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.
Defines a map connecting 3d-index and skein module.
Overview of 3D TQFTs and 3-manifold invariants.
Study 3d N=1 vacua from M-theory compactification on Spin(7) space.
To formulate the universal constraints of quantum statistics data of generic long-range entangled quantum systems, we introduce the geometric-topology surgery theory on spacetime manifolds where quantum systems reside, cutting and gluing the associated quantum amplitudes, specifically in 2+1 and 3+1 spacetime dimension…
Summarizes quantum field theories with discrete symmetry, classifying representations and anomalies.
Recent work extends Turaev's modular categories to non-semisimple settings.
Constructs 3D topological field theories from a specific quantum group, linking to physics invariants.
Extends string-net theory to 3D TQFT via surface graphs and surgery.
We construct a new family of exact quantum field theories modeled on hyperbolic geometry, called {\it quantum hyperbolic field theories} (QHFTs). The QHFTs are defined for a -bordism category based on the set of compact oriented 3-manifolds , equipped with properly embedded framed links $L_\Ff$ and with flat …
3D dual field theories for Virasoro minimal models constructed using Seifert fiber spaces.
3D HQFTs constructed using graded monoidal categories.
New method uses resurgent analysis to determine growth rate of quantum field theory coefficients.
Study fermionic theories, their anomalies, and modular transformations.
We give a construction of the abelian Chern-Simons gauge theory from the point of view of a 2+1 dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas which have been previously explored in connection to the nonabelian Chern-Simons theory [JW,ADW]. We f…
We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.
The paper explores mapping class groups and their quantum field theory representations.
We identify a large class R of three-dimensional N=2 superconformal field theories. This class includes the effective theories T_M of M5-branes wrapped on 3-manifolds M, discussed in previous work by the authors, and more generally comprises theories that admit a UV description as abelian Chern-Simons-matter theories w…
We propose a method to assign non-unitary TQFTs to certain SCFTs, deriving bounds and examples.
We explain how, starting with a stack of D4-branes ending on an NS5-brane in type IIA string theory, one can, via T-duality and the topological-holomorphic nature of the relevant worldvolume theories, relate (i) the lattice models realized by Costello's 4d Chern-Simons theory, (ii) links in 3d analytically-continued Ch…
Link homology theories connect to 4-manifold invariants and TQFTs.
Study classifies moduli spaces of spin connections on 3D homogeneous spaces.
We investigate link homology theories for stable equivalence classes of link diagrams on orientable surfaces. We apply (1+1)-dimensional unoriented topological quantum field theories to Bar-Natan's geometric formalism to define new theories for stable equivalence classes.
Tropical geometry aids in computing topological quantum field theories.
In this article we prove that any unitary, axiomatic topological quantum field theory in four-dimensions can not detect changes in the smooth structure of M, a simply connected, closed (compact without boundary), oriented smooth manifold. However, as Donaldson-Witten theory (a topological quantum field theory but not a…
We present some ideas for a possible Noncommutative Floer Homology. The geometric motivation comes from an attempt to build a theory which applies to practically every 3-manifold (closed, oriented and connected) and not only to homology 3-spheres. There is also a physical motivation: one would like to construct a nonco…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions of 'quantum invariants' of manifolds inspired by ideas originating from physics.…
A quantum field theory for Spin(7)-instantons derived from moduli spaces.
We establish a relation between the trace evaluation in SO(3) topological quantum field theory and evaluations of a topological Tutte polynomial. As an application, a generalization of the Tutte golden identity is proved for graphs on the torus.
We define some new invariants for 3-manifolds using the space of taut codim-1 foliations along with various techniques from noncommutative geometry. These invariants originate from our attempt to generalise Topological Quantum Field Theories in the Noncommutative geometry / topology realm.
Paper connects 3D gravity averages to 2D CFT correlators.
New framework for quantum invariants of 3-manifolds using homology.
We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d theories where such structures a priori are not manifest. These modular structures include: mock modular forms, Weil representations, quantum mo…
We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical transformations of a remarkable ``ultra-local'' Poisson bracket algebra defined on di…
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological extension of the action and the topological flux quantization conditions, in terms …
Cone structures in quantum field theory linked to information geometry.
Mednykh proved that for any finite group G and any orientable surface S, there is a formula for #Hom(pi_1(S), G) in terms of the Euler characteristic of S and the dimensions of the irreducible representations of G. A similar formula in the nonorientable case was proved by Frobenius and Schur. Both of these proofs use c…
Graph potentials link to topological QFTs, with computational methods.
Homotopy Quantum Field Theories (HQFTs) generalize more familiar Topological Quantum Field Theories (TQFTs). In generalization of the surgery construction of 3-dimensional TQFTs from modular categories, we use surgery to derive 3-dimensional HQFTs from G-modular categories.
This paper explores a particular statistical model on 6-valent graphs with special properties which turns out to be invariant with respect to certain Roseman moves if the graph is the singular point graph of a diagram of a 2-knot. The approach uses the technic of the tetrahedral complex cohomology. We emphasize that th…
The paper explores how the unit inclusion affects topological quantum field theories in non-semisimple categories.
Researchers create projective representations of Hecke groups using TQFT.
We study the Chern-Simons topological quantum field theory with an inhomogeneous gauge group, a non-semi-simple group obtained from a semi-simple one by taking its semi-direct product with its Lie algebra. We find that the standard knot observables (i.e. traces of holonomies along knots) essentially vanish, but yet, th…
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
New method describes entanglement of straight lines in 3D space.
Program connects quantum computing and topological field theories.
New approach connects 3D Chern-Simons theory to spectral networks.
3D HQFT comparison proves state sum equals surgery.
We extend the topological field theory (``itsy bitsy topological field theory"') of our previous work from mod-2 to twisted coefficients. This topological field theory is derived from sutured Floer homology but described purely in terms of surfaces with signed points on their boundary (occupied surfaces) and curves on …