arXiv subjects

Jiang Long

Publications and source records attributed to Jiang Long.

At least 19 recordsLinked to original sources

arXiv2026

Spacelike reduction of the gravitational topological terms and associated helicity densities

Helicity in gravity is a multifaceted concept, and several inequivalent definitions exist in the literature. In this work, we reduce the topological Pontryagin and Nieh-Yan terms to a constant time spacelike hypersurface. Remarkably, upon applying the SVT decomposition at the linearized level, we obtain four distinct helicity densities. The helicity density arising from the Nieh-Yan term is termed the spin-1 and spin-2 gravitomagnetic helicity density, depending on whether it originates from vector or tensor modes. Meanwhile, the helicity density arising from the Pontryagin term is termed the spin-1 and spin-2 gravito-current helicity density, according to the corresponding mode contributions. We study the mode and multipole expansions of these helicity functionals and apply them to leading order Newtonian two-body systems, weak field boosted Kerr, a locally defined slowly varying gyratonic pp-wave model, and a linearized gravitational Hopfion.

gr-qc↗

arXiv2026

Covariant variation and its applications

We define a covariant variation of tensor fields by combining its Lie derivative with the metric variation. This operator preserves the metric, contractions, and Hodge duality, but its commutator is not closed due to an anomaly. We derive its algebraic and geometric properties, and compare it with the Kosmann derivative. Combining the covariant variation with Kosmann derivative gives total covariant variation for the fields with both spacetime and Lorentz structure, all of which belong to the metric Lie derivative. Moreover, we introduce families of extended operators which contain the affine connection, Lie derivative, and covariant variation. From the anomaly of the covariant variation along the superrotation, an electromagnetic helicity flux appears at null hypersurfaces in four dimensions. We also apply the covariant variation and its anomaly to tensor fields in arbitrary spacetime dimensions, and especially focus on the $p$-forms in $d=2p+2$ dimensions.

hep-th↗

arXiv2026

SQL-RewriteBench: A Correctness-Gated, Full-Denominator Benchmark for Statement-Level SQL Rewriting [Experiment,Analysis & Benchmark]

Statement-level SQL rewriting can improve query performance and maintainability without changing the DBMS kernel, but existing benchmarks do not evaluate rewrite methods as deployable systems. They typically focus on DBMS performance, rule regression, query equivalence, or dialect translation, while missing the full path from accepting an input query to producing an executable, result-consistent, and operationally useful rewrite. We present SQL-RewriteBench, a benchmark for statement-level SQL rewriting that applies correctness gating and full-denominator accounting. Its metric suite explicitly separates Source Acceptance, Generation Rate, Execution Coverage, Result Consistency, UnsafeRewrite Rate, and speedup distribution. It also defines SCS, a deterministic index of static SQL structure, and CGOQ, a correctness-gated optimization-quality score that gives optimization credit only after the case-specific Checker Contract is satisfied. CGOQ combines runtime improvement with structural simplification through a continuous scoring function, making it suitable for deployment-oriented rewrite assessment. As an artifact, SQL-RewriteBench provides 180 executable Benchmark Instances organized into EQUIV, PERF, ROBUST, and DIALECT pools, each packaged with SQL, schema metadata, provenance, evidence, and rewrite-opportunity documentation. Across seven representative academic and LLM-based methods, every full-benchmark CGOQ is negative. Existing methods often fail before rewriting, fail result checks, or return correct rewrites that are slower or no better than the input. These results show that deployable SQL rewrite requires broader input handling, result validation, and benefit-aware rewrite decisions.

cs.DB↗

arXiv2026

Spinning bulk-to-boundary correlators in the massless theories with Poincar\'e symmetry

We classify the bulk-to-boundary correlators for general integer-spin $s$ operators in a Poincar\'e-invariant theory by imposing suitable fall-off conditions near future/past null infinity. Any bulk-to-boundary correlator is a linear superposition of a set of basic tensor structures fixed by the little group \text{ISO}(2) of massless particles. We map the independent tensor structures to all possible non-crossing double-line diagrams. A further mapping of the double-line diagrams to circular diagrams shows that all independent tensor structures are tensor products of loop diagrams. By extrapolating the bulk-to-boundary correlators to boundary-to-boundary correlators, we find a rich structure for general spin-$s$ operators. Furthermore, we show that the extrapolated operator lies in a type Ib spin-$s$ multiplet representation of Carrollian conformal field theory (CCFT). This is a net representation that generated by the Wigner translation generators.

hep-th↗

arXiv2026

Carrollian correlators in black hole perturbation theory

In this note, we clarify the relationship between the two-point Carrollian correlator and massless scattering in black hole background. It turns out that there are two kinds of Carrollian correlators at the null boundaries of each asymptotically flat spacetime. The correlator from $\mathscr I^-$ to $\mathscr I^+$ should be regularized by subtracting the flat space analog, and it is the position space version of the reflection amplitude of massless scattering. On the other hand, the correlator from $\mathscr I^-$ to the future horizon $\mathcal H^+$ is absent in flat space, and it is the position space version of the transmission amplitude. The poles of the Carrollian correlators are governed by the null geodesics from $\mathscr I^-$ to $\mathscr I^+$ or $\mathcal H^+$, and they define two kinds of classical equations in Carrollian space. These equations establish the relationship between the Shapiro time delay and the deflection angle for light rays and should be understood as the dual descriptions of the quasinormal modes (QNMs) and the branch cut of the Green's function. We find that the time delay contains a logarithmic/quadratic behavior for the correlator from $\mathscr I^-$ to $\mathscr I^+/\mathcal H^+$ for small deflection angles. On the other hand, the time delay is always increasing linearly for both correlators when the deflection angle is large.

gr-qc↗

arXiv2026

Constraining bulk-to-boundary correlators under Poincar\'e symmetry

It is well known that a general two-point function cannot be uniquely determined by Poincar\'e symmetry. In this paper, we show that bulk-to-boundary correlators are highly constrained after imposing suitable fall-off conditions near future/past null infinity. More precisely, scalar bulk-to-boundary correlators are fixed to a unique form up to a normalization constant, whereas fermionic bulk-to-boundary correlators are fixed to a linear superposition of scalar and fermionic branches. This is established by asymptotically expanding the Ward identities, where upon the leading terms decouple from the subleading ones. In the fermionic branch, the power-law exponent of the bulk-to-boundary correlator is greater by one than the fall-off index. Consequently, we revisit the relation between Carrollian correlators and momentum space scattering amplitudes for fermionic operators. In this context, we find that the Fourier transform bridging the two acquires an extra factor of $\sqrt{\omega}$ for each fermionic operator. Furthermore, we reduce the bulk-to-boundary correlator to the boundary-to-boundary correlator and identify a critical fall-off index $\Delta=1$. For $0 < \Delta < 1$, only a magnetic branch exists for scalars. For $\Delta > 1$, the electric branch is always divergent for both scalar and fermionic branches and thus requires regularization.

hep-th↗

arXiv2025

Reduction of topological invariants on null hypersurfaces

Gravitational helicity flux density represents the angular distribution of helicity flux in general relativity. In this work, we explore its relationship to the reduction of topological invariants at future null infinity. Contrary to initial expectations, the Pontryagin term, which contributes to the gravitational chiral anomaly, is not related to the gravitational helicity flux density. Instead, the Nieh-Yan term, another topological invariant within the teleparallel equivalent of general relativity (TEGR), can reproduce this flux density. We also reduce these two topological invariants to null hypersurfaces describing near-horizon geometry. In this near-horizon context, the Pontryagin term yields a non-trivial quantity that may characterize a Carrollian fluid helicity relevant to near-horizon physics.

hep-th↗

arXiv2025

Extrapolating the massive fields to future timelike infinity

It is well-known that future timelike infinity ($i^+$) in four-dimensional Minkowski spacetime is conformal to the unit three-dimensional hyperboloid ($H^3$). We asymptotically expand massive fields with spin $0,1,2$ near $i^+$ and extrapolate them onto this hyperboloid. These fields oscillate with a frequency equal to their mass and exhibit a universal asymptotic decay $\tau^{-3/2}$. The fundamental fields are free and encode the outgoing scattering data. They are local operators defined on the boundary $H^3$ with which we construct the Poincar\'e charges. The Poincar\'e algebra can be extended to $\text{MDiff}(H^3)\ltimes C^{\infty}(H^3)$ using smeared operators associated with energy and angular momentum densities. For spinning fields, a spin operator must be included to close the algebra. The extended algebra shares the same form as the five-dimensional intertwined Carrollian diffeomorphism and reduces to the BMS algebra at $i^+$ by restricting the choice of test functions and vectors.

hep-th↗

arXiv2025

Electromagnetic helicity flux density for radiative systems

We show that the helicity flux density is distinguished from magnetic helicity by analysing Hopf solitons. The electromagnetic (EM) helicity flux and the magnetic helicity are Chern-Simons terms at different hypersurfaces. We find the helicity flux density for a point charge moving with an acceleration, extending the Li\'enard-Wiechert angular distribution of radiant power. We also derive the multipole expansion of the helicity flux density, generalizing the Larmor's formula for the radiant power. These formulae have been applied to discuss the helicity flux density in several toy models such as circular and helical motion as well as soft bremsstrahlung. We also comment on the potential applications of the EM helicity flux density to pulsar systems.

hep-th↗

arXiv2025

Thermal correlator at null infinity

We study the thermal Carrollian correlators at null infinity in the real-time formalism. We derive the Feynman rules to calculate these correlators in the position space. We compute the bulk-to-bulk, bulk-to-boundary and boundary-to-boundary propagators for massless scalar theory. Due to the doubling of the fields degrees of freedom, the number of each propagator is quadrupled. The bulk-to-boundary propagators have the form of (extended) Bose-Einstein distribution in the position space. Utilizing the contour integral of the propagators, we can transform the Feynman rules to momentum space. Interestingly, while the external lines and amplitudes in momentum space depend on the contour, Carrollian correlators in position space are independent of it. We show how to compute four-point correlators at finite temperature. The tree level correlators can be written as the summation of Barnes zeta functions and reduce to the ones in the zero temperature limit.

hep-th↗

arXiv2025

Multi-View Factorizing and Disentangling: A Novel Framework for Incomplete Multi-View Multi-Label Classification

Multi-view multi-label classification (MvMLC) has recently garnered significant research attention due to its wide range of real-world applications. However, incompleteness in views and labels is a common challenge, often resulting from data collection oversights and uncertainties in manual annotation. Furthermore, the task of learning robust multi-view representations that are both view-consistent and view-specific from diverse views still a challenge problem in MvMLC. To address these issues, we propose a novel framework for incomplete multi-view multi-label classification (iMvMLC). Our method factorizes multi-view representations into two independent sets of factors: view-consistent and view-specific, and we correspondingly design a graph disentangling loss to fully reduce redundancy between these representations. Additionally, our framework innovatively decomposes consistent representation learning into three key sub-objectives: (i) how to extract view-shared information across different views, (ii) how to eliminate intra-view redundancy in consistent representations, and (iii) how to preserve task-relevant information. To this end, we design a robust task-relevant consistency learning module that collaboratively learns high-quality consistent representations, leveraging a masked cross-view prediction (MCP) strategy and information theory. Notably, all modules in our framework are developed to function effectively under conditions of incomplete views and labels, making our method adaptable to various multi-view and multi-label datasets. Extensive experiments on five datasets demonstrate that our method outperforms other leading approaches.

cs.CV↗

arXiv2024

Quantum flux operators in the fermionic theory and their supersymmetric extension

We construct quantum flux operators with respect to the Poincar\'e symmetry in the massless Dirac theory at future null infinity. An anomalous helicity flux operator emerges from the commutator of the superrotation generators. The helicity flux operator corresponds to the local chiral symmetry which is the analog of superduality in the gauge theories. We also find its relation to the non-closure of the Lie transport of the spinor field around a loop. We discuss various algebras formed by these operators and constrain the test functions by the requirement of eliminating the non-local terms and satisfying the Jacobi identities. Furthermore, we explore their $\mathcal{N}=1$ supersymmetric extension in the Wess-Zumino model. There are four kinds of quantum flux operators, which correspond to the supertranslation, superrotation, superduality and supersymmetry, respectively. Interestingly, besides the expected supertranslation generator, a helicity flux operator will also emerge in the commutator between the superflux operators. We check that our flux algebra can give rise to the super-BMS and super-Poincar\'e algebras with appropriate choice of parameters. In the latter reduction, we find the helicity flux reduces to behaving like a $R$ symmetry generator in the commutator with the superflux. For completion, we derive the $R$ flux which also includes a charge flux for complex scalar besides the helicity flux for spinor field.

hep-th↗

arXiv2024

Incomplete Multi-view Multi-label Classification via a Dual-level Contrastive Learning Framework

Recently, multi-view and multi-label classification have become significant domains for comprehensive data analysis and exploration. However, incompleteness both in views and labels is still a real-world scenario for multi-view multi-label classification. In this paper, we seek to focus on double missing multi-view multi-label classification tasks and propose our dual-level contrastive learning framework to solve this issue. Different from the existing works, which couple consistent information and view-specific information in the same feature space, we decouple the two heterogeneous properties into different spaces and employ contrastive learning theory to fully disentangle the two properties. Specifically, our method first introduces a two-channel decoupling module that contains a shared representation and a view-proprietary representation to effectively extract consistency and complementarity information across all views. Second, to efficiently filter out high-quality consistent information from multi-view representations, two consistency objectives based on contrastive learning are conducted on the high-level features and the semantic labels, respectively. Extensive experiments on several widely used benchmark datasets demonstrate that the proposed method has more stable and superior classification performance.

cs.CV↗

arXiv2024

Carrollian propagator and amplitude in Rindler spacetime

We study the three-dimensional Carrollian field theory on the Rindler horizon which is dual to a bulk massless scalar field theory in the four-dimensional Rindler wedge. The Carrollian field theory could be mapped to a two-dimensional Euclidean field theory in the transverse plane by a Fourier transform. After defining the incoming and outgoing states at the future and past Rindler horizon, respectively, we construct the boundary-to-boundary and bulk-to-boundary propagators that are consistent with the bulk Green's function in the literature. We investigate the tree-level Carrollian amplitudes up to four points. The tree-level four-point Carrollian amplitude in $\Phi^4$ theory has the same structure as the one-loop triangle Feynman integral in the Lee-Pomeransky representation with complex powers in the propagators and spacetime dimension. Moreover, the four-point Carrollian amplitude with a zero energy state inserted at infinity in $\Phi^4$ theory is proportional to the three-point Carrollian amplitude in $\Phi^3$ theory.

hep-th↗

arXiv2024

Task-Augmented Cross-View Imputation Network for Partial Multi-View Incomplete Multi-Label Classification

In real-world scenarios, multi-view multi-label learning often encounters the challenge of incomplete training data due to limitations in data collection and unreliable annotation processes. The absence of multi-view features impairs the comprehensive understanding of samples, omitting crucial details essential for classification. To address this issue, we present a task-augmented cross-view imputation network (TACVI-Net) for the purpose of handling partial multi-view incomplete multi-label classification. Specifically, we employ a two-stage network to derive highly task-relevant features to recover the missing views. In the first stage, we leverage the information bottleneck theory to obtain a discriminative representation of each view by extracting task-relevant information through a view-specific encoder-classifier architecture. In the second stage, an autoencoder based multi-view reconstruction network is utilized to extract high-level semantic representation of the augmented features and recover the missing data, thereby aiding the final classification task. Extensive experiments on five datasets demonstrate that our TACVI-Net outperforms other state-of-the-art methods.

cs.CV↗

arXiv2024

On the definition of Carrollian amplitudes in general dimensions

Carrollian amplitude is the natural object that defines the correlator of the boundary Carrollian field theory. In this work, we will elaborate on its proper definition in general dimensions. We use the vielbein field on the unit sphere to define the fundamental field with non-vanishing helicity in the local Cartesian frame which is the building block of the Carrollian amplitude. In general dimensions, the Carrollian amplitude is related to the momentum space scattering matrix by a modified Fourier transform. The Poincar\'e transformation law of the Carrollian amplitude in this definition has been discussed. We also find an isomorphism between the local rotation of the vielbein field and the superduality transformation.

hep-th↗

arXiv2024

Electromagnetic helicity flux operators in higher dimensions

The helicity flux operator is a fascinating quantity that characterizes the angular distribution of the helicity of radiative photons or gravitons and it has many interesting physical consequences. In this paper, we construct the electromagnetic helicity flux operators which form a non-Abelian group in general dimensions, among which the minimal helicity flux operators form the massless representation of the little group, a finite spin unitary irreducible representation of the Poincar\'e group. As in four dimensions, they generate an extended angle-dependent transformation on the Carrollian manifold. Interestingly, there is no known corresponding bulk duality transformation in general dimensions. However, we can construct a topological Chern-Simons term that evaluates the minimal helicity flux operators at $\mathcal{I}^+$.

hep-th↗

arXiv2024

Gravitational helicity flux density from two-body systems

The helicity flux density is a novel quantity which characterizes the angle-dependence of the helicity of radiative gravitons and it may be tested by gravitational wave experiments in the future. We derive a quadrupole formula for the helicity flux density due to gravitational radiation in the slow motion and the weak field limit. We apply the formula to the bound and unbound orbits in two-body systems and find that the total radiative helicity fluxes are always zero. However, the radiative helicity flux density, which is $\mathcal{O}(G^3)$ in the Newtonian limit, still has non-trivial dependence on the angle. Furthermore, we also find a formula for the total helicity flux by including all contributions of the higher multipoles.

gr-qc↗