In this talk, I will present a generalization of eigenvalues/eigenvectors to tensors and how they are affected by the presence of a Gaussian noise. We will focus on symmetric and Gaussian random tensors of order 3. I will introduce two eigenvalue distributions: the signed and the genuine, both computed using field theoretical tools (supersymmetry and Schwinger-Dyson equations), yielding an exact expression for the former distribution and an asymptotic one for the latter. I will compare those results to earlier probabilistic methods based on random matrices. Finally, from a saddle-point analysis, I will show how the largest eigenvalue changes as the variance of the noise increases. The work is based on https://arxiv.org/abs/2405.07731, with Naoki Sasakura.