The Embedding Model of Induced Gravity with Bosonic Sources

Abstract

We consider a theory in which spacetime is an n-dimensional surface $V_n$ embedded in an $N$-dimensional space $V_N$. In order to enable also the Kaluza-Klein approach we admit $n > 4$. The dynamics is given by the minimal surface action in a curved embedding space. The latter is taken, in our specific model, as being a conformally flat space. In the quantization of the model we start from a generalization of the Howe-Tucker action which depends on the embedding variables $η^a (x)$ and the (intrinsic) induced metric $g_{μν}$ on $V_n$. If in the path integral we perform only the functional integration over $η^a (x)$, we obtain the effective action which functionally depends on $g_{μν}$ and contains the Ricci scalar $R$ and its higher orders $R^2$ etc. But due to our special choice of the conformal factor in $V_N$ enterig our original action, it turns out that the effective action contains also the source term. The latter is in general that of a $p$-dimensional membrane ($p$-brane); in particular we consider the case of a point particle. Thus, starting from the basic fields $η^a (x)$, we induce not only the kinetic term for $g_{μν}$, but also the "matter" source term.