Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

REFERENCES 121
The partition function is finally given by
In this “dual action” the G field is not dynamical and can be integrated
out. The integration of this auxiliary field gives
The fields B cannot be rescaled if we impose “periodicity” conditions on
them. Thus, this dual action has inverted coupling with respect to the
original one (compare with [15] for the Abelian case).
6. CONCLUDING REMARKS
In this work we have shown the road to the formulation of an analog
of S –duality in gravity, following similar procedures to those well known
in non–Abelian nonsupersymmetric Yang-Mills theories. We constructed
for dual theories for pure topological gravity, for MacDowell–Mansouri
gauge theory of gravity, and for 2 + 1 Chern–Simons gravity. Work for
the supersymmetric versions of these theories has been done.
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