A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study electric-magnetic duality in M-theory compactifications.
New Langlands duality conjectures for 3-manifold skein modules.
We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian manifolds. Our approach generalizes previous treatments using the Hamiltonian formalism …
We consider the reduction along two compact directions of a twisted N=4 gauge theory on a 4-dimensional orientable manifold which is not a global product of two surfaces but contains a non-orientable surface. The low energy theory is a sigma-model on a 2-dimensional worldsheet with a boundary which lives on branes cons…
We present an explicit expression for the topological invariants associated to monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding topological quantum field theory, and it turns out that they can be expressed in …
In the first of these two lectures, I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q. The two main steps are to reinterpret three-dimensional Chern-Simons gauge theory in four dimensional terms and then to apply electric-magnetic duality. The var…
It has been argued based on electric-magnetic duality and other ingredients that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four dimensions. Here, we attempt to verify this directly by analyzing the equations and counting their solut…
This paper studies the interplay between the N=2 gauge theories in three and four dimensions that have a geometric description in terms of twisted compactification of the six-dimensional (2,0) SCFT. Our main goal is to construct the three-dimensional domain walls associated to any three-dimensional cobordism. We find t…
We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin classes of spacetime, in terms of obstructions to having bundles with certain structure groups. Using a generalization of th…
Revisits Vafa-Witten theory, deriving new invariants and homologies.
We generalize the analysis by Moore and Witten in [arXiv:hep-th/9709193], and consider integration over the u-plane in Donaldson theory with surface operators on a smooth four-manifold X. Several novel aspects will be developed in the process; like a physical interpretation of the "ramified" Donaldson and Seiberg-Witte…
Let A be the space of irreducible connections (vector potentials) over a SU(n)-principal bundle on a three-dimensional manifold M. Let T be the fiber product of the tangent and cotangent bundles of A. We endow T with a symplectic structure Ωwhich is represented by a vortex formula. The corresponding Poisson bracket wil…
The proper action functional of (4k+3)-dimensional U(1)-Chern-Simons theory including the instanton sectors has a well known description: it is given on the moduli space of fields by the fiber integration of the cup product square of classes in degree-(2k+2) differential cohomology. We first refine this statement from …
Unified view of spectral networks linking geometry and gauge theory.
In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two dimensional topological phases, it is relatively easy to describe only single fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations. To incorporate charged and dyonic excitations in (doubled) topological p…
We continue our program initiated in [arXiv:0912.4261] to consider supersymmetric surface operators in a topologically-twisted N=2 pure SU(2) gauge theory, and apply them to the study of four-manifolds and related invariants. Elegant physical proofs of various seminal theorems in four-manifold theory obtained by Ozsvat…
A necessary and sufficient condition for energy-momentum conservation is proved within a topological, pre-metric approach to classical electrodynamics including magnetic as well as electric charges. The extended Lorentz force, consisting of mutual actions by F=(E, B) on the electric current and G=(H, D) on the magnetic…
Proves Poincaré duality for Hopf algebroids with bijective antipode.
New proof of chain duality for simplicial complexes.
Introduces Kähler duality between domains in complex space.
Research on dualities in geometric stereotypes.
Duality restored in gauge theory, gravity, and string theory models.
Unified proof of four Bavard dualities and new results on quasimorphisms.
Verma Howe duality connects tensor products of Verma modules to LKB representations.
Cohomological and homological spectral sequences are shown to be isomorphic.
The paper proves T-duality and Hori formulae for winding loop spaces.
Equivariant T-duality connects bundles with twists.
We give the definition of a duality that is applicable to arbitrary -forms. The operator that defines the duality depends on a fixed form . Our definition extends in a very natural way the Hodge duality of -forms in dimensional spaces and the generalized duality of two-forms. We discuss the properties of …
The paper establishes T-duality for 2D σ-models with H-flux.
QP perspective on Poisson-Lie T-duality topology changes.
Unified framework for T-duality in both trivial and non-trivial topologies.
Geometric duality connects graph isomorphism and knot equivalence.
Koszul duality for manifold modules proven.
This dissertation explores T-duality between hyperkähler structures and branes on algebraic integrable systems.
Maps self-duality in little disks operad to framed manifolds.
We study generalized complex structures and -duality (in the sense of Bouwknegt, Evslin, Hannabuss and Mathai) on Lie algebras and construct the corresponding Cavalcanti and Gualtieri map. Such a construction is called "Infinitesimal -duality". As an application we deal with the problem of finding symplectic stru…
New spherical T-duality for higher degree forms in fiber bundles.
The paper establishes a duality between non-compact and compact symmetric pairs.
We find the T-duality transformation rules for 2-dimensional (2,1) supersymmetric sigma-models in (2,1) superspace. Our results clarify certain aspects of the (2,1) sigma model geometry relevant to the discussion of T-duality. The complexified duality transformations we find are equivalent to the usual Buscher duality …
We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n-1) dimensional duality group and X is a coarse Poincare duality space of formal dimension n, then a free simplicial action of G on X d…
The paper shows plentiful non-homotopy finite Poincaré duality spaces.
Study S-duality and supersymmetry on curved manifolds using localization.
We study the convex duality method for robust utility maximization in the presence of a random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true for a wide class of utility functions on the whole real line and unbounded random endo…
In this paper, we show that if G is a finite p-group (p prime) acting by automorphisms on a -hyperbolic Poincare Duality group, then the fixed subgroup is a Poincare Duality group over Z/p. We also provide examples to show that the fixed subgroup might not even be a Duality group over Z.
Unified treatment of reinforcement learning via convex duality.
Dualities in physics help in machine learning tasks.
New approach to T-duality using Courant algebroids.
Proves a theorem for 3D Poincaré duality pairs.