Chiral pair fluctuations for the inhomogeneous chiral transition

Abstract

The effects of fluctuations are discussed around the phase boundary of the inhomogeneous chiral transition between the inhomogeneous chiral phase and the chiral-restored phase. The particular roles of thermal and quantum fluctuations are elucidated and a continuity of their effects across the phase boundary is suggested. In addition, it is argued that anomalies in the thermodynamic quantities should have phenomenological implications for the inhomogeneous chiral transition. Some common features for other phase transitions, such as those from the normal to the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov state in superconductivity, are also emphasized.

Inhomogeneous chiral condensate in the quark-meson model

“…To be specific, we focus on a chiral-density wave (CDW). The problem of inhomogeneous phases has been addressed before in the context of the Ginzburg-Landau approach [16][17][18][19], the NJL [20][21][22][23][24][25] and PNJL models [26,27], the QM model [22,28,29], and the nonlocal chiral quark model [30]. Numerical methods for the calculation of the phase diagram for a general inhomogeneous condensate are available [31,32], but we resort to a chiral-density wave ansatz in order to present analytical results.…”

Inhomogeneous Chiral Phase in Quark Matter

“…iCP is surrounded by the two phase boundaries and the meeting point (Lifshitz point) is the triple point where two uniform phases (SSB and chiral-restored phases) and iCP coexist. Recently, the right boundary between iCP and the chiral-restored phase has been carefully discussed by taking into account the quantum and thermal fluctuations of the chiral pair fluctuations [4,5].…”

“…In the recent papers we have studied the effects of fluctuations near the phase boundary of iCP to see change of the properties of the phase transition [4,5]. There are two boundaries which surround iCP in the density-temperature plane.…”

Effects of Fluctuations on Inhomogeneous Chiral Transitions

“…2), which implies that the phase transition is prohibited at T 0, while there is no divergence for τ R = 0 at T = 0. This difference can be understood via the contribution of the Matsubara frequencies to the one-loop integral for τ R [6], where a kind of dimensional reduction occurs. Next we examine the forth-order vertex function.…”

“…] within the two-flavor NJL model in the chiral limit [5,6], we derive the effective action, after introducing the auxiliary fields ϕ a = −2G(ψ q ψ q ,ψ q iγ 5 τψ q ) with a = 0, 1, 2, 3 being the component in the isospace, respecting S U(2) L × S U(2) R ∼ O(4) symmetry and then integrating out the quark fields:…”