Establishes explicit resurgent duality between zero-radius weak-coupling and infinite-radius strong-coupling expansions, illustrated on Airy/Pearcey integrals and applied to phi^4 Dyson-Schwinger equations and Gross-Neveu kink-antikink heat kernel.
Başar, G.V
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abstract
We analyze the thermodynamical properties, at finite density and nonzero temperature, of the (1+1)-dimensional chiral Gross-Neveu model (the NJL_2 model), using the exact inhomogeneous (crystalline) condensate solutions to the gap equation. The continuous chiral symmetry of the model plays a crucial role, and the thermodynamics leads to a broken phase with a periodic spiral condensate, the "chiral spiral", as a thermodynamically preferred limit of the more general "twisted kink crystal" solution of the gap equation. This situation should be contrasted with the Gross-Neveu model, which has a discrete chiral symmetry, and for which the phase diagram has a crystalline phase with a periodic kink crystal. We use a combination of analytic, numerical and Ginzburg-Landau techniques to study various parts of the phase diagram.
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At large chemical potential the Gross-Neveu model enters a crystalline phase in which a-particle bound states condense, producing a periodically oscillating chiral condensate governed by two new scales Λ_n and Λ_c that replace the usual Λ.
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Weak-Strong Resurgence Duality
Establishes explicit resurgent duality between zero-radius weak-coupling and infinite-radius strong-coupling expansions, illustrated on Airy/Pearcey integrals and applied to phi^4 Dyson-Schwinger equations and Gross-Neveu kink-antikink heat kernel.
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Perturbative, Nonperturbative and Exact Aspects of Crystalline Phases in the Gross-Neveu Model
At large chemical potential the Gross-Neveu model enters a crystalline phase in which a-particle bound states condense, producing a periodically oscillating chiral condensate governed by two new scales Λ_n and Λ_c that replace the usual Λ.