Title: Bound states around vacuum in scalar ModMax model Show Chinese title

Title: 标量ModMax模型中的真空附近束缚态

Abstract: In this work, we consider a two-dimensional scalar field model inspired by the dimensional reduction of a four-dimensional ModMax theory. Upon projecting out the 4D theory down to a 2D theory we obtain a theory which presents a constant electric field and two scalar fields. In order to investigate kinks, we include the presence of a potential and consider the static case with one of the fields in the vacuum, showing that the solutions for the non-uniform field can be mapped into the ones arising from the canonical model. By studying the linear stability of the model, we show that fluctuations around the uniform field are described by a Sturm-Liouville eigenvalue equation whose weight function depends on the non-uniform solution and the parameter of the ModMax model. Remarkably, the presence of the aforementioned weight may bring bound states to light, contrary to what occurs in the canonical model. Show Chinese abstract

Abstract: 在这项工作中，我们考虑了一个二维标量场模型，该模型受到四维ModMax理论维度约化的启发。通过将4D理论投影到2D理论中，我们得到了一个呈现恒定电场和两个标量场的理论。为了研究孤立子（kinks），我们引入了势的存在，并考虑了静态情况下的其中一个场处于真空状态，表明非均匀场的解可以映射到源于规范模型的解。通过研究该模型的线性稳定性，我们展示了围绕均匀场的涨落由一个Sturm-Liouville本征值方程描述，其权函数依赖于非均匀解和ModMax模型的参数。值得注意的是，上述权重的存在可能揭示束缚态，这与规范模型中的情况相反。