  This study delves into the application of Conformal Field Theory (CFT) to
understand information diffusion within digital media and its broader social
implications. Focusing on the digital native generation, vulnerable to
misinformation and data privacy issues, the research highlights the urgency of
addressing psychological health in the digital realm. By leveraging CFT's
analytical power, particularly in tracing information flows and assessing the
impact of misinformation, the study offers novel insights into the dynamics of
digital communication. It proposes a model for predicting and analyzing the
spread of biased content, emphasizing the need for improved information
literacy and personal data protection. This paper explores the concept of
infinitesimal conformal transformations using the Virasoro operator, forming a
conformal transformation group. In the examination of multiple analytical
methods, the approach to quantitatively analyze cases that are likely to expose
the risk of spreading filter bubbles such as negative information, rumors, and
fake news is to incorporate a two-dimensional conformal field theory approach
using the Ward-Takahashi identity and path integral with trace anomalies and
metric are introduced. Trace anomalies and metrics were introduced. A trace
anomaly refers to the spread of information in an unexpected way, usually
indicating anomalous behavior or hidden dynamics in the system. Metric
variation hypothesized and analyzed how diffusion characteristics, such as the
rate and pattern of information diffusion, vary over time.
