arXiv subjects

Ran Luo

Publications and source records attributed to Ran Luo.

At least 19 recordsLinked to original sources

arXiv2026

Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism

We present a systematic study of finite, non-split 2-group symmetries with a non-trivial Postnikov class, focusing on the simplest example with a $\mathbb{Z}_2$ 0-form symmetry and a $\mathbb{Z}_2$ 1-form symmetry, intertwined together by the non-trivial Postnikov class in $H^3(B\mathbb{Z}_2;\mathbb{Z}_2)\cong\mathbb{Z}_2$, denoted by $\mathcal{G}$. We classify the anomalies of this 2-group symmetry for physical theories in $d$-dimensional spacetime, by computing the oriented bordism groups $Ω_{d+1}^{\rm SO}(B\mathcal{G})$ and the spin bordism groups $Ω_{d+1}^{\rm Spin}(B\mathcal{G})$ for $d\leq 5$. For the case of $d=3$, we investigate the Symmetry TFT/TO of the 2-group symmetry $\mathcal{G}$ using the language of fusion 2-categories, as well as (3+1)D TQFT actions, for the cases without or with the 2-group anomaly classified by $\operatorname{Hom}\left(\widetildeΩ_4^{\rm SO}(B\mathcal{G}),U(1)\right) \cong H^4(B\mathcal{G};U(1))\cong\mathbb{Z}_2$. We classify the minimal topological and physical boundary conditions of the Symmetry TFTs, and carry out the categorical Landau paradigm for such a non-split finite 2-group.

hep-th↗

arXiv2026

Droplets obstruct Onsager-type solutions of the Ising model in a magnetic field

Onsager solved the two-dimensional Ising model in zero field, but no solution is known in a magnetic field. We prove that in any dimension $d\ge2$, at every fixed dimensionless field outside a countable set, the free energy obeys no algebraic differential equation in the coupling, even locally. The obstruction arises from droplet geometry: the maximal droplet volume grows as the $d/(d-1)$ power of its boundary size, while an integer band in the pressure coefficients protects the extremal contributions against cancellation. Our result excludes Onsager-type solutions and closed forms in elliptic, hypergeometric, or Painlevé functions of the coupling at these fields.

cond-mat.stat-mech↗

arXiv2026

Lifts of symmetries to minimal nondegenerate extensions are unique up to fermion attachment

Gauging fermion parity in a $(2+1)$-dimensional fermionic topological order requires lifting its symmetries to the resulting bosonic theory. We give a direct tensor-categorical proof that, for a slightly degenerate braided fusion category $\mathcal{C}$ and a fixed minimal nondegenerate extension ${\cal E}$, the restriction homomorphism $r\colon\operatorname{Aut}_{\mathrm{LR}}(\mathcal{E})\to \operatorname{Aut}_{\mathrm{LR}}(\mathcal{C})$ on classes of complex-linear locality-respecting (LR) braided autoequivalences is surjective with central kernel $\mathbb{Z}/2$, generated by fermion attachment. Thus each symmetry class has exactly two LR lift classes, related by attaching the fermion to every vortex. We apply graded Morita theory to reduce the kernel to two module types on the vortex sector, corresponding to tensoring with the vacuum or the fermion. We then prove relative rigidity to show that each type determines a unique LR class, which are distinguished by fermionic self-braiding even when their actions on simple-object labels coincide. We prove surjectivity by extending graph algebras in $\mathcal{C}^{\mathrm{rev}}\boxtimes\mathcal{C}$ to Lagrangian algebras in $\mathcal{E}^{\mathrm{rev}}\boxtimes\mathcal{E}$. Our results require neither unitarity nor a ribbon structure. We illustrate the lifting ambiguity in the Laughlin state, the $SO(3)_3$ theory and the Ising topological order.

math.QA↗

arXiv2026

Inequivalent modular tensor categories with identical $S$, $T$ and $W$

It remains an open question whether the modular data $(S,T)$ together with the Whitehead-link matrix $W$ determine a modular tensor category up to ribbon equivalence. We answer negatively by constructing two braided-inequivalent Dijkgraaf--Witten modular categories for $(\mathbb Z/p\mathbb Z)^3$ for prime $p\ge5$ with identical $(S,T,W)$ and, more generally, identical Reshetikhin--Turaev invariants of all framed oriented links with at most two components under a single bijection of simple objects. The construction varies an alternating $3$-cocycle while fixing a quadratic cohomology class, using restriction to subgroups of rank at most two to match link invariants and the quadratic and alternating classes together to obstruct braided equivalence. A complete classification of modular tensor categories up to ribbon equivalence therefore requires invariants beyond those of colored framed links with at most two components. We also analytically evaluate an uncolored partition function on a closed oriented three-manifold that separates all $(p-1)/2$ equivalence classes in the family.

math.QA↗

arXiv2026

Categorical spin-networks: state-sum invariants of 4-manifolds from higher-gauge theory

In this work, we define $(3+1)$-dimensional topological quantum field theories (TQFTs) and their lattice realizations with input data given by a pivotal fusion 2-category; more precisely, our framework applies in wider generality to presemisimple locally fusion pivotal tensor $2$-categories, which are equipped with a so-called \textit{shadow trace}. We introduce a decoration of triangulated manifolds by the input data, and develop a $20j$-symbol formalism for computing 4-simplex scattering amplitudes. We verify the topological invariance of 20$j$-symbol summations under the 4-dimensional Pachner moves. Furthermore, we also construct explicitly a 3-dimensional Levin-Wen-type lattice Hamiltonian model realizing the state-sum invariant. Our construction can be understood as a higher-dimensional analogue of the spin-networks construction for the Turaev-Viro invariant. Examples arising from $2$-groups are discussed from the perspective of higher gauge theory.

math-ph↗

arXiv2026

Lattice-QCD validation of hadron mass and trace-anomaly decomposition sum rules

We present the first lattice-QCD validation of multiple sum rules associated with quark-gluon decomposition of hadron mass by computing all components from first principles. We achieve this through nonperturbative renormalization of the QCD energy-momentum tensor, including its trace, in a gradient-flow scheme, followed by continuum extrapolations, two-loop matching to the $\overline{\mathrm{MS}}$ scheme, and zero-flow-time extrapolations. These ingredients enable a direct and simultaneous verification, in a common renormalization scheme and scale, of multiple energy-density-based and trace-based mass decomposition sum rules proposed in the literature. We demonstrate the framework for the $η_c$ and $J/ψ$ charmonia using three fine lattice spacings with a physical strange-quark and near-physical up- and down-quark masses. We present the first lattice-QCD results for the gravitational form factor $\bar{C}$. We find sizable gluonic contributions to charmonia masses at the hadronic scale, $\sim 15\%$ in the Lorcé and Metz-Pasquini-Rodini decompositions. The trace-anomaly contribution in the Ji sum rule is $\sim 6\%$, while the gluonic component of the trace anomaly in the Hatta-Rajan-Tanaka sum rule is $\sim 35\%$. The method is general and can be straightforwardly adopted for lattice-QCD calculations of mass and spin decompositions as well as gravitational form factors of other hadrons and nuclei.

hep-lat↗

arXiv2026

Static Quark-Antiquark Interactions Under Rotation

We study static quark--antiquark interactions in rotating SU(3) gluodynamics using quenched lattice simulations at imaginary angular velocity. At zero temperature, we extract the static potential from Wilson loops for quark--antiquark pairs aligned with the rotation axis, for transverse pairs with one source on the rotation axis, and for symmetric transverse pairs across the rotation axis. Within the present accuracy, no significant rotation dependence or anisotropy is observed in the zero-temperature potential. At finite temperature, imaginary rotation suppresses the color-averaged free energies obtained from Polyakov-loop correlators in both longitudinal and transverse geometries. Axial-diagonal comparisons are used to identify a bulk region where open-boundary artifacts are reduced. In this region, the large-distance longitudinal free-energy shift is well described by $ΔF_z(R_{xy})=A R_{xy}^2+B$. The transverse channels exhibit the same qualitative suppression, while their distance dependence additionally reflects the radial arrangement of the static sources and is compatible with a radial single-source free-energy shift in the bulk region. For the finite-temperature observables studied above $T_c$, the response weakens as the temperature is increased. These results provide lattice evidence for a position- and geometry-dependent response of bare static-source free energies to imaginary rotation in a gluonic medium.

hep-lat↗

arXiv2026

Categorical Symmetries via Operator Algebras

We propose that the symmetry category associated to a 2D quantum field theory with 0-form $G$-symmetry with 't Hooft anomaly $k\in H^4(BG,\mathbb{Z})$ for a large class of Lie groups $G$ is the category of twisted measurable fields of Hilbert spaces over $G$ denoted by $\mathrm{Hilb}^k(G)$, which is equivalent to the category of unitary representations of $C_0(G)$ with convolution product twisted by a multiplicative bundle gerbe labeled by $k$ denoted by $\textbf{Rep}^k(C_0(G))$. We find that the Drinfeld center of the symmetry category $\mathcal{Z}(\mathrm{Hilb}^{k}(G))$ equivalent to the category of unitary representations of the groupoid $C^*$-algebra of the Fell line bundle $Σ_k$ over the conjugation action groupoid $G//_{\rm Ad} G$, denoted by $\textbf{Rep}(C^*(G//_{\rm Ad}G,Σ_k))$, where the twist is characterized by the transgression $τ(k)\in H^2(G//_{\rm Ad}G,U(1))$. To the full generality, our framework applies to a Lie group $G$ that is a direct product of a compact connected Lie group and a number of $\mathbb{R}$ or $GL(1,\mathbb{C})$ factors. We compute the braiding of anyon lines in the bulk 3D SymTFT from this formalism. Finally we provide physical examples for abelian and non-abelian $G$, and discuss the physical consequences of flat gauging continuous global symmetries.

hep-th↗

arXiv2025

Anomaly of Continuous Symmetries from Topological Defect Network

We show that the 't Hooft anomaly of a quantum field theory with continuous flavor symmetry can be detected from rearrangements of the topological defect webs implementing the global symmetry in general spacetime dimension, which is concretized in 2D by the F-moves of the defect lines. Via dualizing the defects to flat background gauge field configurations, we characterize the 't Hooft anomaly by various cohomological data of the symmetry group, where the cohomology of Lie groups with discrete topology plays the central role. We find that an extra dimension emerges naturally as a consequence of the mathematical description of the 't Hooft anomaly in the case of flat gauging.

hep-th↗

arXiv2025

Categorical Continuous Symmetry

We define the symmetry category in 1+1d for continuous 0-form $G$-symmetry to be $\textbf{Sky}^τ(G)$, the category of skyscraper sheaves of finite dimensional vector spaces with finite support on the group manifold of $G$, where $τ\in H^4(BG,\mathbb{Z})$ is the anomaly. We propose that the corresponding 2+1d SymTFT is described by the Drinfeld center of $\textbf{Sky}^τ(G)$. We show explicitly the way that $τ$ twists the convolution tensor product of the objects of $\textbf{Sky}^τ(G)$. As a concrete example, we present the $S$ and $T$-matrices for the simple anyons of the resulting $Z(\textbf{Sky}^τ(G))$ category for $G = U(1)$, both for the cases without or with anomaly and discuss the topological boundary conditions as Lagrangian algebra of $Z(\textbf{Sky}^τ(U(1)))$. We also present the definition of $\textbf{Sky}^τ(G)$ and $Z(\textbf{Sky}^τ(G))$ for the non-abelian case of $G=SU(2)$, as well as the speculated modular data. We point out that in order to have a physically relevant center and Lagrangian algebras it is necessary to generalize $\textbf{Sky}^τ(G)$ to a larger category, which we argue to be closely related to the category of quasi-coherent sheaves on $G_\mathbb{C}$ with convolution tensor product twisted by $τ$.

hep-th↗

arXiv2025

ArchiLense: A Framework for Quantitative Analysis of Architectural Styles Based on Vision Large Language Models

Architectural cultures across regions are characterized by stylistic diversity, shaped by historical, social, and technological contexts in addition to geograph-ical conditions. Understanding architectural styles requires the ability to describe and analyze the stylistic features of different architects from various regions through visual observations of architectural imagery. However, traditional studies of architectural culture have largely relied on subjective expert interpretations and historical literature reviews, often suffering from regional biases and limited ex-planatory scope. To address these challenges, this study proposes three core contributions: (1) We construct a professional architectural style dataset named ArchDiffBench, which comprises 1,765 high-quality architectural images and their corresponding style annotations, collected from different regions and historical periods. (2) We propose ArchiLense, an analytical framework grounded in Vision-Language Models and constructed using the ArchDiffBench dataset. By integrating ad-vanced computer vision techniques, deep learning, and machine learning algo-rithms, ArchiLense enables automatic recognition, comparison, and precise classi-fication of architectural imagery, producing descriptive language outputs that ar-ticulate stylistic differences. (3) Extensive evaluations show that ArchiLense achieves strong performance in architectural style recognition, with a 92.4% con-sistency rate with expert annotations and 84.5% classification accuracy, effec-tively capturing stylistic distinctions across images. The proposed approach transcends the subjectivity inherent in traditional analyses and offers a more objective and accurate perspective for comparative studies of architectural culture.

cs.CV↗

arXiv2025

FloorplanMAE:A self-supervised framework for complete floorplan generation from partial inputs

In the architectural design process, floorplan design is often a dynamic and iterative process. Architects progressively draw various parts of the floorplan according to their ideas and requirements, continuously adjusting and refining throughout the design process. Therefore, the ability to predict a complete floorplan from a partial one holds significant value in the design process. Such prediction can help architects quickly generate preliminary designs, improve design efficiency, and reduce the workload associated with repeated modifications. To address this need, we propose FloorplanMAE, a self-supervised learning framework for restoring incomplete floor plans into complete ones. First, we developed a floor plan reconstruction dataset, FloorplanNet, specifically trained on architectural floor plans. Secondly, we propose a floor plan reconstruction method based on Masked Autoencoders (MAE), which reconstructs missing parts by masking sections of the floor plan and training a lightweight Vision Transformer (ViT). We evaluated the reconstruction accuracy of FloorplanMAE and compared it with state-of-the-art benchmarks. Additionally, we validated the model using real sketches from the early stages of architectural design. Experimental results show that the FloorplanMAE model can generate high-quality complete floor plans from incomplete partial plans. This framework provides a scalable solution for floor plan generation, with broad application prospects.

cs.AI↗

arXiv2025

Segment Any Architectural Facades (SAAF):An automatic segmentation model for building facades, walls and windows based on multimodal semantics guidance

In the context of the digital development of architecture, the automatic segmentation of walls and windows is a key step in improving the efficiency of building information models and computer-aided design. This study proposes an automatic segmentation model for building facade walls and windows based on multimodal semantic guidance, called Segment Any Architectural Facades (SAAF). First, SAAF has a multimodal semantic collaborative feature extraction mechanism. By combining natural language processing technology, it can fuse the semantic information in text descriptions with image features, enhancing the semantic understanding of building facade components. Second, we developed an end-to-end training framework that enables the model to autonomously learn the mapping relationship from text descriptions to image segmentation, reducing the influence of manual intervention on the segmentation results and improving the automation and robustness of the model. Finally, we conducted extensive experiments on multiple facade datasets. The segmentation results of SAAF outperformed existing methods in the mIoU metric, indicating that the SAAF model can maintain high-precision segmentation ability when faced with diverse datasets. Our model has made certain progress in improving the accuracy and generalization ability of the wall and window segmentation task. It is expected to provide a reference for the development of architectural computer vision technology and also explore new ideas and technical paths for the application of multimodal learning in the architectural field.

cs.CV↗

arXiv2025

FloorPlan-DeepSeek (FPDS): A multimodal approach to floorplan generation using vector-based next room prediction

In the architectural design process, floor plan generation is inherently progressive and iterative. However, existing generative models for floor plans are predominantly end-to-end generation that produce an entire pixel-based layout in a single pass. This paradigm is often incompatible with the incremental workflows observed in real-world architectural practice. To address this issue, we draw inspiration from the autoregressive 'next token prediction' mechanism commonly used in large language models, and propose a novel 'next room prediction' paradigm tailored to architectural floor plan modeling. Experimental evaluation indicates that FPDS demonstrates competitive performance in comparison to diffusion models and Tell2Design in the text-to-floorplan task, indicating its potential applicability in supporting future intelligent architectural design.

cs.CL↗

arXiv2025

Topological Holography for Mixed-State Phases and Phase Transitions

We extend the symmetry topological field theory (SymTFT) framework to open quantum systems. Using canonical purification, we embed mixed states into a doubled (2+1)-dimensional topological order and employ the slab construction to study (1+1)-dimensional mixed-state phases through condensable algebras in the doubled SymTFT. Hermiticity and positivity of the density matrix impose additional constraints on allowable anyon condensations, enabling a systematic classification of mixed-state phases - including strong-to-weak symmetry breaking (SWSSB) and average symmetry-protected topological (ASPT) phases. We present examples of mixed-state phase transitions involving SWSSB and show how gauging within the open SymTFT framework reveals connections among different mixed-state phases.

cond-mat.str-el↗

arXiv2025

Automated Review Generation Method Based on Large Language Models

Literature research, vital for scientific work, faces the challenge of surging information volumes exceeding researchers' processing capabilities. We present an automated review generation method based on large language models (LLMs) to overcome efficiency bottlenecks and reduce cognitive load. Our statistically validated evaluation framework demonstrates that the generated reviews match or exceed manual quality, offering broad applicability across research fields without requiring users' domain knowledge. Applied to propane dehydrogenation (PDH) catalysts, our method swiftly analyzed 343 articles, averaging seconds per article per LLM account, producing comprehensive reviews spanning 35 topics, with extended analysis of 1041 articles providing insights into catalysts' properties. Through multi-layered quality control, we effectively mitigated LLMs' hallucinations, with expert verification confirming accuracy and citation integrity while demonstrating hallucination risks reduced to below 0.5\% with 95\% confidence. Released Windows application enables one-click review generation, enhancing research productivity and literature recommendation efficiency while setting the stage for broader scientific explorations.

cs.CL↗

arXiv2025

Symmetry Topological Field Theory for Flavor Symmetry

In this Letter, we demonstrate that the Symmetry Topological Field Theory (SymTFT) associated to a Quantum Field Theory (QFT) with continuous non-abelian $G$-flavor symmetry is a $BF$-theory with gauge group $G$. We show that gauging $G$-symmetry with a flat connection yields a theory with global symmetry characterized by exchanging the conjugate variables in the quantization of $BF$-theory. We construct the extended operators that generate the $G$-flavor symmetry and the $(d-2)$-form $\text{Rep}(G)$-symmetry of the gauged QFT. We demonstrate that $BF$-theory arises as the theory characterizing $G$-flavor symmetry of a QFT in the AdS/CFT setup. 't Hooft anomalies of the $G$-flavor symmetry are realized as extra terms in the action.

hep-th↗

arXiv2024

Understanding Fermionic Generalized Symmetries

We explore new aspects of internal fermionic shifting symmetries, present in physical systems such as free Dirac spinors and p-form tensor-spinor fields. We propose a novel procedure to gauge these global symmetries, which also introduces a new Stückelberg mechanism to give a mass to free fermionic fields. Furthermore, we find new magnetic fermionic symmetries in these physical systems whose charged objects are disorder operators. For the case of a Dirac spinor, we discuss an dual description, where the magnetic symmetry acts on the holonomies of a dual 2-form tensor-spinor. Further generalizations such as higher-group-like structures are also discussed.

hep-th↗