The paper by Claudia de Rham and Gregory Gabadadze investigates the consistency of a covariant polynomial potential for a relativistic, symmetric rank-2 tensor field in four-dimensional flat space-time. They focus on the decoupling limit, where the dynamics of the helicity-0 mode can be studied, and explore the interactions up to fifth order in nonlinearities. The authors calculate the self-interactions of the helicity-0 mode and the nonlinear mixing between the helicity-0 and -2 modes. They show that ghost-like pathologies in these interactions disappear for specific choices of the polynomial interactions and argue that this result holds to all orders in the decoupling limit. Additionally, they demonstrate that some of the nonlinear mixing terms can be absorbed by a local change of variables, generating cubic, quartic, and quintic Galileon interactions. They also note that the mixing between the helicity-0 and 2 modes can be at most quartic in the decoupling limit. The findings have implications for the consistency of the effective field theory away from the decoupling limit and for the Boulware-Deser problem. The paper concludes with a discussion on the stability of the full theory and the potential for a consistent effective field theory below a certain scale.The paper by Claudia de Rham and Gregory Gabadadze investigates the consistency of a covariant polynomial potential for a relativistic, symmetric rank-2 tensor field in four-dimensional flat space-time. They focus on the decoupling limit, where the dynamics of the helicity-0 mode can be studied, and explore the interactions up to fifth order in nonlinearities. The authors calculate the self-interactions of the helicity-0 mode and the nonlinear mixing between the helicity-0 and -2 modes. They show that ghost-like pathologies in these interactions disappear for specific choices of the polynomial interactions and argue that this result holds to all orders in the decoupling limit. Additionally, they demonstrate that some of the nonlinear mixing terms can be absorbed by a local change of variables, generating cubic, quartic, and quintic Galileon interactions. They also note that the mixing between the helicity-0 and 2 modes can be at most quartic in the decoupling limit. The findings have implications for the consistency of the effective field theory away from the decoupling limit and for the Boulware-Deser problem. The paper concludes with a discussion on the stability of the full theory and the potential for a consistent effective field theory below a certain scale.