Interdisciplinary study of gravity and curvature effect in strongly coupled systems

在上一个财政年度进行的研究集中在两个主题：一个是关于有限密度下非线性sigma模型中量子真空的变形。对于这些理论，我们已经证明，通常被认为是均匀的基态，在临界密度以上变得不均匀。我们进一步证明了在高密度时，基态变得均匀，就像在低密度时一样。这种行为表明非线性sigma模型和它们的费米子表兄弟Gross-Neveu模型之间的相似性，Gross-Neveu模型表现出类似的行为。一篇关于这方面的论文已经提交给《高能物理学杂志》发表，目前正在修订中，第二篇论文正在准备中。我们进行的第二条研究路线集中于分析Mermin-Wagner定理对Casimir效应的含义。通过这项工作，我们已经表明，卡西米尔效应表现出异常的功能。此外，我们还将非线性sigma模型的质量间隙的某些考虑推广到高维，解决了最近争论的话题。目前正在编写一份关于的文件。

Research carried out during the last fiscal year has focused on two topics: one regarded the deformation of the quantum vacuum in nonlinear sigma models at finite density. For these theories we have shown that the ground state, usually believed to be homogeneous, it becomes inhomogeneous above a critical density. We have further shown that at high density, the ground state becomes homogeneous as for small density. This behavior indicates a sharp similarity between nonlinear sigma models and their fermion cousins, the Gross-Neveu models which manifest a similar behavior. A paper about this has been submitted to the journal of high energy physics for publication and is currently under revision, and a second paper is preparation. The second research line that we have conducted has focused on analyzing the implication of the Mermin-Wagner theorem for the Casimir effect. With this work we have shown that the Casimir effect manifests anomalous features. Furthermore we have generalized certain consideration regarding the mass gap for nonlinear sigma models to high dimensionality, settling a recently debated topic. A paper about is currently in preparation.