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.
Paper connects 3D gravity averages to 2D CFT correlators.
problem Understanding 3D gravity partition functions.
method 3D topological field theories and mapping class group averages.
result Established a correspondence between 3D gravity averages and 2D CFT correlators.
We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d N=2 theories where such structures a priori are not manifest. These modular structures include: mock modular forms, SL(2,Z) Weil representations, quantum mo…
We describe two simple obstructions to the existence of Ricci-flat Kahler cone metrics on isolated Gorenstein singularities or, equivalently, to the existence of Sasaki-Einstein metrics on the links of these singularities. In particular, this also leads to new obstructions for Kahler-Einstein metrics on Fano orbifolds.…
In this paper we address several aspects of flat Bogomolnyi-Prasad-Sommerfeld (BPS) domain walls together with their Lorentz invariant vacua of 4d N=1 supergravity coupled to a chiral multiplet. The scalar field spans a one-parameter family of 2d Kähler manifolds satisfying a Kähler-Ricci flow equation. We find that BP…
A new complex space resolves projective structures on surfaces.
problem Understanding projective structures on compact surfaces.
method Proposed a complex analytic space Pg and analyzed it for g=1. result The space Pg naturally resolves the orbifold locus of Ag=1. We formulate and solve the analog of the universal Conformal Ward Identity for the stress-energy tensor on a compact Riemann surface of genus g>1, and present a rigorous invariant formulation of the chiral sector in the induced two-dimensional gravity on higher genus Riemann surfaces. Our construction of the action f…
Generalizes embedding formalism for CFTs on curved backgrounds.
problem Capturing CFTs on curved backgrounds and non-trivial states.
method Using ambient metric and geometric invariants of the ambient space.
result Exact agreement with holographic computations and thermal OPEs.
Geometries and dual field theories linked by AdS/CFT.
problem Understanding the AdS/CFT correspondence.
method Geometric extremization principles informed by physical considerations.
result Key role of Sasaki-Einstein and GK geometry.
To pave the way for the journey from geometry to conformal field theory (CFT), these notes present the background for some basic CFT constructions from Calabi-Yau geometry. Topics include the complex and Kaehler geometry of Calabi-Yau manifolds and their classification in low dimensions. I furthermore discuss CFT const…
We find a Sasaki-Einstein metric from a CFT state in AdS5.
problem Finding a Sasaki-Einstein metric from a CFT state.
method Using supergravity in AdS5 and a superconformal gauge theory in R3,1 in the t'Hooft limit. result Explicit finite N-approximations to the Sasaki-Einstein metric. Study uses holography to analyze entanglement entropy in deformed CFTs.
problem Analyzing entanglement entropy in $Tar{T}$-deformed CFTs.
method Holographic methods and direct bulk gravitational action evaluation.
result Agreement with known results for entanglement entropy.
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 …
New formalism solves kinematical constraints in curved backgrounds and non-trivial states.
problem Solving kinematical constraints due to Weyl invariance in curved backgrounds and non-trivial states.
method Constructing Weyl covariant geometric objects and identifying them as building blocks of correlation functions.
result Exact agreement with thermal OPEs and holographic computations for thermal 2-point functions.
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.
We discuss classical gravitational aspects of the AdS/CFT correspondence, with the aim of obtaining a rigorous (mathematical) understanding of the semi-classical limit of the gravitational partition function. The paper surveys recent progress in the area, together with a selection of new results and open problems.
We examine the Banados-Teitelboim-Zanelli (BTZ) black hole in terms of the information geometry and consider what kind of quantum information produces the black hole metric in close connection with the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence. We find a Hessian potential that exactly produce…
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…
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…
Motivated by recent proposals for a de Sitter version of the AdS/CFT correspondence, we give some topological restrictions on spacetimes of de Sitter type, i.e., spacetimes with Λ>0, which admit a regular past and/or future conformal boundary. For example we show that if Mn+1, n≥2, is a globally hyperbolic…
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.
Geometrically constructs twist-field correlation functions in CFT.
problem Understanding entanglement entropy in quantum systems.
method Using Cauchy-Hadamard renormalization of Polyakov anomaly integral on surfaces with conical singularities.
result Provides a purely mathematical interpretation of entanglement entropy results.
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…
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…
Researchers construct a probabilistic model for a WZW theory on hyperbolic space and link it to Liouville theory.
problem Rigorous probabilistic construction of WZW models on curved spaces.
method Path integral approach on closed Riemann surfaces twisted by gauge fields.
result Correspondence between correlation functions of H3-WZW and Liouville CFT. 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…