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.
Anomaly in free fermion theory revealed in functorial field theory.
Using the notion of vacuum pairs we show how the (square of the) mass matrix of the fermions can be considered geometrically as curvature. This curvature together with the curvature of space-time, defines the total curvature of the Clifford module bundle representing a ``free'' fermion within the geometrical setup of s…
Constructs a path integral for fermionic SPTs, solving anomalies in 2+1D topological orders.
Study fermionic theories, their anomalies, and modular transformations.
The paper defines a category of Lagrangian correspondences in super Hilbert spaces and constructs a functorial field theory.
We propose a statistical mechanical derivation of Kahler-Einstein metrics, i.e. solutions to Einstein's vacuum field equations in Euclidean signature (with a cosmological constant) on a compact Kahler manifold X. The microscopic theory is given by a canonical free fermion gas on X whose one-particle states are plurican…
New MCMC method speeds up quantum physics simulations by a factor of 100.
We show how Ramond free neutral Fermi fields lead to a -function theory of BKP type which describes iso-orthogonal deformations of systems of ortogonal curvilinear coordinates. We also provide a vertex operator representation for the classical Ribaucour transformation.
Given a smooth family of massless free fermions parametrized by a base manifold , we show that the (mathematically rigorous) Batalin-Vilkovisky quantization of the observables of this family gives rise to the determinant line bundle for the corresponding family of Dirac operators.
Topological Quantum Field Theories (TQFTs) pertinent to some emergent low energy phenomena of condensed matter lattice models in 2+1 and 3+1D are explored. Many of our field theories are highly-interacting without free quadratic analogs. Some of our bosonic TQFTs can be regarded as the continuum field theory formulatio…
A novel quantum model improves RBM performance and is efficiently trainable.
Derives a formula for fermion dimensions in spherically symmetric monopole backgrounds.
Proposes a lattice formulation of APS index using η invariant.
We introduce the deformed fermionic numbers, corresponding to the skein relations, the main characteristics of knots and links. These fermionic numbers allow one to restore the skein relations. For the Alexander (Jones) skein relation we introduce corresponding Alexander (Jones) fermionic q-numbers, and for the HOMFLY …
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…
Reformulates mod-two APS index using domain-wall fermion.
No time-periodic Majorana fermions found in Kerr-Newman spacetimes with nontrivial charge.
Develops a mathematical framework for causal fermion systems in infinite dimensions.
In this paper we study a Clifford algebra generalization of the quaternions and its relationship with braid group representations related to Majorana fermions. The Fibonacci model for topological quantum computing is based on the fusion rules for a Majorana fermion. Majorana fermions can be seen not only in the structu…
We define an index of the fermionic signature operator on even-dimensional globally hyperbolic spin manifolds of finite lifetime. The invariance of the index under homotopies is studied. The definition is generalized to causal fermion systems with a chiral grading. We give examples of space-times and Dirac operators th…
We give a brief introduction to causal fermion systems with a focus on the geometric structures in space-time.
Proves a positive mass theorem for static causal fermion systems.
Semisimple 4D field theories can't distinguish smooth 4-manifolds.
Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential…
A new, simplified form of 10D supergravity action is derived up to all fermion orders.
Massive fermions help understand index theorems without chiral symmetry.
The hierarchy structure associated with a (2+1)-dimensional Nonlinear Schroedinger equation is discussed as an extension of the theory of the KP hierarchy. Several methods to construct special solutions are given. The relation between the hierarchy and a representation of toroidal Lie algebras are established by using …
Mathematician-friendly formulation of Atiyah-Patodi-Singer index.
We formulate a family of spin Topological Quantum Filed Theories (spin-TQFTs) as fermionic generalization of bosonic Dijkgraaf-Witten TQFTs. They are obtained by gauging -equivariant invertible spin-TQFTs, or, in physics language, gauging the interacting fermionic Symmetry Protected Topological states (SPTs) with a …
Study perturbs Dirac operators in any dimension, focusing on Majorana fermions.
We show that Chern-Simons gauge theory with appropriate cutoffs is equivalent, term by term in perturbation theory, to a Fermionic theory with a nonlocal interaction term. When an additional cutoff is placed on the Fermi fields, this Fermionic theory gives rise to a convergent perturbation expansion. This leads us to c…
The fundamental group and rational cohomology of the configuration spaces of the Skyrme and Faddeev-Hopf models are computed. Physical space is taken to be a compact oriented 3-manifold, either with or without a marked point representing an end at infinity. For the Skyrme model, the codomain is any Lie group, while for…
We unveil the geometric nature of the multiplet of fundamental fermions in the Standard Model of fundamental particles as a noncommutative analogue of de Rham forms on the internal finite quantum space.
The fermionic signature operator is analyzed on globally hyperbolic Lorentzian surfaces. The connection between the spectrum of the fermionic signature operator and geometric properties of the surface is studied. The findings are illustrated by simple examples and counterexamples.
In this paper we study unitary braid group representations associated with Majorana Fermions. Majorana Fermions are represented by Majorana operators, elements of a Clifford algebra. The paper recalls and proves a general result about braid group representations associated with Clifford algebras, and compares this resu…
A 12D spinor encodes fermions in a 4D Kaluza-Klein model.
We show that the quantum field theoretical formulation of the -function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we prove that i) the partial charge transformations preserving the neutral sector are Laplace transformations, ii) the basic ver…
There are eight possible Pin groups that can be used to describe the transformation behaviour of fermions under parity and time reversal. We show that only two of these are compatible with general relativity, in the sense that the configuration space of fermions coupled to gravity transforms appropriately under the spa…
Study baryogenesis in conformally flat spacetimes using causal fermion systems.
Derives hyperbolic laws of cosines and sines with fermionic corrections.
Holomorphic residue formula for complex supermanifolds.
The paper explores how non-Killing fields on internal spaces can produce massive gauge fields with chiral interactions.
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive th…
Authors compute anomalies for fermions in 3, 4, and 5 dimensions.
This paper is two-fold. At first we will discuss the generation of source terms in the Einstein-Hilbert action by using (topologically complicated) compact 3-manifolds. There is a large class of compact 3-manifolds with boundary: a torus given as the complement of a (thickened) knot admitting a hyperbolic geometry, den…
In this sequel to works D(11.1) (arXiv:1406.0929 [math.DG]), D(11.2) (arXiv:1412.0771 [hep-th]), and D(11.3.1) (arXiv:1508.02347 [math.DG]), we re-examine --- and reformulate when in need --- several basic notions in super -algebraic geometry as guided by the mathematical formulation of Ramond-Neveu-Schwarz…
Study of operators on loop spaces using Fermionic calculus and stochastic methods.
Geometric derivation of Einstein equations from causal fermion systems.