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.
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.
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.
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 N=(1,0) SCFTs on geometric backgrounds, using contributions from BPS strings and particles. result Explicit expressions for BPS string and particle contributions to partition functions.
We propose a method to assign non-unitary TQFTs to certain SCFTs, deriving bounds and examples.
problem Assigning non-unitary TQFTs to specific SCFTs of rank 0.
method Using degenerate limits of SCFTs, extracting modular data from supersymmetric partition functions, and proposing a dictionary.
result Deriving a lower bound on the free energy of SCFTs and showing it is saturated by a specific SCFT.
New K3 metrics derived from torus orbifold loci.
problem Finding new K3 metrics near torus orbifold loci.
method Hyper-Kähler quotients and BPS spectra analysis.
result Infinitely many constraints on BPS spectra of SCFTs.
5D SCFTs can have confining vacua with strings and unbroken symmetries.
problem Investigating phases of 5D SCFTs by varying couplings.
method Using geometric realisation of M-theory on metrically conical Calabi-Yau threefolds.
result Many 5D SCFTs have couplings leading to massive, confining vacua with strings and unbroken symmetries.
We analyse the moduli spaces of superconformal field theories (SCFTs). For N=2 we find an enhanced moduli space which in geometrical terms corresponds to tori with two independent complex structures. To explain the precise relation with the moduli space of SCFTs on K3 surfaces as described by Aspinwall and Morrison, we…
Extract anomalies from 5D SCFTs using extra-dimensional η-invariants.
problem Anomalies in quantum field theories.
method Use extra-dimensional η-invariants to bypass traditional blowup techniques.
result Anomalies can be determined directly from η-invariants of asymptotic boundaries.
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 …
We use the formalism of generalized geometry to study the generic supersymmetric AdS_5 solutions of type IIB supergravity that are dual to N=1 superconformal field theories (SCFTs) in d=4. Such solutions have an associated six-dimensional generalized complex cone geometry that is an extension of Calabi-Yau cone geometr…
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 …
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.
One of the main challenges in 3d-3d correspondence is that no existent approach offers a complete description of 3d N=2 SCFT T[M3] --- or, rather, a "collection of SCFTs" as we refer to it in the paper --- for all types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres, and hyperbolic surgerie…
We consider supersymmetric AdS3×Y7 and AdS2×Y9 solutions of type IIB and D=11 supergravity, respectively, that are holographically dual to SCFTs with (0,2) supersymmetry in two dimensions and N=2 supersymmetry in one dimension. The geometry of Y2n+1, which can be defined for $…
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 SL(2,Z) monodromy to compute massless string junctions. result Agreement with 6D anomaly cancellation in all cases considered.
A new algebraic method extracts symmetry anomalies from 5D SCFTs.
problem Extracting global symmetry anomalies from 5D superconformal field theories.
method Path algebra of branes probing Calabi-Yau cones provides a complementary approach.
result Combinatorial approach to symmetry anomalies in 5D SCFTs.
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).
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…
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.
Flat stable minimal hypersurfaces found in 6D space.
problem Existence of stable minimal hypersurfaces in R6. method Adapted Chodosh-Li-Minter-Stryker strategy with volume estimates.
result Complete, two-sided stable minimal hypersurfaces in R6 are flat. Novel mathematical approach using resurgent analysis reveals new structures in complex Chern-Simons theory.
problem Curious bijection in vertex algebras and SCFTs.
method Resurgent analysis, numerical algorithms, singularity elimination.
result New structures and patterns in complex Chern-Simons theory on hyperbolic 3-manifolds.
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 K- and KO-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 R5 and R6 under certain smoothness conditions. result Complete, stable anisotropic minimal hypersurfaces in R5 or R6 are flat if the anisotropic area functional is C4-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.
New cohomology η for deformed Sasaki-Einstein manifolds derived from Dolbeault cohomology.
problem Developing a new cohomology structure for deformed Sasaki-Einstein manifolds.
method Introducing η-cohomology defined by a CR structure and a holomorphic function f with non-vanishing η≡df. result Established a direct relation between the cyclic homologies of the Calabi-Yau algebra and the η-cohomology groups. 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.
Generalized Calabi-Yau structures, a notion recently introduced by Hitchin, are studied in the case of K3 surfaces. We show how they are related to the classical theory of K3 surfaces and to moduli spaces of certain SCFT as studied by Aspinwall and Morrison. It turns out that K3 surfaces and symplectic structures are b…
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 Ric≥0 and π1(M6)=Q/Z 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.
We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional N=2 gauge theories. Under this duality, standard operations on triangulated 3-manifolds and various invariants thereof (classical as well as quantum) find a natural interpretation in field theory. For example, independ…
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 N = 2 class S theories on a closed hyperbolic 3-manifold M3. 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 CP3. 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 J on a manifold M of dimension 6 with non-degenerate Nijenhuis tensor NJ, 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 G2∗. 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 D6=D2imesD4.