Related papers: Wilson lines and their Laurent positivity
The exact or Wilson renormalization group equations can be formulated as a functional Fokker-Planck equation in the infinite-dimensional configuration space of a field theory, suggesting a stochastic process in the space of couplings.…
We consider the unparticle action that is made gauge invariant by inclusion of an open Wilson line factor. In deriving vertexes from such an action it has been customary to use a form of differentiating the Wilson line originally proposed…
We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4 d=3 supersymmetric gauge theory…
We give an algebraic and a geometric criterion for the existence of $G$-connections on $\mathbb{P}^{1}$ with prescribed irregular type with equal slope at $\infty$ (isoclinic) and with regular singularity of prescribed residue at $0$. The…
We investigate the higher-order bulk-boundary correspondence in a family of chiral-symmetric Bloch Hamiltonians with anticommuting mirror symmetries. These models generalize the $\pi$-flux square lattice, the prototypical topological…
We show that a bounded, linear map between C*-algebras is a weighted $\ast$-homomorphism (the central compression of a $\ast$-homomorphism) if and only if it preserves zero-products, range-orthogonality, and domain-orthogonality. It follows…
Given a link L in the 3-sphere, we ask whether the components of L bound disjoint, nullhomologous disks properly embedded in a simply-connected positive-definite smooth 4-manifold; the knot case has been studied extensively in work of…
The contributions of scalars and fermions to the null polygonal bosonic Wilson loops/gluon MHV scattering amplitudes in $\mathcal{N} = 4$ SYM are considered. We first examine the re-summation of scalars at strong coupling. Then, we…
We derive new integral identities for AdS propagators and further develop the Wilson network expansion for AdS Feynman diagrams. In particular, we demonstrate that four-point contact and exchange scalar diagrams in two dimensions can be…
Using preservations of piecewise linear (PL) homeomorphism types under edge contractions (the link condition) as a topological proxy for flagness, we give a quantitative description of the effect flagness on on gamma positivity of…
Let $G$ be a connected graph of genus $g$. The Picard group of degree $g$, $\text{Pic}^g(G)$, is the set of equivalence classes of divisors on $G$ of degree $g$, where two divisors are equivalent if one can be reached from the other through…
The goal of this paper is to construct and describe certain arithmetic subgroups of the automorphism group of a partially commutative group. More precisely, given an arbitrary finite graph $\Gamma$ we construct an arithmetic subgroup…
Let $A_1, \ldots, A_r$ be Hermitian $n \times n$ matrices and $S = \sum A_i \otimes s_i$ the associated matrix semicircle, where $s_1, \ldots, s_r$ are free semicircular variables. We prove that the following are equivalent: (i) the matrix…
Local properties of families of algebraic subsets $W_g$ in Birkhoff strata $\Sigma_{2g}$ of Gr$^{(2)}$ containing hyperelliptic curves of genus $g$ are studied. It is shown that the tangent spaces $T_g$ for $W_g$ are isomorphic to linear…
Amalgamation in the totally non-negative part of positroid varieties is equivalent to gluing copies of $Gr^{TP}(1,3)$ and $Gr^{TP}(2,3)$. Lam has proposed to represent amalgamation in positroid varieties by equivalence classes of relations…
We perform a detailed study of the Yangian symmetry of smooth supersymmetric Maldacena-Wilson loops in planar N=4 super Yang-Mills theory. This hidden symmetry extends the global superconformal symmetry present for these observables. A…
Conformal field theory finds applications across diverse fields, from statistical systems at criticality to quantum gravity through the AdS/CFT correspondence. These theories are subject to strong constraints, enabling a systematic…
We solve a functional version of the problem of twist quantization of a coboundary Lie bialgebra (g,r,Z). We derive from this the following results: (a) the formal Poisson manifolds g^* and G^* are isomorphic; (b) we construct a subalgebra…
Motivated by applications to perverse sheaves, we study combinatorics of two cell decompositions of the symmetric product of the complex line, refining the complex stratification by multiplicities. Contingency matrices, appearing in…
We determine the local structure of all pseudo-Riemannian manifolds $(M,g)$ in dimensions $n\ge4$ whose Weyl conformal tensor $W$ is parallel and has rank 1 when treated as an operator acting on exterior 2-forms at each point. If one fixes…