arXiv research

Chiral string integrands simplify to ambitwistor string integrands in the tensionless limit.

Ambitwistor string matches superstring chiral integrands at zero tension.

Local index theorem for chiral geometric operators proved using heat kernel.

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…

In this paper, we investigate simultaneous properties of a convex integrand $γ$ and its dual $δ$. The main results are the following three. (1) For a $C^\infty$ convex integrand $γ: S^n\to \mathbb{R}_+$, its dual convex integrand $δ: S^n\to \mathbb{R}_+$ is of class $C^\infty$ if and only if $γ$ is a strictly convex in…

In this paper, the following three are shown. (1) For a $C^\infty$ convex integrand $γ: S^n\to \mathbb{R}_+$, its dual convex integrand $δ: S^n\to \mathbb{R}_+$ is of class $C^\infty$. (2) For a stable convex integrand $γ: S^n\to \mathbb{R}_+$, its dual convex integrand $δ: S^n\to \mathbb{R}_+$ is stable. (3) Let $γ: S…

Two new minor minimal intrinsically chiral graphs identified.

Kernel-based quadrature rules are becoming important in machine learning and statistics, as they achieve super-$\sqrt{n}$ convergence rates in numerical integration, and thus provide alternatives to Monte Carlo integration in challenging settings where integrands are expensive to evaluate or where integrands are high d…

Paper restricts chirally cosmetic surgeries on knots.

3-manifolds are chiral if not finitely covered by sphere or product.

Quantum speedup for Monte Carlo integration reduces integrand calls.

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 …

Tensor measures chirality for curves, even those with rough edges.

Study shows most odd pretzel knots don't allow chirally cosmetic surgeries.

In this paper, it is shown that the set consisting of stable convex integrands $S^n\to \mathbb{R}_+$ is open and dense in the set consisting of $C^\infty$ convex integrands with respect to Whitney $C^\infty$ topology. Moreover, an application of the proof of this result is also shown.

This paper classifies chiral graphs up to size 12.

Study finds chirally cosmetic surgeries on knots and manifolds, contradicting previous conjectures.

Study describes global sections of chiral de Rham complex on compact Ricci-flat Kähler manifolds.

In anomaly-free quantum field theories the integrand in the bosonic functional integral--the exponential of the effective action after integrating out fermions--is often defined only up to a phase without an additional choice. We term this choice ``setting the quantum integrand''. In the low-energy approximation to M-t…

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…

Study improves chiral photonic metasurface design using neural networks and genetic algorithms.

Study calculates global sections on complex curves.

Constructs chiral rational homology spheres with hyperbolic groups.

Chirality affects the curvature of molecular networks, influencing their shape and stability.

The study confirms that most positive 2-bridge knots up to 31 crossings do not have chirally cosmetic surgeries.

We show that a $(p,q)$-cable of a non-trivial knot $K$ does not admit chirally cosmetic surgery for $q\neq 2$, 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.

In this paper, it is shown that a Wulff shape is strictly convex if and only if its convex integrand is of class $C^1$. Moreover, applications of this result are given.

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.

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.

Develops a braid-theoretic framework to analyze chirality in molecular knots.

Study shows most knots up to 10 crossings can't be chirally cosmetic.

Massive fermions help understand index theorems without chiral symmetry.

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 $SL(2,\mathbb{C})$ version of Casson invariant…

The abstract discusses connecting quantum mechanics and algebraic index theories.

Given a smooth $G$-vector bundle $E \to M$ with a connection $\nabla$, we propose the construction of a sheaf of vertex algebras $\mathcal{E}^{ch(E,\nabla)}$, which we call a \textit{chiral vector bundle}. $\mathcal{E}^{ch(E,\nabla)}$ contains as subsheaves the sheaf of superalgebras $Ω\otimes Γ(SE \otimes ΛE)$ 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…

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.

New Heegaard Floer homology findings block chirally cosmetic surgeries.

It is known that the first two-variable Links--Gould quantum link invariant $LG\equiv LG^{2,1}$ 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…

Novel approach for estimating conditional expectations using Bayesian quadrature.

Paper constructs and proves existence of chiral triply-periodic minimal surfaces.