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.
In this paper, we define the Green function for the Dirac operator under two local boundary conditions: the condition associated with a chirality operator (also called the chiral bag boundary condition) and the $\MIT$ bag boundary condition. Then we give some applications of these constructions for each Green function.…
Study of Dirac operator with chiral boundary conditions on spin manifolds.
problem Reconstructing metrics and connections from boundary data.
method Defining boundary conjugation map and showing its symbolic determination.
result Reconstruction of Riemannian manifolds and spin structures from boundary data.
On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of the Dirac operator under the chiral bag boundary condition. More precisely, we s…
Authors compute anomalies for fermions in 3, 4, and 5 dimensions.
problem Quantum anomalies in fermions with boundaries in odd dimensions.
method Explicit computation of anomalies for fermions in dimensions 3, 4, and 5.
result New boundary terms for chiral anomaly in 4 dimensions.
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.
Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and chiral conditions). This result is a generalisation of Friedrich's inequality for …
In this paper, we prove the Hijazi inequality on compact Riemannian spin manifolds under two boundary conditions: the condition associated with a chirality operator and the Riemannian version of the $\MIT$ bag condition. We then show that the limiting-case is characterized as being a half-sphere for the first condition…
Paper finds solutions to a complex equation on surfaces with boundary conditions.
problem Existence of solutions to a super-Liouville equation on compact Riemannian surfaces with boundary.
method Introduced a weighted Dirac operator and constructed a Nehari manifold to show existence of non-trivial solutions.
result Existence of non-trivial solutions to the super-Liouville equation.
We investigate the gauging of the Wess-Zumino term of a sigma model with boundary. We derive a set of obstructions to gauging and we interpret them as the conditions for the Wess-Zumino term to extend to a closed form in a suitable equivariant relative de Rham complex. We illustrate this with the two-dimensional sigma …
The paper proves a positive mass theorem for non-compact static domains in hyperbolic space.
problem Proving a positive mass theorem for non-compact static domains in hyperbolic space.
method Formulating and proving a positive mass theorem under natural dominant energy conditions, using elliptic boundary conditions on spinors.
result Retrieve a sharper version of a recent result by Souam about the rigidity of non-compact static domains.
3D dual field theories for Virasoro minimal models constructed using Seifert fiber spaces.
problem Constructing 3D dual field theories for Virasoro minimal models.
method 3D-3D correspondence and Seifert fiber spaces.
result 3D dual field theories constructed for Virasoro minimal models.
WZW models are abstract conformal field theories with an infinite dimensional symmetry which accounts for their integrability, and at the same time they have a sigma model description of closed string propagation on group manifolds which, in turn, endows the models with an intuitive geometric meaning. We exploit this d…
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 …
Lower bounds for Dirac eigenvalues on manifolds with boundary.
problem Finding lower bounds for eigenvalues of the Dirac operator on manifolds with boundary.
method Using the relative Yamabe constant to derive a conformal lower bound.
result Equality in the lower bound holds if and only if the manifold is a hemisphere and the eigenfunction is a Killing spinor.
We construct a global geometric model for the bosonic sector and Killing spinor equations of four-dimensional N=1 supergravity coupled to a chiral non-linear sigma model and a Spin0c structure. The model involves a Lorentzian metric g on a four-manifold M, a complex chiral spinor and a map $\varph…
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.
We define a notion of stability for chiral ring of four dimensional N=1 theory by introducing test chiral rings and generalized a maximization. We conjecture that a chiral ring is the chiral ring of a superconformal field theory if and only if it is stable. We then study N=1 field theory derived from D3 branes probing …
We consider a Dirac-type operator DP on a vector bundle V over a compact Riemannian manifold (M,g) with a nonempty boundary. The operator DP is specified by a boundary condition $P(u|_{\p M})=0$ where P is a projector which may be a non-local, i.e. a pseudodifferential operator. We assume the existence of a…
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 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.
We classify which complete multipartite graphs are intrinsically chiral.
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…
New algorithm constructs characters of rational VOAs from knot complements.
problem Constructing characters of rational VOAs from knot complements.
method 3D N=2 gauge theories, Dimofte-Gaiotto-Gukov construction, 3D N=4 rank-0 SCFT, topological twist. result New Nahm-sum-like expressions for Virasoro minimal model characters.
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.
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.
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.
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. We show that a (p,q)-cable of a non-trivial knot K does not admit chirally cosmetic surgery for q=2, or q=2 with additional assumptions. In particular, we show that (p,q)-cable of non-trivial knot K does not admit chirally cosmetic surgery as long as the JSJ piece of knot exterior does not contain $(2,r…
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.
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.
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…
We study chirally cosmetic surgeries, that is, a pair of Dehn surgeries on a knot producing homeomorphic 3-manifolds with opposite orientations. Several constraints on knots and surgery slopes to admit such surgeries are given. Our main ingredients are the original and the SL(2,C) version of Casson invariant…
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…
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…