تقرير
The fermion-boson map for large d
| العنوان: | The fermion-boson map for large d |
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| المؤلفون: | Filothodoros, Evangelos G., Petkou, Anastasios C., Vlachos, Nicholas D. |
| سنة النشر: | 2018 |
| المجموعة: | High Energy Physics - Theory |
| مصطلحات موضوعية: | High Energy Physics - Theory |
| الوصف: | 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 $\pi$. Comment: 34 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.nuclphysb.2019.01.015 |
| URL الوصول: | http://arxiv.org/abs/1803.05950 |
| رقم الأكسشن: | edsarx.1803.05950 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.nuclphysb.2019.01.015 |
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