Motivated by recent developments in the AdS/CFT correspondence, we provide several alternative bulk descriptions of an arbitrary Wilson loop operator in Chern-Simons theory. Wilson loop operators in Chern-Simons theory can be given a description in terms of a configuration of branes or alternatively anti-branes in the …
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48 results for “Wilson loop”
Wilson loops in supersymmetric Yang-Mills theory correspond at strong coupling to extremal surfaces in . We study a class of extremal surfaces known as special Legendrian submanifolds. The "hemisphere" corresponding to the circular Wilson loop is an example of a special Legendrian submanifold, and w…
Researchers compute knot invariants in Seifert manifolds using Wilson loops.
problem Calculating BPS invariants for knots in Seifert manifolds.
method Analytically continued Chern-Simons level and representation from Wilson loop operator.
result Homological blocks for knots in Seifert manifolds and Seifert integer homology spheres.
We give, using an explicit expression obtained in [V. Jones, Ann. of Math. 126, 335 (1987)], a basic hypergeometric representation of the HOMFLY polynomial of torus knots, and present a number of equivalent expressions, all related by Heine's transformations. Using this result the s…
Computes Wilson Loop observable using Einstein-Hilbert and Chern-Simons path integrals.
problem Computing Wilson Loop observable using path integrals.
method Uses Einstein-Hilbert action and axial-gauge fixing to express as Chern-Simons integrals, then computes observable from link diagram.
result Wilson Loop observable can be computed from a hyperlink's link diagram, invariant under equivalence relation.
We reconsider Chern-Simons gauge theory on a Seifert manifold M, which is the total space of a nontrivial circle bundle over a Riemann surface, possibly with orbifold points. As shown in previous work with Witten, the path integral technique of non-abelian localization can be used to express the partition function of C…
We introduce and study the Wilson loops in a general 3D topological field theories (TFTs), and show that the expectation value of Wilson loops also gives knot invariants as in Chern-Simons theory. We study the TFTs within the Batalin-Vilkovisky (BV) and Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) framework, and the…
An NQ-manifold is a non-negatively graded supermanifold with a degree 1 homological vector field. The focus of this paper is to define the Wilson loops/lines in the context of NQ-manifolds and to study their properties. The Wilson loops/lines, which give the holonomy or parallel transport, are familiar objects in usual…
The string bracket introduced by Chas and Sullivan [math.GT/9911159] is reinterpreted from the point of view of topological field theories in the Batalin-Vilkovisky or BRST formalisms. Namely, topological action functionals for gauge fields (generalizing Chern-Simons and BF theories) are considered together with genera…
We study the supersymmetric Wilson loop as introduced by Caron-Huot, which attaches to lightlike polygons certain edge and vertex operators, whose shape is determined by supersymmetry constraints. We state explicit formulas for the vertex operators to all orders in the Graßmann expansion, thus filling a gap in the lite…
L-CNNs learn gauge invariant quantities on lattices.
problem Learning gauge invariant quantities on lattices.
method Novel convolutional layer preserving gauge equivariance and forming Wilson loops.
result L-CNNs can approximate any gauge covariant function on the lattice.
Area law proven for 2D Yang-Mills in generalized axials.
problem Proving area law for 2D Yang-Mills theory in generalized axials.
method Homotopy invariance of iterated integrals, complex gauge-fixing, integration cycle deformation.
result Wilson loop expectation values obey area law up to second order.
This paper analyzes in details the Batalin-Vilkovisky quantization procedure for BF theories on n-dimensional manifolds and describes a suitable superformalism to deal with the master equation and the search of observables. In particular, generalized Wilson loops for BF theories with additional polynomial B-interaction…
The classical Wilson loop is the gauge-invariant trace of the parallel transport around a closed path with respect to a connection on a vector bundle over a smooth manifold. We build a precise mathematical model of the super Wilson loop, an extension introduced by Mason-Skinner and Caron-Huot, by endowing the objects o…
We study twisted N=2 superconformal gauge theory on a product of two Riemann surfaces Sigma and C. The twisted theory is topological along C and holomorphic along Sigma and does not depend on the gauge coupling or theta-angle. Upon Kaluza-Klein reduction along Sigma, it becomes equivalent to a topological B-model on C …
We relate the author's Lie cobracket in the module additively generated by loops on a surface with the Connes-Kreimer Lie bracket in the module additively generated by trees. To this end we introduce a pre-Lie coalgebra and a (commutative) Hopf algebra of pointed loops on a surface. In the last version I added sections…
Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structurehep-th
The paper computes group factors and properties of Wilson loops in Chern-Simons theory.
problem Computing group factors and properties of Wilson loops in Chern-Simons theory.
method Developed a method for computing group factors of the perturbative series expansion of Wilson loops.
result Provided a combinatorial description of group factors with clear dependence on rank and representation.
Study evaluates Chern-Simons theory on Seifert fibred 3-manifolds.
problem Evaluate Chern-Simons theory on Seifert fibred 3-manifolds.
method Use Abelianisation method to evaluate the partition function and Wilson loops.
result Obtain closed formulae for expectation values of torus knots.
In an abstract Wiener space setting, we constract a rigorous mathematical model of the one-loop approximation of the perturbative Chern-Simons integral, and derive its explicit asymptotic expansion for stochastic Wilson lines.
This paper compares exact 2D Yang-Mills theory with perturbative approaches.
problem Investigating the relationship between exact and perturbative approaches in 2D Yang-Mills theory.
method Mathematical rigorous formulation of perturbative quantization and comparison of Wilson loop expectation values.
result Exact lattice Wilson loop expectations on agree with perturbative expectations in holomorphic gauge for simple closed curves to all orders.
Euler characteristics, lengths of loops in hyperbolic 3-manifolds, and Wilson's Freiheitssatzmath.GT
Study Euler characteristics and loop lengths in hyperbolic 3-manifolds.
problem Analyzing Euler characteristics and loop lengths in hyperbolic 3-manifolds.
method Examining subgroups generated by loops and their index of freedom.
result Euler characteristic is bounded by the index of freedom.
Novel discretization method for Yang-Mills theory on the plane.
problem Quantum Yang-Mills theory on .
method Algebraic stochastic calculus with indefinite covariance matrix.
result Equivalence of different gauge formulations of Yang-Mills theory.
We study Wilson-'t Hooft loop operators in a class of N=2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify all possible loop operators in terms of their electric and magnetic charges subject to the Dirac quantization condition. We t…
Study Yang-Mills connections on surfaces via Fréchet reduction.
problem Characterize Yang-Mills connections on orientable closed surfaces.
method Fréchet reduction to define and constrain gauge equivalence classes of connections.
result Deduced stratified symplectic structure on unbased Yang-Mills connections.
Study uses cohomology theory to analyze 2008 financial crisis in Thai stock market.
problem Analyzing the 2008 financial crisis in the Thai stock market.
method Hybrid mathematical superstructure with cohomology theory, Pauli matrix, and Wilson loop.
result Identified the 2008 financial market crash using cohomology group of sphere over tensor field.
A new discretisation of a doubled, i.e. BF, version of the pure abelian Chern-Simons theory is presented. It reproduces the continuum expressions for the topological quantities of interest in the theory, namely the partition function and correlation function of Wilson loops. Similarities with free spinor field theory a…
We find a splitting in a special cohomology theory for complex manifolds.
problem Finding a splitting in a specific cohomology theory.
method Construct Hodge filtered function spaces and show they satisfy an unstable splitting.
result Obtain an analog of Quillen's theorem for Hodge filtered Brown-Peterson cohomology.
Paper studies colored Alexander polynomials and their relation to KP soliton τ-functions.
problem Exploring group theoretic structures of colored HOMFLY polynomials in a specific limit.
method Perturbative analysis of Chern-Simons Wilson loops and their relation to KP soliton τ-functions.
result Colored Alexander polynomial is embedded in the action of KP generating function on soliton τ-function.
Simplicial versions of topological abelian gauge theories are constructed which reproduce the continuum expressions for the partition function and Wilson expectation value of linked loops, expressible in terms of R-torsion and linking numbers respectively. The new feature which makes this possible is the introduction o…
New 2D TQFT connects Chern-Simons theory on circle bundles to gauge theory.
problem Localization of Chern-Simons theory on circle bundles.
method Caloron correspondence and symplectic structure.
result Wilson loops on circle fibers described naturally.
We study the expectation value of a nonplanar Wilson graph operator in SL(2,C) Chern-Simons theory on . In particular we analyze its asymptotic behaviour in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. When the Wilson gr…
Correspondence found between Askey-Wilson polynomials and genus-two handlebody skein module.
problem Understanding the genus-two handlebody skein module.
method Using q-difference operators for the genus-two skein algebra.
result Correspondence between reduced Askey-Wilson polynomials and genus-two handlebody skein module.
Study Wilson lines junctions in quantum groups with one-parameter deformations.
problem Understanding local relations of Wilson lines in quantum groups.
method Analyzing junctions of Wilson lines in refined SU(N) Chern-Simons theory and proposing local relations.
result Realization of one-parameter deformations of quantum groups.
Develops Hamiltonian quantization for complex Chern-Simons theory at even level k.
problem Quantum holonomies and representation theory in complex Chern-Simons theory.
method Combinatorial quantization and operator algebra construction.
result Physical Hilbert space identified and Fenchel-Nielsen representation demonstrated.
Researchers conjecture HOMFLY polynomial for figure eight knot.
problem Finding HOMFLY polynomial for figure eight knot.
method Differential expansion for Wilson loop averages, focusing on rectangular representations.
result Conjecture for rectangularly colored HOMFLY polynomial of figure eight knot.
On two-Dimensional Holonomymath.DG
We define the thin fundamental categorical group of a based smooth manifold as the categorical group whose objects are rank-1 homotopy classes of based loops on , and whose morphisms are rank-2 homotopy classes of homotopies between based loops on . Here two maps are rank- homotop…
New model calculates Wilson surfaces in higher gauge theory.
problem Calculating Wilson surfaces in higher gauge theory.
method Derived geometric framework, topological coadjoint orbit model, functional integral framework.
result Strong evidence that model underlies Wilson surfaces partition function.
Wilson lines generate positive Laurent polynomials in decorated triangulations.
problem Wilson lines and their coefficients in function algebras.
method Study of Wilson lines on marked surfaces and their matrix coefficients in function algebras.
result Matrix coefficients of Wilson lines give Laurent polynomials with positive integral coefficients.
The Smith-Wilson method is analyzed for its peculiar hedges and negative discount factors.
problem Analyzing the Smith-Wilson method for discounting under EU regulation Solvency II.
method Novel stochastic representation of the Smith-Wilson method for hedging analysis.
result Negative discount factors and singularities in convergence criterion are linked.
New method defines Wilson surface observables on arbitrary 2D surfaces.
problem Defining Wilson surface observables on arbitrary surfaces.
method Using equivariant cohomology and Poisson σ-models.
result Wilson surface observables are nontrivial for non-simply connected groups.
Two Smith-Wilson method variants improve yield curve derivation and compliance.
problem Deriving accurate yield curves for insurance applications with varying market data reliability.
method Two variants of the Smith-Wilson method, incorporating market data weight and ultimate forward rate requirement.
result Improved yield curve derivation and compliance with Solvency II and IFRS 17 requirements.
Two superholonomy theories are shown equivalent.
problem Equivalence of two superholonomy theories.
method Comparison Theorem and de Rham-Wu decomposition theorem.
result Holonomy theories are equivalent.
We make a precision test of a recently proposed conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold. First, we develop a systematic procedure to extract string amplitudes from vacuum expectation values (vevs) of Wilson loops in Chern-Simons gauge theory, and then…
New methods reveal symmetries in Chern-Simons theory.
problem Understanding symmetries in Chern-Simons theory.
method Introduced a special basis in the center of the universal enveloping algebra to present group factors in arbitrary representations.
result Computed Vassiliev invariants and proved the tug-the-hook symmetry of the colored HOMFLY polynomial.
We study three-dimensional Chern-Simons theory with complex gauge group SL(2,C), which has many interesting connections with three-dimensional quantum gravity and geometry of hyperbolic 3-manifolds. We show that, in the presence of a single knotted Wilson loop in an infinite-dimensional representation of the gauge grou…
The expectation value of Wilson loop operators in three-dimensional SO(N) Chern-Simons gauge theory gives a known knot invariant: the Kauffman polynomial. Here this result is derived, at the first order, via a simple variational method. With the same procedure the skein relation for Sp(N) are also obtained. Jones polyn…
Study detects Hopf elements and Kervaire classes in sphere spectra.
problem Detecting Hopf elements and Kervaire classes in stable homotopy groups.
method Using Hurewicz map and Real Johnson-Wilson theories.
result Certain families of elements are detected by Real Johnson-Wilson theories.
New proof of Duflo isomorphism for Lie algebras with scalar products.
problem Duflo isomorphism for Lie algebras with scalar products.
method Explicit calculation of first order deformation of differential on Hochschild complex.
result Knot invariant matches Kontsevich integral for unknot.