具有O(2)$_L\ imes$O(2)$_R$手征对称性的Gross-Neveu模型：与Zakharov-Mikhailov模型的对偶性及大$N$解
Gross-Neveu model with O(2)$_L\times$O(2)$_R$ chiral symmetry: Duality with Zakharov-Mikhailov model and large $N$ solution
AI总结：
本文构建了具有O(2)手征对称性的Gross-Neveu模型，证明其与Zakharov-Mikhailov模型对偶，并利用大N极限半经典方法求解，为竞争的手征与库珀凝聚提供了可解模型。
摘要：
在1+1维中，具有U(2)$_L\ imes$U(2)$_R$手征对称性的双味Gross-Neveu模型被用来构建一种具有O(2)$_L\ imes$O(2)$_R$手征对称性的新型四费米子理论变体。O(2)群（一个具有两个连通分量：旋转和反射的连续群）的自发破缺产生了新的现象。它特别适合描述两种不同类型的凝聚竞争的情况，特别是手征对称性破缺（粒子-空穴凝聚）和库珀配对（粒子-粒子凝聚）。在详细求解O(2)手征Gross-Neveu模型后，我们证明它与Zakharov和Mikhailov提出的另一个经典可积模型是对偶的。这种对偶性使我们能够用半经典方法在大$N$极限下求解该模型的量子版本，支持其在量子层面的可积性。由此得到的模型是唯一与自由无质量费米子共享完整Pauli-Gürsey对称性的四费米子理论（“完美Gross-Neveu模型”），并为我们提供了一个可解模型，用于描述竞争的手征凝聚和库珀对凝聚，包括显式的孤子动力学和相图。
英文摘要：
The two-flavor Gross-Neveu model with U(2)$_L\times$U(2)$_R$ chiral symmetry in 1+1 dimensions is used to construct a novel variant of four-fermion theories with O(2)$_L\times$O(2)$_R$ chiral symmetry. The spontaneous breaking of the group O(2), a continuous group with two connected components (rotations and reflections), gives rise to new phenomena. It is ideally suited to describe a situation where two distinct kinds of condensation compete, in particular chiral symmetry breaking (particle-hole condensation) and Cooper pairing (particle-particle condensation). After solving the O(2) chiral Gross-Neveu model in detail, we demonstrate that it is dual to another classically integrable model due to Zakharov and Mikhailov. The duality enables us to solve the quantum version of this model in the large $N$ limit with semiclassical methods, supporting its integrability at the quantum level. The resulting model is the unique four-fermion theory sharing the full Pauli-Gürsey symmetry with free, massless fermions (``perfect Gross-Neveu model") and provides us with a solvable model for competing chiral and Cooper pair condensates, including explicit soliton dynamics and the phase diagram.
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