Interdisciplinary study of gravity and curvature effect in strongly coupled systems

在上一财年进行的研究主要集中在两个主题上：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，我们已经证明了基态，通常被认为是均匀的，它在临界密度以上变得不均匀。我们进一步证明，在高密度下，基态与在小密度下是均匀的。这种行为表明，非线性西格玛模型与它们的费米子表亲，即表现出类似行为的Gross-Neveu模型之间有明显的相似性。这方面的一篇论文已经提交给高能物理杂志发表，目前正在修改中，第二篇论文正在准备中。我们进行的第二项研究重点是分析Mermin-Wagner定理对卡西米尔效应的影响。通过这项工作，我们证明了卡西米尔效应表现出反常的特征。此外，我们还将非线性模型的质量间隙问题推广到高维，从而解决了最近争论的一个问题。一篇关于的论文目前正在准备中。

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.