Stability of chiral rings in N=1 theories linked to K-stability of X.
problem Understanding the stability of chiral rings in N=1 theories.
method Introducing test chiral rings and generalized maximization, studying N=1 field theory derived from D3 branes probing a three-fold singularity X.
result K-stability of X is equivalent to the stability of chiral ring of the corresponding field theory.
In this paper, we study the perturbative aspects of the half-twisted variant of Witten's topological A-model coupled to a non-dynamical gauge field with Kahler target space X being a G-manifold. Our main objective is to furnish a purely physical interpretation of the equivariant cohomology of the chiral de Rham complex…
Tying knots and linking microscopic loops of polymers, macromolecules, or defect lines in complex materials is a challenging task for material scientists. We demonstrate the knotting of microscopic topological defect lines in chiral nematic liquid crystal colloids into knots and links of arbitrary complexity by using l…
This research builds foundations for D3-branes in string theory.
problem Constructing dynamical fermionic D3-branes in string theory.
method Develops algebraic and geometric foundations, hybrid connections, and chiral maps.
result Provides a framework for constructing supersymmetric actions.
Two new minor minimal intrinsically chiral graphs identified.
problem Identifying intrinsically chiral graphs in molecular structures.
method Analyzing graph symmetry and embedding properties.
result Found two new minor minimal intrinsically chiral graphs Γ7 and Γ8. Chiral string integrands simplify to ambitwistor string integrands in the tensionless limit.
problem Understanding the relationship between chiral and ambitwistor string integrands.
method Analyzing the tensionless limit of chiral superstring integrands.
result Chiral superstring integrands reduce to ambitwistor string integrands in the tensionless limit.
Paper restricts chirally cosmetic surgeries on knots.
problem Chirally cosmetic surgeries on knots.
method Examined exceptional or half-integral chirally cosmetic surgeries.
result Obtained several restrictions on chirally cosmetic surgeries.
3-manifolds are chiral if not finitely covered by sphere or product.
problem Characterizing chiral 3-manifolds.
method Analyzing finite covers and self-homeomorphisms.
result Prime 3-manifolds not finitely covered by sphere or product are chiral.
Tensor measures chirality for curves, even those with rough edges.
problem Quantifying chirality for complex, possibly irregular curves.
method Developed a tensorial chirality measure for rigid filaments and curves.
result A curve's chirality can be determined by its twist about perpendicular axes.
Study shows most odd pretzel knots don't allow chirally cosmetic surgeries.
problem Characterizing chirally cosmetic surgeries on specific knot types.
method Recent methods of Ichihara, Ito, and Saito applied to genus 2 and 3 alternating odd pretzel knots.
result Most genus 2 and 3 alternating odd pretzel knots do not admit chirally cosmetic surgeries.
This paper classifies chiral graphs up to size 12.
problem Understanding the chirality of simple graphs to predict molecular behavior.
method Classifying minor minimal intrinsically chiral graphs among simple graphs of size up to 12.
result Complete set of minor minimal graphs for intrinsic properties of chiral molecules.
Study finds chirally cosmetic surgeries on knots and manifolds, contradicting previous conjectures.
problem Disprove conjectures about chirally cosmetic surgeries and purely cosmetic surgeries.
method Construct infinite families of chirally cosmetic surgeries and purely cosmetic surgeries on specific geometric objects.
result Found chirally cosmetic surgeries and purely cosmetic surgeries that contradict previous conjectures.
Study chirally cosmetic surgeries on knots with constraints and invariants.
problem Understanding chirally cosmetic surgeries on knots.
method Use original and SL(2,C) Casson invariants. result Complete classification of chirally cosmetic surgeries on genus one alternating knots.
Study describes global sections of chiral de Rham complex on compact Ricci-flat Kähler manifolds.
problem None explicitly stated; focuses on description of global sections.
method Complete description of vertex algebra of global sections.
result Complete description of vertex algebra of global sections of chiral de Rham complex.
Ambitwistor string matches superstring chiral integrands at zero tension.
problem Matching scattering amplitudes in superstring theory and ambitwistor string theory.
method Direct computation and reduction to ordinary moduli space.
result Chiral half integrands of superstring match those of ambitwistor string in the zero tension limit.
Study shows (p,q)-cable knots cannot undergo certain types of surgery.
problem Chirally cosmetic surgery on (p,q)-cable knots. method Analyzes JSJ pieces and torus exteriors to prove non-existence of chirally cosmetic surgery.
result Proves (p,q)-cable knots do not admit chirally cosmetic surgery under certain conditions. Given a two-dimensional quantum field theory with (0,2) supersymmetry, one can construct a chiral (or vertex) algebra. The chiral algebra of a (0,2) supersymmetric sigma model is, perturbatively, the cohomology of a sheaf of chiral differential operators on a string Kähler manifold. However, it vanishes in some cases w…
Study improves chiral photonic metasurface design using neural networks and genetic algorithms.
problem Optimizing chiral photonic metasurfaces for high chiral dichroism and reflectivity.
method Combines neural network and genetic algorithm approaches with improved fitness functions and data augmentation.
result Demonstrates a significant increase in chiral dichroism and reflectivity.
We classify which complete multipartite graphs are intrinsically chiral.
Constructs chiral rational homology spheres with hyperbolic groups.
problem Existence of strongly chiral rational homology spheres with hyperbolic fundamental groups.
method Construction of rational homology spheres using r-spins and investigation of self-map degrees. result Strongly chiral rational homology spheres with hyperbolic fundamental groups constructed.
Study calculates global sections on complex curves.
problem Global sections of chiral de Rham complexes on complex curves.
method Calculation on closed complex curves with genus g ≥ 2.
result Space of global sections determined.
Chirality affects the curvature of molecular networks, influencing their shape and stability.
problem Understanding how chirality influences the curvature of molecular networks.
method Langevin dynamics simulations and constrained gradient optimization of square lattice networks.
result Linking chirality dictates the sign of Gaussian curvature in molecular chainmail networks.
The study confirms that most positive 2-bridge knots up to 31 crossings do not have chirally cosmetic surgeries.
problem Determining which positive 2-bridge knots up to 31 crossings have chirally cosmetic surgeries.
method Using the obstruction formula from arXiv:2112.03144 and a Python program to compute classical knot invariants.
result Positive 2-bridge knots up to 31 crossings, except (2,2n+1) torus knots, do not admit chirally cosmetic surgeries. Paper studies knotoid chirality using shadow quandle colorings and invariants.
problem Distinguishing knotoids from their mirrors.
method Shadow quandle colorings and cocycle invariants.
result Knotoid 31 is shown to be chiral. It is known that the bundle of Dirac spinors is produced as a direct sum of two bundles - the bundle of chiral spinors and its Hermitian conjugate bundle. In this paper some aspects of metric connections for chiral and Dirac spinors are resumed and their relation is studied.
Designs chiral photonic structures using machine learning for efficient optical properties.
problem Optimizing chiral photonic nanostructures for light-matter interactions.
method Evolutionary algorithm and neural network approach for rapid optimization.
result Frequency-dependent modification in reflected light's degree of circular polarization.
We explore two-dimensional sigma models with (0,2) supersymmetry through their chiral algebras. Perturbatively, the chiral algebras of (0,2) models have a rich infinite-dimensional structure described by the cohomology of a sheaf of chiral differential operators. Nonperturbatively, instantons can deform this structure …
Study finds new knot distances and chirally cosmetic bands using grid diagrams.
problem Computing distances and identifying chirally cosmetic bands between knots.
method Using grid diagrams to explore non-coherent band attachments between knots.
result Discovery of 33 new H(2)-distance one pairs for knots up to 8 crossings.
Develops a braid-theoretic framework to analyze chirality in molecular knots.
problem Analyzing chirality in molecular knots constructed using circuit topology.
method Translated circuit topology approach to knot engineering into braid-theoretic framework, calculating Jones polynomial for binary combinations.
result Jones polynomial provides a powerful tool for analyzing chirality of molecular knots.
Study shows most knots up to 10 crossings can't be chirally cosmetic.
problem Identifying knots that can undergo chirally cosmetic surgeries.
method Used invariants from 3-manifold theory, including quantum SO(3)-invariant and Heegaard Floer homology.
result Approximately 75% of knots up to 10 crossings do not admit chirally cosmetic surgeries.
Massive fermions help understand index theorems without chiral symmetry.
problem Understanding index theorems in massive fermion systems.
method Reformulate chiral anomaly and index theorems with massive Dirac operators.
result Nontrivial mathematical relations between massless and massive fermions.
We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation-reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does not admit a self-map of degree -1. We prove that there are strongly chiral, smoo…
The abstract discusses connecting quantum mechanics and algebraic index theories.
problem Exploring the connection between quantum mechanics and algebraic index theories.
method Explains how the classical algebraic index theorem can be proved in terms of BV quantization of topological quantum mechanics and 2d chiral CFT.
result Shows how the generating function of all genus Gromov-Witten invariants on elliptic curves is mirror equivalent to an elliptic chiral index.
Given a smooth G-vector bundle E→M with a connection ∇, we propose the construction of a sheaf of vertex algebras Ech(E,∇), which we call a \textit{chiral vector bundle}. Ech(E,∇) contains as subsheaves the sheaf of superalgebras Ω⊗Γ(SE⊗ΛE) and the…
Study calculates global sections on special geometric spaces.
problem Calculating global sections on compact Ricci-flat Kähler manifolds.
method Expressed as an invariant subspace of a βγ-bc system under Lie algebra action.
result Space of global sections is an invariant subspace.
We explore the nonperturbative aspects of the chiral algebras of N = (0,2) sigma models, which perturbatively are intimately related to the theory of chiral differential operators (CDOs). The grading by charge and scaling dimension is anomalous if the first Chern class of the target space is nonzero. This has some nont…
This paper extends T-duality to exotic chiral de Rham complexes.
problem Extending T-duality to new mathematical structures.
method Introducing exotic chiral de Rham complexes and isomorphisms.
result Established an isomorphism between chiral de Rham complexes.
New Heegaard Floer homology findings block chirally cosmetic surgeries.
problem Chirally cosmetic surgeries on knots and manifolds.
method Heegaard Floer homology, immersed curve formulations, and surgery formula.
result New obstructions to chirally cosmetic surgeries identified.
It is known that the first two-variable Links--Gould quantum link invariant LG≡LG2,1 is more powerful than the HOMFLYPT and Kauffman polynomials, in that it distinguishes all prime knots (including reflections) of up to 10 crossings. Here we report investigations which greatly expand the set of evaluations o…
According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold up to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and to obtain a pure deformati…
Paper constructs and proves existence of chiral triply-periodic minimal surfaces.
problem Existence of chiral triply-periodic minimal surfaces of genus 4.
method Construction based on dual qtz--qzd nets, existence proof using Weierstrass method on branched torus.
result Family of chiral triply-periodic minimal surfaces of genus 4 constructed and proved to exist.
Study sigma-models on flag manifolds with curvature zero and relate to chiral models.
problem Understanding sigma-models on flag manifolds with zero curvature.
method Use zero-curvature representation and nilpotent orbits theory.
result Established relation between flag manifold sigma-models and principal chiral models.
No chiral field theory for quantum spin chain limits.
problem Chiral conformal field theory limits of quantum spin chains.
method Block spin renormalization, Hamiltonian analysis.
result No continuous limit to chiral field theory.
Geometric model for supergravity on Riemann surfaces solves a long-standing conjecture.
problem Constructing a geometric model for N=1 supergravity on Riemann surfaces. method Developed a novel geometric structure called chiral triple, reduced Killing spinor equations to Riemann surfaces, and characterized solutions.
result Proved the existence of N=1 chiral geometric supergravity on spin four-manifolds. The chiral de Rham complex of Malikov, Schechtman, and Vaintrob, is a sheaf of differential graded vertex algebras that exists on any smooth manifold Z, and contains the ordinary de Rham complex at weight zero. Given a closed 3-form H on Z, we construct the twisted chiral de Rham differential DH, which coincid…
We investigate properties of spatial graphs on the standard torus. It is known that nontrivial embeddings of planar graphs in the torus contain a nontrivial knot or a nonsplit link due to [1],[2]. Building on this and using the chirality of torus knots and links [3],[4], we prove that nontrivial embeddings of simple 3-…
Study Dirac-Einstein equations on manifolds with boundary, focusing on constant volume and chiral conditions.
problem Analyzing Dirac-Einstein equations on manifolds with boundary conditions.
method Characterizing bubbling phenomena and classifying ground state bubbles, proving an Aubin-type inequality.
result Proved an Aubin-type inequality and existence result.
We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived in a mathematically…