(2)\times O(N)$ multiscalar model with coupling $r^{-d-δ}$ in $d=4-ε$ dimension. We compute the critical exponents of the long-range fixed points (LRFPs) to three loops. The phase diagram of the model is dominated by two processes: the short-range crossover and merger-annihilation of LRFPs. The two processes intersect at the lower edge of the conformal window, below which the LRFPs disappear into the complex plane. We propose a novel scenario for the short-range crossover of complex LRFPs, in which the short-range crossover occurs on a vertical line in the complex plane of $δ$. The complex marginal operator generates renormalization group flow on the transition line and significantly enriches the short-range crossover of complex LRFPs.

hep-th↗

arXiv2024

Generative Diffusion Model-based Downscaling of Observed Sea Surface Height over Kuroshio Extension since 2000

Satellite altimetry has been widely utilized to monitor global sea surface dynamics, enabling investigation of upper ocean variability from basin-scale to localized eddy ranges. However, the sparse spatial resolution of observational altimetry limits our understanding of oceanic submesoscale variability, prevalent at horizontal scales below 0.25o resolution. Here, we introduce a state-of-the-art generative diffusion model to train high-resolution sea surface height (SSH) reanalysis data and demonstrate its advantage in observational SSH downscaling over the eddy-rich Kuroshio Extension region. The diffusion-based model effectively downscales raw satellite-interpolated data from 0.25o resolution to 1/16o, corresponding to approximately 12-km wavelength. This model outperforms other high-resolution reanalysis datasets and neural network-based methods. Also, it successfully reproduces the spatial patterns and power spectra of satellite along-track observations. Our diffusion-based results indicate that eddy kinetic energy at horizontal scales less than 250 km has intensified significantly since 2004 in the Kuroshio Extension region. These findings underscore the great potential of deep learning in reconstructing satellite altimetry and enhancing our understanding of ocean dynamics at eddy scales.

physics.ao-ph↗

arXiv2024

Bootstrapping the Abelian Lattice Gauge Theories

We study the $\mathbb{Z}_2$ and $U(1)$ Abelian lattice gauge theories using a bootstrap method, in which the loop equations and positivity conditions are employed for Wilson loops with lengths $L\leqslant L_{\textrm{max}}$ to derive two-sided bounds on the Wilson loop averages. We address a fundamental question that whether the constraints from loop equations and positivity are strong enough to solve lattice gauge theories. We answer this question by bootstrapping the 2D $U(1)$ lattice gauge theory. We show that with sufficiently large $L_{\textrm{max}}=60$, the two-sided bounds provide estimates for the plaquette averages with precision near $10^{-8}$ or even higher, suggesting the bootstrap constraints are sufficient to numerically pin down this theory. We compute the bootstrap bounds on the plaquette averages in the 3D $\mathbb{Z}_2$ and $U(1)$ lattice gauge theories with $L_{\textrm{max}}=16$. In the regions with weak or strong coupling, the two-sided bootstrap bounds converge quickly and coincide with the perturbative results to high precision. The bootstrap bounds are well consistent with the Monte Carlo results in the nonperturbative region. We observe interesting connections between the bounds generated by the bootstrap computations and the Griffiths' inequalities. We present results towards bootstrapping the string tension and glueball mass in Abelian lattice gauge theories.

hep-th↗

arXiv2023

Large $N$ analytical functional bootstrap I: 1D CFTs and total positivity

We initiate the analytical functional bootstrap study of conformal field theories with large $N$ limits. In this first paper we particularly focus on the 1D $O(N)$ vector bootstrap. We obtain a remarkably simple bootstrap equation from the $O(N)$ vector crossing equations in the large $N$ limit. The bootstrap bound is saturated by the generalized free field theory. We study the analytical extremal functionals of this crossing equation, for which the total positivity of the $SL(2,\mathbb{R})$ conformal block plays a critical role. We prove the $SL(2,\mathbb{R})$ conformal block is totally positive for large scaling dimension $Δ$ and show that the total positivity is violated below a critical value $Δ_{\textrm{TP}}^*\approx 0.32315626$. The conformal block forms a surprisingly sophisticated mathematical structure, which for instance can violate total positivity at the order $10^{-5654}$ for a normal value $Δ=0.1627$! We construct a series of analytical functionals $\{α_M\}$ which satisfy the bootstrap positive conditions up to a range $Δ\leqslant Λ_M$. The functionals $\{α_M\}$ have a trivial large $M$ limit. Surprisingly, due to total positivity, they can approach the large $M$ limit in a way consistent with the bootstrap positive conditions for arbitrarily high $Λ_M$, therefore proving the bootstrap bound analytically. Our result provides a concrete example to illustrate how the analytical properties of the conformal block lead to nontrivial bootstrap bounds. We expect this work paves the way for large $N$ analytical functional bootstrap in higher dimensions.

hep-th↗

arXiv2022

Lesion detection in contrast enhanced spectral mammography

Background \& purpose: The recent emergence of neural networks models for the analysis of breast images has been a breakthrough in computer aided diagnostic. This approach was not yet developed in Contrast Enhanced Spectral Mammography (CESM) where access to large databases is complex. This work proposes a deep-learning-based Computer Aided Diagnostic development for CESM recombined images able to detect lesions and classify cases. Material \& methods: A large CESM diagnostic dataset with biopsy-proven lesions was collected from various hospitals and different acquisition systems. The annotated data were split on a patient level for the training (55%), validation (15%) and test (30%) of a deep neural network with a state-of-the-art detection architecture. Free Receiver Operating Characteristic (FROC) was used to evaluate the model for the detection of 1) all lesions, 2) biopsied lesions and 3) malignant lesions. ROC curve was used to evaluate breast cancer classification. The metrics were finally compared to clinical results. Results: For the evaluation of the malignant lesion detection, at high sensitivity (Se>0.95), the false positive rate was at 0.61 per image. For the classification of malignant cases, the model reached an Area Under the Curve (AUC) in the range of clinical CESM diagnostic results. Conclusion: This CAD is the first development of a lesion detection and classification model for CESM images. Trained on a large dataset, it has the potential to be used for helping the management of biopsy decision and for helping the radiologist detecting complex lesions that could modify the clinical treatment.

eess.IV↗

arXiv2022

Conformality and self-duality of $N_f=2$ QED$_3$

We study the IR phase of three dimensional quantum electrodynamics (QED$_3$) coupled to $N_f=2$ flavors of two-component Dirac fermions, which has been controversial for decades. This theory has been proposed to be self-dual with symmetry enhancement $(SU(2)_f\times U(1)_t )/\mathbb{Z}_2\rightarrow O(4)$ at the IR fixed point. We focus on the four-point correlator of monopole operators with unit topological charge of $U(1)_t$. We illustrate the $O(4)\rightarrow SU(2)_f\times U(1)_t $ branching rules based on an $O(4)$ symmetric positive structure in the monopole four-point crossing equations. We use conformal bootstrap method to derive nonperturbative constraints on the CFT data and test the conformality and self-duality of $N_f=2$ QED$_3$. In particular we find the CFT data obtained from previous lattice simulations can be ruled out by introducing irrelevant assumptions in the spectrum, indicating the IR phase of $N_f=2$ QED$_3$ is not conformal.

hep-th↗

arXiv2022

Symmetries of conformal correlation functions

A program of wide interest in modern conformal bootstrap studies is to numerically solve general conformal field theories, based on a critical assumption that the dynamics is encoded in the conformal four-point crossing equations and positivity condition. In this letter we propose and verify a novel algebraic property of the crossing equations which provides strong restriction for this program. We show for various types of symmetries $\cal G$, the crossing equations can be linearly converted into the $SO(N)$ vector crossing equations associated with the $SO(N)\rightarrow \cal G$ branching rules and the transformations satisfy positivity condition. The dynamics constrained by the $\cal G$-symmetric crossing equations combined with positivity condition degenerates to the $SO(N)$ symmetric cases, while the non-$SO(N)$ symmetric theories are not directly solvable without introducing the $SO(N)$ symmetry breaking assumptions on the spectrum.

hep-th↗

arXiv2022

Bootstrapping conformal QED$_3$ and deconfined quantum critical point

We bootstrap the deconfined quantum critical point (DQCP) and 3D Quantum Electrodynamics (QED$_3$) coupled to $N_f$ flavors of two-component Dirac fermions. We show the lattice and perturbative results on the $SO(5)$ symmetric DQCP are excluded by the bootstrap bounds combined with an irrelevant condition of the lowest singlet scalar. Remarkably, we discover a new family of kinks in the 3D $SO(N)$ vector bootstrap bounds with $N\geqslant6$. We demonstrate bound coincidences between $SU(N_f)$ adjoint and $SO(N_f^2-1)$ vector bootstrap which result from a novel algebraic relation between their crossing equations. By introducing gap assumptions breaking the $SO(N_f^2-1)$ symmetry, the $SU(N_f)$ adjoint bootstrap bounds with large $N_f$ converge to the $1/N_f$ perturbative results of QED$_3$. Our results provide strong evidence that the $SO(5)$ DQCP is not continuous and the critical flavor number of QED$_3$ is slightly above $2$: $N_f^*\in(2,4)$. Bootstrap results near $N_f^*$ are well consistent with the merger and annihilation mechanism for the loss of conformality in QED$_3$.

hep-th↗

arXiv2022

Bootstrapping $N_f=4$ conformal QED$_3$

We present the results of a conformal bootstrap study of the presumed unitary IR fixed point of quantum electrodynamics in three dimensions (QED$_3$) coupled to $N_f=4$ two-component Dirac fermions. Specifically, we study the four-point correlators of the $SU(4)$ adjoint fermion bilinear $r$ and the monopole of lowest topological charge $\mathcal{M}_{1/2}$. Most notably, the scaling dimensions of the fermion bilinear $r$ and the monopole $\mathcal{M}_{1/2}$ are found to be constrained into a closed island with a combination of spectrum assumptions inspired by the $1/N_f$ perturbative results as well as a novel interval positivity constraint on the next-lowest-charge monopole $\mathcal{M}_1$. Bounds in this island on the $SU(4)$ and topological $U(1)_t$ conserved current central charges $c_J$, $c_J^t$, as well as on the stress tensor central charge $c_T$, are comfortably consistent with the perturbative results. Together with the scaling dimensions, this suggests that a part of estimates from the $1/N_f$ expansion -- even at $N_f=4$ -- provide a self-consistent solution to the bootstrap crossing relations, despite some of our assumptions not being strictly justified.

hep-th↗

arXiv2021

Searching for gauge theories with the conformal bootstrap

Infrared fixed points of gauge theories provide intriguing targets for the modern conformal bootstrap program. In this work we provide some preliminary evidence that a family of gauged fermionic CFTs saturate bootstrap bounds and can potentially be solved with the conformal bootstrap. We start by considering the bootstrap for $SO(N)$ vector 4-point functions in general dimension $D$. In the large $N$ limit, upper bounds on the scaling dimensions of the lowest $SO(N)$ singlet and traceless symmetric scalars interpolate between two solutions at $Δ=D/2-1$ and $Δ=D-1$ via generalized free field theory. In 3D the critical $O(N)$ vector models are known to saturate the bootstrap bounds and correspond to the kinks approaching $Δ=1/2$ at large $N$. We show that the bootstrap bounds also admit another infinite family of kinks ${\cal T}_D$, which at large $N$ approach solutions containing free fermion bilinears at $Δ=D-1$ from below. The kinks ${\cal T}_D$ appear in general dimensions with a $D$-dependent critical $N^*$ below which the kink disappears. We also study relations between the bounds obtained from the bootstrap with $SO(N)$ vectors, $SU(N)$ fundamentals, and $SU(N)\times SU(N)$ bi-fundamentals. We provide a proof for the coincidence between bootstrap bounds with different global symmetries. We show evidence that the proper symmetries of the underlying theories of ${\cal T}_D$ are subgroups of $SO(N)$, and we speculate that the kinks ${\cal T}_D$ relate to the fixed points of gauge theories coupled to fermions.

hep-th↗

arXiv2020

Bootstrapping Veneziano Amplitude of Vasiliev Theory and $3D$ Bosonization

Three-dimensional conformal field theories (CFTs) with slightly broken higher spin symmetry provide an interesting laboratory to study general properties of CFTs and their roles in the AdS/CFT correspondence. In this work we compute the four-point functions at arbitrary 't Hooft coupling $λ$ in the CFTs with slightly broken higher spin symmetry. We use a bootstrap approach based on the approximate higher spin Ward identity. We show that the bootstrap equation is separated into two parts with opposite parity charges, and it leads to a recursion relation for the $λ$ expansions of the correlation functions. The $λ$ expansions terminate at order $λ^2$ and the solutions are exact in $λ$. Our work generalizes the approach proposed by Maldacena and Zhiboedov to four-point correlators, and it amounts to an on-shell study for the $3D$ Chern-Simons vector models and the Vasiliev theory in $AdS_4$. Besides, we show that the same results can also be obtained rather simply from bosonization duality of $3D$ Chern-Simons vector models. The odd term at order $O(λ)$ in the spinning four-point function relates to the free boson correlator through a Legendre transformation. This provides new evidence on the $3D$ bosonization duality at the spinning four-point function level. We expect this work can be generalized to a complete classification of general four-point functions of single trace currents.

hep-th↗

arXiv2020

Superconformal Partial Waves for Stress-tensor Multiplet Correlator in $4D$ $\mathcal{N}=2$ SCFTs

We compute the superconformal partial waves of the four-point correlator $\langle JJJJ\rangle$, in which the external operator $J$ is the superconformal primary of the $4D$ $\mathcal{N}=2$ stress-tensor multiplet $\mathcal{J}$. We develop the superembedding formalism for the superconformal field theories (SCFTs) with extended supersymmetry. In $\mathcal{N}=2$ SCFTs, the three-point functions $\langle \mathcal{J}\mathcal{J}\mathcal{O}\rangle$ with general multiplet $\mathcal{O}$ contain two independent nilpotent superconformal invariants and new superconformal tensor structures, which can be nicely constructed from variables in superembedding space, and the three-point functions can be solved in compact forms. We compute the superconformal partial waves corresponding to the exchange of long multiplets using supershadow approach. The results are consistent with the non-trivial constraints by decomposing the $\mathcal{N}=2$ superconformal blocks into $\mathcal{N}=1$ superconformal blocks. Our results provide the necessary ingredient to study the fascinating $4D$ $\mathcal{N}=2$ SCFTs using conformal bootstrap.

hep-th↗

arXiv2018

Simulation of breast compression using a new biomechanical model

Mammography is currently the primary imaging modality for breast cancer screening and plays an important role in cancer diagnostics. A standard mammographic image acquisition always includes the compression of the breast prior x-ray exposure. The breast is compressed between two plates (the image receptor and the compression paddle) until a nearly uniform breast thickness is obtained. The breast flattening improves diagnostic image quality 1 and reduces the absorbed dose 2. However, this technique can also be a source of discomfort and might deter some women from attending breast screening by mammography 3,4. Therefore, the characterization of the pain perceived during breast compression is of potential interest to compare different compression approaches. The aim of this work is to develop simulation tools enabling the characterization of existing breast compression techniques in terms of patient comfort, dose delivered to the patient and resulting image quality. A 3D biomechanical model of the breast was developed providing physics-based predictions of tissue motion and internal stress and strain intensity. The internal stress and strain intensity are assumed to be directly correlated with the patient discomfort. The resulting compressed breast model is integrated in an image simulation framework to assess both image quality and average glandular dose. We present the results of compression simulations on two breast geometries, under different compression paddles (flex or rigid).

physics.med-ph↗