Dirac fermions under imaginary rotation

par M. Tudor Patuleanu (Université de l'Ouest de Timișoara, Roumanie)

jeudi 27 févr. 2025, 14:00 → 15:00 Europe/Paris

Salle 1180, bâtiment E2 (Salle des séminaires )

The growing interest in the thermodynamic properties of strongly-interacting systems under rotation, particularly using lattice gauge techniques on the Euclidean manifold and with an imaginary angular velocity $\mathrm{\Omega }=i{\mathrm{\Omega }}_I$, has motivated the current study of Dirac fields under imaginary rotation.

For the frequency $\nu =\beta {\mathrm{\Omega }}_I/2\pi$ a rational number, the imaginary rotation thermal expectation values of free scalar fields, in the large volume limit, depend only on the denominator $q$ of the irreducible fraction $\nu =p/q$, while they are $0$ for the irrational frequency case. This behavior, similar to that of the Thomae function, is called "fractal" and its non-analytic structure raises potential issues when considering an analytic continuation back to the real rotation case.

We consider the same problem for free, massless fermions at finite temperature $T={\beta }^{-1}$ and chemical potential $\mu$ and confirm that the thermodynamics fractalizes in the case $\mu =0$. Curiously, fractalization has no effect on the chemical potential $\mu$, which dominates the thermodynamics at large values of $q$. This fractal behavior is shown for the fermionic condensate, the charge currents, and the energy-momentum tensor. For these observables, the values on the rotation axis and the large-temperature behavior are validated by analytic continuation and comparison with the results obtained in the case of real rotation. Enclosing the system in a fictitious cylinder of radius $R$ and length $L_z$ allows constructing averaged thermodynamic quantities that satisfy the Euler relation and also fractalize.