Modeling feature interactions is crucial for click-through rate (CTR) prediction, particularly when it comes to high-order explicit interactions. Traditional methods struggle with this task because they often predefine a maximum interaction order, which relies heavily on prior knowledge and can limit the model's effectiveness. Additionally, modeling high-order interactions typically leads to increased computational costs. Therefore, the challenge lies in adaptively modeling high-order feature interactions while maintaining efficiency. To address this issue, we introduce Kolmogorov-Arnold Represented Sparse Efficient Interaction Network (KarSein), designed to optimize both predictive accuracy and computational efficiency. We firstly identify limitations of directly applying Kolmogorov-Arnold Networks (KAN) to CTR and then introduce KarSein to overcome these issues. It features a novel architecture that reduces the computational costs of KAN and supports embedding vectors as feature inputs. Additionally, KarSein employs guided symbolic regression to address the challenge of KAN in spontaneously learning multiplicative relationships. Extensive experiments demonstrate KarSein's superior performance, achieving significant predictive accuracy with minimal computational overhead. Furthermore, KarSein maintains strong global explainability while enabling the removal of redundant features, resulting in a sparse network structure. These advantages also position KarSein as a promising method for efficient inference.