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Chiral Symmetry Restoration through

The concepts of chiral, chiral symmetry and/or chiral rotation appear in a large part of theoretical physics [1]. We can see a wide variety of usage in, for example, the superstrings/M-theory (holomorphic and antiholomorphic) [2], the chiral theories of grand unification [3], the supergravity (superconformal tensor calculi [4]), chiral symmtery and its restoration in the phenomena of QCD [5], nucleus and nuclear matter [6,7,8], and also in superconductivity of condensed matter [9]. Recently, I have published a paper on the dynamical chiral symmetry breaking and its restoration for a uniformly accelerated observer [10]. Here, I would like to make a short explanation on it, and also give a speculation on the extension of its supersymmeric version. The Hawking-Unruh effect predicts that the accelerated observer sees a thermal excitation of particles of a system in Minkowski spacetime, with the Unruh temperature T U = a/2π (a is an acceleration constant) [11]. This is called the thermalization theorem. To study the effect of uniform acceleration, we employ Rindler metric embeded in flat Minkowski spacetime, which are appropriate for the spacetime for a uniformly accelerated observer. It should be noticed that the thermally excited particles are not the original Minkowski particles but the Rindler particles determined by the ground (vacuum) state of the system of Rindler coordinates. The coordinate transformation arises the different picture for particle. In fact, the structure of the spacetime which has a suitable boundary condition (the event holizon) is the origin of the thermal spectrum. It has been generally proved that, in Rindler coordinates, Euclidean two-point functions are periodic in the direction of time with period 2π, and these functions satisfy the Kubo-Martin-Schwinger condition. Therefore, Green's functions in Rindler coordinates with period 2π may be interpreted as finite-temperature Green's functions. To examine what will be observed by a uniformly accelerated observer who moves relative to a system in which the chiral symmetry was dynamically broken, the following situation is considered: After a fermion system in Minkowski spacetime dynamically generated a chiral mass, an observer will be accelerated uniformly. The acceleration may give a thermal effect on the observation of the system. Of particular interest here is the question whether the thermalization effect of acceleration gives the restoration of broken symmetry or not. For the purpose to study the problem, we employ the Nambu−Jona-Lasinio model. The field theory in Rindler coordinates can be described by the method of curved background …