Cargando…

The fermion-boson map for large $d$

We show that the three-dimensional map between fermions and bosons at finite temperature generalises for all odd dimensions d>3 . We further argue that such a map has a nontrivial large d limit. Evidence comes from studying the gap equations, the free energies and the partition functions of the U...

Descripción completa

Detalles Bibliográficos
Autores principales: Filothodoros, Evangelos G., Petkou, Anastasios C., Vlachos, Nicholas D.
Lenguaje:eng
Publicado: 2018
Materias:
Acceso en línea:https://dx.doi.org/10.1016/j.nuclphysb.2019.01.015
http://cds.cern.ch/record/2311696
_version_ 1780957917544972288
author Filothodoros, Evangelos G.
Petkou, Anastasios C.
Vlachos, Nicholas D.
author_facet Filothodoros, Evangelos G.
Petkou, Anastasios C.
Vlachos, Nicholas D.
author_sort Filothodoros, Evangelos G.
collection CERN
description We show that the three-dimensional map between fermions and bosons at finite temperature generalises for all odd dimensions d>3 . We further argue that such a map has a nontrivial large d limit. Evidence comes from studying the gap equations, the free energies and the partition functions of the U(N) Gross–Neveu and CP N−1 models for odd d≥3 in the presence of imaginary chemical potential. We find that the gap equations and the free energies can be written in terms of the Bloch–Wigner–Ramakrishnan Dd(z) functions analysed by Zagier. Since D2(z) gives the volume of ideal tetrahedra in 3 d hyperbolic space our three-dimensional results are related to resent studies of complex Chern–Simons theories, while for d>3 they yield corresponding higher dimensional generalizations. As a spinoff, we observe that particular complex saddles of the partition functions correspond to the zeros and the extrema of the Clausen functions Cld(θ) with odd and even index d respectively. These saddles lie on the unit circle at positions remarkably well approximated by a sequence of rational multiples of π .
id cern-2311696
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2018
record_format invenio
spelling cern-23116962023-10-04T06:56:24Zdoi:10.1016/j.nuclphysb.2019.01.015http://cds.cern.ch/record/2311696engFilothodoros, Evangelos G.Petkou, Anastasios C.Vlachos, Nicholas D.The fermion-boson map for large $d$hep-thParticle Physics - TheoryWe show that the three-dimensional map between fermions and bosons at finite temperature generalises for all odd dimensions d>3 . We further argue that such a map has a nontrivial large d limit. Evidence comes from studying the gap equations, the free energies and the partition functions of the U(N) Gross–Neveu and CP N−1 models for odd d≥3 in the presence of imaginary chemical potential. We find that the gap equations and the free energies can be written in terms of the Bloch–Wigner–Ramakrishnan Dd(z) functions analysed by Zagier. Since D2(z) gives the volume of ideal tetrahedra in 3 d hyperbolic space our three-dimensional results are related to resent studies of complex Chern–Simons theories, while for d>3 they yield corresponding higher dimensional generalizations. As a spinoff, we observe that particular complex saddles of the partition functions correspond to the zeros and the extrema of the Clausen functions Cld(θ) with odd and even index d respectively. These saddles lie on the unit circle at positions remarkably well approximated by a sequence of rational multiples of π .We show that the three-dimensional map between fermions and bosons at finite temperature generalises for all odd dimensions $d>3$. We further argue that such a map has a nontrivial large $d$ limit. Evidence comes from studying the gap equations, the free energies and the partition functions of the $U(N)$ Gross-Neveu and CP$^{N-1}$ models for odd $d\geq 3$ in the presence of imaginary chemical potential. We find that the gap equations and the free energies can be written in terms of the Bloch-Wigner-Ramakrishnan $D_d(z)$ functions analysed by Zagier. Since $D_2(z)$ gives the volume of ideal tetrahedra in 3$d$ hyperbolic space our three-dimensional results are related to resent studies of complex Chern-Simons theories, while for $d>3$ they yield corresponding higher dimensional generalizations. As a spinoff, we observe that particular complex saddles of the partition functions correspond to the zeros and the extrema of the Clausen functions $Cl_d(\theta)$ with odd and even index $d$ respectively. These saddles lie on the unit circle at positions remarkably well approximated by a sequence of rational multiples of $\pi$.arXiv:1803.05950CERN-TH-2018-049oai:cds.cern.ch:23116962018-03-15
spellingShingle hep-th
Particle Physics - Theory
Filothodoros, Evangelos G.
Petkou, Anastasios C.
Vlachos, Nicholas D.
The fermion-boson map for large $d$
title The fermion-boson map for large $d$
title_full The fermion-boson map for large $d$
title_fullStr The fermion-boson map for large $d$
title_full_unstemmed The fermion-boson map for large $d$
title_short The fermion-boson map for large $d$
title_sort fermion-boson map for large $d$
topic hep-th
Particle Physics - Theory
url https://dx.doi.org/10.1016/j.nuclphysb.2019.01.015
http://cds.cern.ch/record/2311696
work_keys_str_mv AT filothodorosevangelosg thefermionbosonmapforlarged
AT petkouanastasiosc thefermionbosonmapforlarged
AT vlachosnicholasd thefermionbosonmapforlarged
AT filothodorosevangelosg fermionbosonmapforlarged
AT petkouanastasiosc fermionbosonmapforlarged
AT vlachosnicholasd fermionbosonmapforlarged