We study knots in 3d Chern-Simons theory with complex gauge group , in the context of its relation with 3d theory (the so-called 3d-3d correspondence). The defect has either co-dimension 2 or co-dimension 4 inside the 6d theory, which is compactified on a 3-manifold . …
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48 results for “3d/3d correspondence”
Study of 3d-3d correspondence involving -Weyl algebra and 3d-index.
problem Understanding the action of a -Weyl algebra on the 3d-index of knots.
method Investigation of the -Weyl algebra's module action on the 3d-index, conjecturing structural properties.
result Bilinear factorization, pair of linear -difference equations, and rational function matrix for the 3d-index determination.
The paper tackles mapping tori by proposing a new approach to 3d-3d correspondence.
problem No existing approach fully describes 3d SCFTs for all types of 3-manifolds.
method Systematic study of 3d gauge theories with non-linear matter fields.
result Recovery of 3-manifold invariants from indices and proposal of new -series invariants.
for 3d theorieshep-th
Proposes a new effective central charge for 3d N=2 theories.
problem Understanding the effective central charge in 3d N=2 theories.
method Analyzes the superconformal index to propose a new quantity and discusses its properties and computation.
result Proposes a new effective central charge for 3d N=2 theories.
3D dual field theories for Virasoro minimal models constructed using Seifert fiber spaces.
problem Constructing 3D dual field theories for Virasoro minimal models.
method 3D-3D correspondence and Seifert fiber spaces.
result 3D dual field theories constructed for Virasoro minimal models.
The study connects knot complements to 3d theories via half-index calculations.
problem Understanding the relationship between knot complements and 3d theories.
method Using half-index calculations and inverted Habiro series, the study realizes knot complements as homological blocks.
result The colored Jones polynomial is derived from choosing specific poles in the half-index integral expression.
3D topological models link to HOMFLYPT homology via braids.
problem Understanding topological invariants of links and braids.
method 3D topological B-models with Hilbert schemes of points.
result Hilbert space of braids corresponds to HOMFLYPT homology.
Study large N oscillations in 3D theories related to black hole physics.
problem Understanding large N sign oscillations in 3D theories via holography.
method Holographic computation of on-shell actions for Euclidean supergravity solutions, Wick rotation of magnetically charged AdS4 black holes.
result Proposed a non-trivial mathematical conjecture regarding phase factors of twisted Reidemeister-Ray-Singer torsion.
Proposes Teichmüller TQFT as a Chern-Simons theory with a new integration cycle.
problem Defining Teichmüller TQFT as a Chern-Simons theory with a novel integration cycle.
method Analytically continues Chern-Simons path-integral with an unusual integration cycle.
result Teichmüller TQFT is dual to complex SL(2,C) Chern-Simons theory at integer level k=1.
Study of IR phases in 3D class R theories linked to non-hyperbolic 3-manifolds.
problem Understanding IR phases of 3D class R theories associated with non-hyperbolic 3-manifolds.
method Analysis of IR phenomena through `exceptional' Dehn fillings and gauging of flavor symmetries.
result 3D class R theories associated with certain atoroidal non-hyperbolic 3-manifolds exhibit supersymmetry enhancement at low energy.
We study supersymmetric probe M5-branes in the AdS_4 solution that arises from M5-branes wrapped on a hyperbolic 3-manifold M_3. This amounts to introducing internal defects within the framework of the 3d-3d correspondence. The BPS condition for a probe M5-brane extending along all of AdS_4 requires it to wrap a surfac…
We use the 3d-3d correspondence together with the DGG construction of theories labelled by 3-manifolds M to define a non-perturbative state-integral model for SL(n,C) Chern-Simons theory at any level k, based on ideal triangulations. The resulting partition functions generalize a widely studied k=1 state-integ…
The paper connects quivers to knot complements and studies their BPS states and 3d N=2 theories.
problem Understanding the relationship between quivers and knot complements.
method Assigning quivers to knot complements and exploring their physical interpretation.
result Proposed a physical interpretation of quivers in terms of BPS states and 3d N=2 theories.
Improved 3D scene understanding from partial point sets using multiview fusion.
problem Challenging task of 3D scene semantic understanding from partial point clouds.
method Multiview representation of 360° point clouds and fusion with original data.
result Overall increase of 31.9% and 4.3% in segmentation accuracy for partial and complete scenes.
DepthNets learns 3D face geometry and transformations without supervision.
problem Learning 3D face geometry and transformations from a single image.
method Unsupervised learning of facial keypoints depth, using backpropable loss for 3D transformations.
result DepthNets can predict 3D transformations and re-target faces to new poses or geometries.
3D good continuation model explains stereo vision using neurogeometry.
problem Understanding how the brain processes 3D visual correspondence.
method Developed a neurogeometric model involving spatial and orientation disparities.
result Provides insight into neural organization and correspondence problem.
In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N=2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomia…
In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d theory of type on a 3-manifold . The so-called 3d-3d correspondence is a relation between complexified Chern-Simons theory (with gauge group ) on and a 3d theo…
Study of 3-manifold homology using fivebrane compactifications.
problem Understanding homological invariants of 3-manifolds.
method Fivebrane compactifications and 3d/3d correspondence.
result Explicit calculations of 3-manifold homology invariants.
3D gauge theories link knot polynomials to vortex partition functions.
problem Connecting knot polynomials to gauge theory partition functions.
method Construct 3D abelian gauge theories on .
result Colored Jones polynomials derived from vortex partition functions.
New algorithm constructs characters of rational VOAs from knot complements.
problem Constructing characters of rational VOAs from knot complements.
method 3D gauge theories, Dimofte-Gaiotto-Gukov construction, 3D rank-0 SCFT, topological twist.
result New Nahm-sum-like expressions for Virasoro minimal model characters.
New framework segments 3D scenes using neural algorithms and sub-Riemannian geometry.
problem Effective scene segmentation in 3D vision.
method Neurogeometric sub-Riemannian model, harmonic analysis, neural-based stereo correspondence.
result Sub-Riemannian metric is central to effective scene segmentation.
A class of 3d supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applying the Dimofte-Gaiotto-Gukov construction in 3d/3d correspondence to certain graph complement 3-manifolds. Given a gauge theory in this class…
A machine learning method predicts rock permeability from 3D images.
problem Efficiently predict permeability of heterogeneous rocks for planetary and robotic applications.
method Machine learning guided 3D properties recognition of rock morphology from 3D micro CT and MRI images.
result The morphology decoder method accurately predicts permeability from 3D images.
Unoriented 3d TFTshep-th
Paper generalizes properties of oriented 3d TFTs to unoriented case.
problem Generalize properties of oriented 3d TFTs to unoriented case.
method Show how Turaev-Viro construction can be generalized to unoriented 3d TFTs and Pin^+ TFTs.
result Pin^+ TFTs can be constructed from unoriented TFTs with a mixed anomaly.
Paper classifies brain signals using eigenvalues for 2D and 3D educational content questions.
problem Classifying brain signals for 2D and 3D educational content questions.
method Eigenvalues of covariance matrix used as features; KNN and SVM classifiers applied.
result No significant difference in learning, memory retention, and recall between 2D and 3D educational content.
New solutions to 3D integrability equations using quantum cluster algebras.
problem Constructing solutions to the tetrahedron and 3D reflection equations.
method Extending quantum cluster algebra approach to Fock-Goncharov quivers and investigating cluster transformations.
result Explicit formulas for matrix elements of solutions derived for typical representations.
A 3d-3d appetizerhep-th
We test the 3d-3d correspondence for theories that are labelled by Lens spaces. We find a full agreement between the index of the 3d "Lens space theory" and the partition function of complex Chern-Simons theory on . In particular, for , we show how the familiar partition func…
Paper connects 3D gravity averages to 2D CFT correlators.
problem Understanding 3D gravity partition functions.
method 3D topological field theories and mapping class group averages.
result Established a correspondence between 3D gravity averages and 2D CFT correlators.
Nesting behind -invariantsmath.RT
Proposes categorification of Z-invariants for specific 3-manifolds.
problem Categorification of Z-invariants for negative definite plumbed 3-manifolds.
method Abelian categorification using 3d N=2 theory and log VOAs.
result Nested Weyl-type character formulas reconstruct -invariants.
Voxel-FPN detects 3D objects from point clouds using raw LIDAR data.
problem 3D object detection in point cloud data for autonomous driving.
method Bottom-up voxel extraction and top-down feature fusion.
result Voxel-FPN outperforms baselines on the KITTI-3D benchmark.
Researchers map knot complements using 3d theories and half-index calculations.
problem Mapping knot complements using mathematical theories.
method Using 3d theories and half-index calculations.
result Realized homological blocks and HOMFLY-PT polynomials for knot complements.
The paper explores the connection between 3d gravity and Chern-Simons theory using affine group connections.
problem Exploring the relationship between 3d gravity and Chern-Simons theory.
method A variational problem of Chern-Simons type on a principal fiber bundle with general affine group structure is studied. The connection is established through a generalized notion of extension and reduction of connections.
result Established a correspondence between 3d gravity and Chern-Simons theory using affine group connections.
New framework for 3D spatial topology enumeration and identification.
problem Efficient navigation through complex engineering system topologies.
method Mathematical spatial graph theory to represent, enumerate, and identify unique topological classes.
result Identification of distinctive 3D topological classes for engineering systems.
A modular functor is constructed from non-semisimple 3d TFTs.
problem Constructing modular functors from non-semisimple 3d topological field theories.
method Using a 3d TFT defined in [arXiv:1912.02063], a symmetric monoidal 2-functor is constructed from a 2-category of bordisms to a 2-category of finite linear categories.
result A modular functor is explicitly described as a symmetric monoidal 2-functor.
New relations link knot theory to quiver representations in 3d physics.
problem Exploring new connections between knot theory and quiver representations.
method Observing multi-cover skein relations and embedding them into M-theory.
result Obtained dualities of 3d theories associated to quivers.
A 1D-fully convolutional network classifies 3D point clouds efficiently.
problem Efficiently classifying 3D point clouds with reliable features.
method Directly consumes terrain-normalized points and spectral data, implicitly learning contextual features.
result Ranked second in ISPRS 3D Semantic Labeling Contest with 81.6% overall accuracy.
Sequencing BPS Spectrahep-th
The paper explores BPS states in physics and their spectral sequences.
problem Understanding how BPS states vary with continuous parameters.
method Proposes a spectral sequence to describe the relationship between unperturbed and perturbed BPS spectra.
result Identifies a sliding property in colored HOMFLY homology and explains it using modular S-matrix.
Classifies polar actions on 3D homogeneous spaces.
problem Classifying polar isometric actions on 3D homogeneous spaces.
method Orbit equivalence classification and study of cohomogeneity one actions.
result Classification of extrinsically homogeneous surfaces and orbit foliations.
Transformer-M learns molecular data in 2D or 3D formats.
problem Learning models for molecules are limited to specific data formats.
method Developed a Transformer-based model that can handle 2D and 3D molecular data.
result Transformer-M achieves strong performance on both 2D and 3D molecular tasks.
Symmetrizes 4d and 3d BPS quivers for Argyres-Douglas theories.
problem Understanding the relationship between 4d and 3d BPS quivers.
method Analyzes geometric backgrounds and uses skein modules to derive quiver partition functions.
result Proves isomorphism between 4d wall-crossing and unlinking of symmetric quivers.
ObSuRF converts a single image into a 3D model with NeRFs.
problem Creating a 3D model from a single image with object segmentation.
method Unsupervised volume segmentation using Neural Radiance Fields (NeRFs).
result ObSuRF can segment a 3D scene into objects from a single image.
3D Adversarial Autoencoder learns compact binary descriptors from 3D point clouds.
problem Learning meaningful representations of 3D shapes for various tasks.
method End-to-end Adversarial Autoencoder model trained on 3D input and output.
result 3D Adversarial Autoencoder (3dAAE) generates state-of-the-art results for 3D points clustering and retrieval.
Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional latent scenes, due to challenges in both modeling and inference. Accounting for th…
Flexible pipeline for 3D vehicle detection from 2D images.
problem Current methods lack 3D perception of vehicles and other objects.
method Adopt any 2D detection network, fuse with 3D point cloud, develop model fitting algorithm, refine with CNN.
result 3D detection results rank second among algorithms, demonstrating competencies.
Overview of 3D TQFTs and 3-manifold invariants.
problem Quantum invariants of 3-manifolds.
method Recall and review of TQFTs, fusion categories, and recent generalizations.
result Overview of various 3D TQFTs and their invariants.
Conservation laws vanishing along characteristic directions of a given system of PDEs are known as characteristic conservation laws, or characteristic integrals. In 2D, they play an important role in the theory of Darboux-integrable equations. In this paper we discuss characteristic integrals in 3D and demonstrate that…
Hamilton's Ricci flow (RF) equations were recently expressed in terms of the edge lengths of a d-dimensional piecewise linear (PL) simplicial geometry, for d greater than or equal to 2. The structure of the simplicial Ricci flow (SRF) equations are dimensionally agnostic. These SRF equations were tested numerically and…