We show that 3D gravity, in its pure connection formulation, admits a natural 6D interpretation. The 3D field equations for the connection are equivalent to 6D Hitchin equations for the Chern-Simons 3-form in the total space of the principal bundle over the 3-dimensional base. Turning this construction around one gets …
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48 results for “6D field theories”
Topological field theories of 2- and 3-forms in 6D, showing no propagating degrees of freedom.
problem Exploring field theories of 2- and 3-forms in six dimensions.
method Analyzing field theories with kinetic term and varying potential terms.
result The theories remain topological even with added potential terms, and their reductions yield 3D gravity.
Anomaly cancellation condition for M5-brane action is proven using twisted Cohomotopy.
problem Anomaly in the 6d Wess-Zumino term of M5-brane action.
method Twisted Cohomotopy theory and a twisted/parametrized Hopf invariant.
result Anomaly cancellation condition is implied by charge quantization in twisted Cohomotopy.
The abstract discusses fiber sum formulas for 4-manifolds using topological modular forms.
problem Understanding fiber sum formulas for 4-manifolds.
method Using the connection between 4-manifolds and topological modular forms from 6d (1,0) SCFTs.
result Even free theories exhibit nontrivial fiber sum formulas, sensitive to individual theories and parameters.
Extended symmetries and anomalies in compactified 6d SCFTs on various internal manifolds.
problem Understanding symmetries and anomalies in compactified 6d SCFTs.
method Extended notion of polarizations, focusing on 2D, 3D, and 4D manifolds.
result Recurring themes in compactifications, including Kaluza-Klein modes and symmetries.
Abstract M5 branes on ADE singularities yields BPS spectrum and partition functions.
problem Determine the BPS spectrum and partition functions for M5 branes on ADE singularities.
method Analyze 6d SCFTs on geometric backgrounds, using contributions from BPS strings and particles.
result Explicit expressions for BPS string and particle contributions to partition functions.
New invariants defined from 6d fivebrane theory BPS states.
problem Homological invariants of 3-manifolds.
method Physical system involving 6d fivebrane theory on 3-manifolds times a 2-disk.
result Hilbert space of BPS states categorifies various partition functions of 3d theories.
We simplify and extend a 6D conformal gravity theory to 8D, linking it to Q-curvature.
problem Constructing and understanding conformal gravity actions in different dimensions.
method Streamlined construction of 6D action, proving existence of 8D action, relating to Q-curvature.
result A unique 8D conformal gravity action exists with Einstein metrics as solutions.
Study 6D localized matter spectrum on singular Calabi-Yau 3-folds.
problem Determining 6D localized charged matter spectrum on singular spaces.
method Using string junctions and monodromy to compute massless string junctions.
result Agreement with 6D anomaly cancellation in all cases considered.
The paper proves transversality for special Lagrangian submanifolds in a 6D manifold.
problem Counting special Lagrangian submanifolds in higher dimensions.
method Proving transversality for the moduli space of perturbed special Lagrangian submanifolds using a Lagrange multipliers problem.
result The moduli space is generically a set of isolated points.
Connects 4-manifold topology to topological modular forms.
problem Understanding the topology of 4-manifolds.
method Topologically twisted compactification of 6d (1,0) theories on 4-manifolds.
result New invariant of 4-manifolds using equivariant weakly holomorphic modular forms.
Corrected an error in a 6D Nijenhuis tensor theorem.
problem Error in a 6D Nijenhuis tensor theorem.
method None specified in the abstract.
result Corrected an error in a theorem.
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.
Classifies complex structures on 6D Lie algebras as products.
problem Identifying all complex structures on 6D Lie algebras.
method Examined 6D Lie algebras of the form for integrable complex structures.
result Listed all integrable complex structures on these Lie algebras.
Study on Dirac operators on 6D manifolds with boundary.
problem Analyzing Dirac operators on manifolds with boundary.
method Establish Kastler-Kalau-Walze type theorems for Dirac and signature operators.
result Two Kastler-Kalau-Walze type theorems for twisted Dirac and signature operators.
6D manifolds with special symmetries have limited automorphism groups.
problem Understanding the maximum symmetry groups of 6D manifolds.
method Analyzing almost product structures and their automorphism groups.
result The automorphism group of 6D manifolds with non-degenerate Nijenhuis tensor has a limited dimension, with the maximum being 14.
Generic low-entropy hypersurfaces in 4-6D flow with only generic singularities.
problem Analyzing mean curvature flow of low-entropy hypersurfaces.
method Proving flow encounters only generic singularities for specific entropy conditions.
result Proves flow encounters only generic singularities for low-entropy initial data.
Modernizes higher-dimensional supergravity, linking it to flux quantization.
problem Constructing infrared completions of higher-dimensional supergravity.
method Using differential nonabelian cohomology and super-torsion constraints.
result Equivalence of solutions in different dimensions and flux quantization.
New result on energy-genus bounds for 6D symplectic Calabi-Yau manifolds.
problem Energy-genus bounds for pseudo-holomorphic curves in almost complex manifolds.
method Compactness and regularity theorems for J-holomorphic currents.
result Established a new result in dimension 6 for symplectic Calabi-Yau 6-manifolds.
Study of black hole entropy from 4d theories on hyperbolic manifolds.
problem Determining the entropy of magnetically charged black holes in .
method Analytic torsions twisted by flat connections on hyperbolic 3-manifolds, perturbative expansion of index.
result The leading part of the index matches the Bekenstein-Hawking entropy of a magnetically charged black hole.
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 . …
The paper derives curvature identities for 5D and 6D Einstein manifolds.
problem Deriving curvature identities for specific dimensions of Einstein manifolds.
method Using Patterson's curvature identities and the Chern-Gauss-Bonnet Theorem, the paper provides explicit formulae for 5D and 6D Einstein manifolds.
result The curvature identities for 5D and 6D Einstein manifolds are confirmed to be consistent with previous work.
Criterion found for blowing down in 6D symplectic geometry.
problem Blowing down criterion in 6D symplectic geometry.
method Criterion for blowing down in 6D symplectic geometry.
result Criterion established for blowing down in 6D symplectic geometry.
We propose a new description of 3d theories which do not admit conventional Lagrangians. Given a quiver and a mutation sequence on it, we define a 3d theory in such a way that the partition function of the theory coincides with the cluster partition f…
In this note we find the metric of 6-dimensional h-space of the [33] type and then determine an important projective group characteristic of this h-space.
We compute the equivariant elliptic genera of several classes of ALE and ALF manifolds using localization in gauged linear sigma models. In the sigma model computation the equivariant action corresponds to chemical potentials for U(1) currents and the elliptic genera exhibit interesting pole structure as a function of …
Classifies theories with eight supercharges using pseudo-periodic maps and Riemann surfaces.
problem Classifying theories with eight supercharges using mathematical tools.
method Assumes theories are given by genus g fibrations of Riemann surfaces, uses pseudo-periodic maps of negative type in mapping class group.
result Identifies dual graphs and 3d mirror quivers, unifies various SCFTs in combinatorial framework.
Researchers found solutions to minimal surface equations in 6D.
problem Equations of minimal surface type in six dimensions.
method Constructed nonlinear entire solutions using parametric elliptic functionals.
result Found solutions to minimal surface equations in 6D.
Towards Symmetry-sensitive Pose Estimation: A Rotation Representation for Symmetric Object Classescs.CV
We introduce SARR for symmetric object pose estimation, improving CNN performance.
problem Ambiguities in symmetric object orientations hinder deep learning pose estimation.
method Numeric rotation representation using symmetry-derived trigonometric identities.
result SARR enables standard CNNs to achieve state-of-the-art performance.
Harmonic morphisms from 7D spaces map to 6D flag manifolds.
problem Mapping from high-dimensional spaces to lower-dimensional ones.
method Distinct harmonic morphisms with minimal circle fibers.
result Infinite family of harmonic morphisms given.
We study the six-dimensional pseudo-Riemannian spaces with two time-like coordinates that admit non-homothetic infinitesimal projective transformations. The metrics are manifestly obtained and the projective group properties are determined. We also find a generic defining of projective motion in the 6-dimensional rigid…
Stable minimal hypersurfaces in math.DG
Flat stable minimal hypersurfaces found in 6D space.
problem Existence of stable minimal hypersurfaces in .
method Adapted Chodosh-Li-Minter-Stryker strategy with volume estimates.
result Complete, two-sided stable minimal hypersurfaces in are flat.
We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become related to objects and operations in dual 2d, 3d, and 4d theories. For example,…
Study of ants' movement rules on a 6D space, revealing distribution structures and singular trajectories.
problem Understanding the movement patterns of ants in a 6D space.
method Analyzing mechanical system rules to derive distribution structures and singular trajectories.
result Distributions and singular trajectories of ants' movement rules in a 6D space.
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 simplifies homotopy groups of 6D manifolds.
problem Homotopy groups of 6D manifolds.
method Double suspension homotopy decomposition.
result Easily determines - and -groups.
Flat stable minimal hypersurfaces in 5 or 6D are always flat.
problem Characterizing stable minimal hypersurfaces in high-dimensional spaces.
method Proving stability of anisotropic minimal hypersurfaces in and under certain smoothness conditions.
result Complete, stable anisotropic minimal hypersurfaces in or are flat if the anisotropic area functional is -close to the area functional.
6D nearly Kähler manifolds with actions are uniquely determined by a function on .
problem Characterizing 6D nearly Kähler manifolds with actions.
method Using a Monge-Ampère type equation on .
result 6D strict nearly Kähler manifolds are completely characterized by a function on .
Scalable approach for object pose estimation across domains.
problem Object pose estimation across different datasets and models.
method Multi-path learning: shared encoder, object-specific decoders.
result Generalizes well from synthetic to real data and across various instances.
Found a 6D Lie group with a closed geodesic.
problem Existence of closed geodesics on homogeneous Riemannian manifolds.
method Provided a specific Lie group example.
result Answered affirmatively to a question about closed geodesics on homogeneous spaces.
Local supertwistors help study 6D conformal supergravity.
problem Understanding conformal supergravity in 6D.
method Local supertwistor formalism with a superconformal connection.
result Derived geometry of (1,0) and (2,0) supergravity multiplets.
Classifies multigraphs for torus actions on 6D manifolds with isolated fixed points.
problem Classifying torus actions on 6D manifolds with isolated fixed points.
method Associate multigraphs to fixed point data, study operations, and prove classification.
result Classifies multigraphs for 6D manifolds by converting them into the empty graph.
Study of knot complements yields quantum modularity insights.
problem Understanding quantum invariants of knot complements.
method Large-N analysis of -series invariants, counts of holomorphic curves.
result Closed-form expressions for -deformed for -torus knots.
We found a 6D manifold with specific geometric properties.
problem Finding a 6D manifold with Ricci curvature ≥ 0 and infinitely generated fundamental group.
method Built a smooth complete manifold with specific geometric properties.
result Found a 6D manifold with and infinitely generated.
Study on solutions near isolated singularities in 6D Yamabe equation.
problem Behavior of solutions near isolated singularities in 6D Yamabe equation.
method Analyze asymptotic behavior of local solutions in non-conformally flat metrics.
result Solutions are asymptotically close to Fowler solutions in 6D.
Born Lie algebrasmath.DG
Born Lie algebras classified up to 6D, with integrable metrics studied.
problem Classifying and understanding Born Lie algebras.
method Bicross product construction from pseudo-Riemannian Lie algebras.
result Classification of Lie algebras up to 6D with integrable Born structures.
The paper calculates the noncommutative residue for a rescaled Dirac operator on 6D manifolds.
problem Computing the noncommutative residue for a specific Dirac operator on 6D manifolds.
method Calculations and proofs for the rescaled Dirac operator fDh on 6D compact manifolds.
result Proof of the Kastler-Kalau-Walze type theorem for the rescaled Dirac operator on 6D compact manifolds with boundary.
Global obstructions found for conformally Einstein metrics in 6D.
problem Obstructing the existence of conformally Einstein metrics in six dimensions.
method Presentation of global conformal invariants.
result Nontrivial global conformal invariant obstructing conformally Einstein metrics.