# Multilocal Fermionization

@article{Rehren2013MultilocalF, title={Multilocal Fermionization}, author={Karl-Henning Rehren and Gennaro Tedesco}, journal={Letters in Mathematical Physics}, year={2013}, volume={103}, pages={19-36} }

We present a simple isomorphism between the algebra of one real chiral Fermi field and the algebra of n real chiral Fermi fields. The isomorphism preserves the vacuum state. This is possible by a “change of localization”, and gives rise to new multilocal symmetries generated by the corresponding multilocal current and stress–energy tensor. The result gives a common underlying explanation of several remarkable recent results on the representation of the free Bose field in terms of free Fermi…

## 14 Citations

Multilocal bosonization

- Mathematics, Physics
- 2015

We present a bilocal isomorphism between the algebra generated by a single real twisted boson field and the algebra of the boson βγ ghost system. As a consequence of this twisted vertex algebra…

Twisted vertex algebras, bicharacter construction and boson-fermion correspondences

- Physics, Mathematics
- 2013

The boson-fermion correspondences are an important phenomena on the intersection of several areas in mathematical physics: representation theory, vertex algebras and conformal field theory,…

Gluing together modular flows with free fermions

- Physics, MathematicsJournal of High Energy Physics
- 2019

A bstractWe revisit the calculation of multi-interval modular Hamiltonians for free fermions using a Euclidean path integral approach. We show how the multi-interval modular flow is obtained by…

Boson-fermion correspondence of type D-A and multi-local Virasoro representations on the Fock space F⊗12

- Physics, Mathematics
- 2014

We construct the bosonization of the Fock space F⊗12 of a single neutral fermion by using a 2-point local Heisenberg field. We decompose F⊗12 as a direct sum of irreducible highest weight modules for…

Prepared for submission to JHEP Gluing together Modular flows with free fermions

- 2018

We revisit the calculation of multi-interval modular Hamiltonians for free fermions using a Euclidean path integral approach. We show how the multi-interval modular flow is obtained by gluing…

Modular Hamiltonians for the massless Dirac field in the presence of a boundary

- Physics, Mathematics
- 2020

We study the modular Hamiltonians of an interval for the massless Dirac fermion on the half-line. The most general boundary conditions ensuring the global energy conservation lead to consider two…

Braided Actions of DHR Categories and Reconstruction of Chiral Conformal Field Theories

- Mathematics
- 2016

Quantum Field Theory (QFT) is our modern understanding of particles and matter at small scales, where quantum behaviour replaces macroscopical phenomena, which are much closer to intuition, and…

On the Modular Operator of Mutli-component Regions in Chiral CFT

- Mathematics, Physics
- 2019

We introduce a new approach to find the Tomita-Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary…

Entropy and modular Hamiltonian for a free chiral scalar in two intervals

- PhysicsPhysical Review D
- 2018

We calculate the analytic form of the vacuum modular Hamiltonian for a two interval region and the algebra of a current $j(x)=\partial \phi(x)$ corresponding to a chiral free scalar $\phi$ in $d=2$.…

Braided Categories of Endomorphisms as Invariants for Local Quantum Field Theories

- Mathematics, Physics
- 2015

We want to establish the “braided action” (defined in the paper) of the DHR category on a universal environment algebra as a complete invariant for completely rational chiral conformal quantum field…

## References

SHOWING 1-10 OF 16 REFERENCES

Extensions of Conformal Nets¶and Superselection Structures

- Mathematics, Physics
- 1998

Abstract:Starting with a conformal Quantum Field Theory on the real line, we show that the dual net is still conformal with respect to a new representation of the Möbius group. We infer from this…

Modular structure and duality in conformal quantum field theory

- Mathematics
- 1993

Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories, i.e. the Tomita-Takesaki modular group associated with…

The CPT-theorem in two-dimensional theories of local observables

- Mathematics
- 1992

Let ℳ be a von Neumann algebra with cyclic and separating vector Ω, and letU(a) be a continuous unitary representation ofR with positive generator and Ω as fixed point. If these unitaries induce for…

ON THE DUALITY CONDITION FOR QUANTUM FIELDS

- Mathematics
- 1976

A general quantum field theory is considered in which the fields are assumed to be operator‐valued tempered distributions. The system of fields may include any number of boson fields and fermion…

Affine Lie algebras and quantum groups

- Mathematics
- 1991

Let g be a finite dimensional simple Lie algebra of simply laced type. Drinfeld has shown that the tensor category of finite-dimensional representations of the corresponding quantized enveloping…

The massless Thirring model: Positivity of Klaiber'sn-point functions

- Physics
- 1985

We present a simple solution to the problem of proving positivity of Klaiber'sn-point functions for the massless Thirring model. The corresponding fields are obtained as strong limits of explicitly…

Reduced density matrix and internal dynamics for multicomponent regions

- Physics
- 2009

We find the density matrix corresponding to the vacuum state of a massless Dirac field in two dimensions reduced to a region of the space formed by several disjoint intervals. We calculate explicitly…

On the equilibrium states in quantum statistical mechanics

- Mathematics
- 1967

AbstractRepresentations of theC*-algebra
$$\mathfrak{A}$$
of observables corresponding to thermal equilibrium of a system at given temperatureT and chemical potential μ are studied. Both for finite…

Soliton Operators for the Quantized Sine-Gordon Equation

- Physics
- 1975

Operators for the creation and annihilation of quantum sine-Gordon solitons are constructed. The operators satisfy the anticommutation relations and field equations of the massive Thirring model. The…

TRANSFORMATION GROUPS FOR SOLITON EQUATIONS

- Mathematics, Materials Science
- 1982

A printing blanket and method of making same is provided wherein such blanket comprises a base structure, a surface layer made of a fluorocarbon elastomer, and a binder layer comprised of a…