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”
The full 6d Hopf-Wess-Zumino term in the action functional for the M5-brane is anomalous as traditionally defined. What has been missing is a condition implying the higher analogue of level quantization familiar from the 2d Wess-Zumino term. We prove that the anomaly cancellation condition is implied by the hypothesis …
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.
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.
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.
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.
We correct an error in the second part of Theorem 3 of our original paper (arXiv:1512.07161).
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.
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 build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1,0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0,1) supersymmetry and, possibly, a residual flavor symmetry. …
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 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…
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.
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.
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.
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.
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.
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.
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.
We study the twisted index of 4d = 2 class S theories on a closed hyperbolic 3-manifold . Via 6d picture, the index can be written in terms of topological invariants called analytic torsions twisted by irreducible flat connections on the 3-manifold. Using the topological expression, we determine the …
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.
Classifies circle actions on 6D manifolds with 4 fixed points.
problem Classifying circle actions on 6D manifolds with specific fixed points.
method Analyzes fixed point data and proves agreement with known actions.
result Agrees with actions on 6-spheres or .
Develops a theorem for a 6D manifold with boundary.
problem No specific problem stated; focuses on extending a theorem.
method Extends a Kastler-Kalau-Walze type theorem to 6D almost product Riemannian spin manifolds with boundary.
result Proves a Kastler-Kalau-Walze type theorem for 6D manifolds.
Researchers compute Connes-Chamseddine cycle on 6D manifolds using noncommutative integral.
problem Computing the Connes-Chamseddine cycle for 6D manifolds.
method Using noncommutative integral on 6D manifolds, they compute the cycle.
result The Connes-Chamseddine cycle on 6D manifolds is computed.
For an almost product structure on a manifold of dimension with non-degenerate Nijenhuis tensor , we show that the automorphism group has dimension at most 14. In the case of equality is the exceptional Lie group . The next possible symmetry dimension is proved to be equal to 10…
The paper studies perturbations of de Rham Hodge operators on manifolds with or without boundaries.
problem Analyzing perturbations of de Rham Hodge operators on manifolds with boundaries.
method Lichnerowicz type formulas and Kastler-Kalau-Walze type theorems for 4D and 6D compact manifolds with or without boundaries.
result Proves Kastler-Kalau-Walze type theorems for perturbations of de Rham Hodge operators on 4D and 6D manifolds with or without boundaries.
Study embedding of achiral Lefschetz fibrations in 6D manifolds.
problem Embedding achiral Lefschetz fibrations in 6D manifolds.
method Analyzing Lefschetz fibrations bounding open books and embedding them in 6D manifolds.
result Every achiral Lefschetz fibration with hyperelliptic monodromy admits LF embedding in .
Almost complex structures in 6D with nondegenerate Nijenhuis tensors and large symmetry groupsmath.DG
For an almost complex structure in dimension 6 with nondegenerate Nijenhuis tensor , the automorphism group of maximal dimension is the exceptional Lie group . In this paper we establish that the sub-maximal dimension of automorphism groups of almost complex structures with nondegenerate ,…
6D symplectic manifold with many homologous but inequivalent submanifolds.
problem Finding many symplectic submanifolds in a 6D manifold.
method Hyperelliptic Lefschetz fibrations on 4-manifolds.
result Infinitely many mutually homologous but homotopy inequivalent submanifolds.
The paper constructs complex hyperbolic 2-manifolds with one cusp.
problem Creating complex hyperbolic 2-manifolds with one cusp.
method Explicit geometric construction of smooth projective surfaces and curves.
result Produces one-cusped complex hyperbolic 2-manifolds of arbitrary large volume.
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 …
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.
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 . …
Researchers found two types of graphs for 6D torus manifolds with Euler number 6.
problem Identifying and constructing 6D almost complex torus manifolds with specific Euler numbers.
method Examined labeled directed graphs associated with fixed points and isotropy spheres, used to construct manifolds and determine Chern numbers.
result Proved the existence of two types of 6D almost complex torus manifolds with Euler number 6.
The article classifies 6D flat solvmanifolds by analyzing conjugacy classes of matrices.
problem Classifying 6-dimensional splittable flat solvmanifolds.
method Analyzing conjugacy classes of integer matrices of finite order in dimensions 4 and 5.
result Classification of 6-dimensional splittable flat solvmanifolds.
The paper classifies and constructs 6D GKM manifolds with 4 fixed points.
problem Classifying and constructing 6-dimensional GKM manifolds with 4 fixed points.
method Classification of GKM graphs and construction of manifolds.
result Six types of 6D GKM manifolds with 4 fixed points are identified.
In this paper, we investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. We show that a gradient descent algorithm with initial value obtained from a spectral method can, in particular, reconstruct a tensor of multilinear ranks $…
The paper classifies circle actions on 6D manifolds with isolated fixed points.
problem Classifying circle actions on 6D manifolds with isolated fixed points.
method Performing equivariant connected sums at fixed points with specific manifolds.
result A sequence of operations can reduce the fixed point data to the empty collection.
Constructing of molecular structural models from Cryo-Electron Microscopy (Cryo-EM) density volumes is the critical last step of structure determination by Cryo-EM technologies. Methods have evolved from manual construction by structural biologists to perform 6D translation-rotation searching, which is extremely comput…
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…
Teichmüller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2,R) Chern-Simons theory. To physicists, it is known in particular in the context of 3d-3d correspondence and also in the holographic description of Virasoro conform…