The Lagrangian of the theory is given by a sum of dimensionally extended Euler densities, and it can be written as follows where Rμναβ represents the Riemann tensor, and where the generalized Kronecker delta δ is defined as the antisymmetric product Each term
This is because a quadratic term is present in the low energy effective action of heterotic string theory, and it also appears in six-dimensional Calabi–Yau compactifications of M-theory.
In the mid-1980s, a decade after Lovelock proposed his generalization of the Einstein tensor, physicists began to discuss the quadratic Gauss–Bonnet term within the context of string theory, with particular attention to its property of being ghost-free in Minkowski space.
The theory is known to be free of ghosts about other exact backgrounds as well, e.g. about one of the branches of the spherically symmetric solution found by Boulware and Deser in 1985.
In general, Lovelock's theory represents a very interesting scenario to study how the physics of gravity is corrected at short distance due to the presence of higher order curvature terms in the action, and in the mid-2000s the theory was considered as a testing ground to investigate the effects of introducing higher-curvature terms in the context of AdS/CFT correspondence.