arXiv research

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 …

The paper proves transversality for special Lagrangian submanifolds in a 6D manifold.

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.

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.

Study 6D localized matter spectrum on singular Calabi-Yau 3-folds.

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…

Flat stable minimal hypersurfaces found in 6D space.

Generic low-entropy hypersurfaces in 4-6D flow with only generic singularities.

Extended symmetries and anomalies in compactified 6d SCFTs on various internal manifolds.

Study of ants' movement rules on a 6D space, revealing distribution structures and singular trajectories.

Found a 6D Lie group with a closed geodesic.

The paper derives curvature identities for 5D and 6D Einstein manifolds.

We correct an error in the second part of Theorem 3 of our original paper (arXiv:1512.07161).

Criterion found for blowing down in 6D symplectic geometry.

Abstract M5 branes on ADE singularities yields BPS spectrum and partition functions.

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. …

We found a 6D manifold with specific geometric properties.

We introduce SARR for symmetric object pose estimation, improving CNN performance.

For an almost complex structure $J$ in dimension 6 with nondegenerate Nijenhuis tensor $N_J$, the automorphism group $G=Aut(J)$ of maximal dimension is the exceptional Lie group $G_2$. In this paper we establish that the sub-maximal dimension of automorphism groups of almost complex structures with nondegenerate $N_J$,…

Study simplifies homotopy groups of 6D manifolds.

Flat stable minimal hypersurfaces in 5 or 6D are always flat.

Local supertwistors help study 6D conformal supergravity.

Classifies multigraphs for torus actions on 6D manifolds with isolated fixed points.

We simplify and extend a 6D conformal gravity theory to 8D, linking it to Q-curvature.

The paper classifies and constructs 6D GKM manifolds with 4 fixed points.

Study on solutions near isolated singularities in 6D Yamabe equation.

Born Lie algebras classified up to 6D, with integrable metrics studied.

The paper calculates the noncommutative residue for a rescaled Dirac operator on 6D manifolds.

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…

We provide a physical definition of new homological invariants $\mathcal{H}_a (M_3)$ of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on $M_3$ times a 2-disk, $D^2$, whose Hilbert space of BPS states plays the role of a basic build…

We study the twisted index of 4d $\mathcal{N}$ = 2 class S theories on a closed hyperbolic 3-manifold $M_3$. 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.

Classifies circle actions on 6D manifolds with 4 fixed points.

Develops a theorem for a 6D manifold with boundary.

Researchers compute Connes-Chamseddine cycle on 6D manifolds using noncommutative integral.

For an almost product structure $J$ on a manifold $M$ of dimension $6$ with non-degenerate Nijenhuis tensor $N_J$, we show that the automorphism group $G=Aut(M,J)$ has dimension at most 14. In the case of equality $G$ is the exceptional Lie group $G_2^*$. 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.

Study embedding of achiral Lefschetz fibrations in 6D manifolds.

A new particle filter avoids resampling to improve state estimation in high dimensions.

We introduce a scalable approach for object pose estimation trained on simulated RGB views of multiple 3D models together. We learn an encoding of object views that does not only describe an implicit orientation of all objects seen during training, but can also relate views of untrained objects. Our single-encoder-mult…

6D symplectic manifold with many homologous but inequivalent submanifolds.

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,…

Classifies 6D homogeneous spaces with holomorphically trivial canonical bundle.

The paper constructs complex hyperbolic 2-manifolds with one cusp.

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 …

In neural networks, it is often desirable to work with various representations of the same space. For example, 3D rotations can be represented with quaternions or Euler angles. In this paper, we advance a definition of a continuous representation, which can be helpful for training deep neural networks. We relate this t…

We study knots in 3d Chern-Simons theory with complex gauge group $SL(N,\mathbb{C})$, in the context of its relation with 3d $\mathcal{N}=2$ theory (the so-called 3d-3d correspondence). The defect has either co-dimension 2 or co-dimension 4 inside the 6d $(2,0)$ theory, which is compactified on a 3-manifold $\hat{M}$. …