Together with the field of gravity and the Kalb–Ramond field, the dilaton field is one of the three massless bosonic fields that appears in effective background quantum field theories of string theory.
Action functional of dilaton gravity
Let be a compact smooth manifold. Write for the configuration space of pseudo-Riemannian metrics (the graviton) and of smooth functions (the dilaton ) on .
The action functional for dilaton gravity is
where is the Riemann curvature scalar of and the Hodge star operator and is the volume form of .
For this reduces to the Einstein-Hilbert action. For it is still a multiple of the Einstein-Hilbert action functional.
The gradient flow of this functional is Ricci flow.
Global cohomological description
The global nature of the gravitational field and the Kalb–Ramond field are well understood conceptually: the gravitational field is a pseudo-Riemannian metric and the Kalb–Ramond field is a cocycle in third integral differential cohomology (for instance realized by a cocycle in Deligne cohomology or by a bundle gerbe with connection).
In generalized complex geometry, both these fields are shown to be unified as one single ∞-Lie algebroid valued form field: a connection on a standard Courant algebroid (as described in more detail there).
While it was clear that the diaton field is locally just a real-valued function, is formal global identification has not been understood in an analogous manner for a long time.
But a proposal for a precise conceptual identification of the dilaton as a structure appearing in the context of generalized complex geometry is in
- Mariana Graña, Ruben Minasian, Michela Petrini, Daniel Waldram, T-duality, generalized geometry and non-geometric backgrounds (arXiv)
The gradient flow of the action functional for dilaton gravity is essentially Ricci flow.
standard model of particle physics
force field (physics) gauge bosons
matter field fermions (spinors)
hadron (bound states of the above quarks)
minimally extended supersymmetric standard model
superpartner gauge field fermions
The derivation of dilaton gravity as part of the effective QFT of string theory is discussed for instance aroung page 911 of
- Eric D'Hoker, String theory in Pierre Deligne, Pavel Etingof, Dan Freed, L. Jeffrey, David Kazhdan, John Morgan, D.R. Morrison and Edward Witten, (eds.) Quantum Fields and Strings, A course for mathematicians, 2 vols. Amer. Math. Soc. Providence 1999. (web version)