Ontology of String Theory

The “usual” one#

Due to pedagogical reason this view is the dominant one in introductory texts to string theory.

The picture is that of a classical string propagating through a spacetime, hence the Polyakov action. Then we try to quantize the theory, finally figuring out that the only consistently quantizable theories are those with a vanishing Weyl anomaly.

Different compactifications are choices for the spacetime the string propagates through.

The CFT view#

String theory is the theory of scattering amplitude as the sum over compact 2-dimensional manifolds (RIeman surfaces) on which certain conformal field theories with non-anomalous Weyl symmetry live. A certain subset of these theories, superconformal \(N=2\) theories are often naturally expressed in terms of an action of fields whose target space is a 10-dimensional manifold.

Different compactifications are choices for the conformal theories.

Deformations#

Conformal field theories can be deformed by marginal operators associated with their renormalization group flow.

Such a deformation corresponds to

1. the variation of some vacuum expectation value of some field or combination of fields;
2. the changing of the shape of the target space of the associated CFT.

Thus deformations map out the moduli of the target space. A smooth variation in the CFT is associated to a variation in spacetime structure. This is not a smooth one in the ordinary sense of classical geometry; the variation in moduli can cause the topology of the target space to change.

If we understood the dynamics that governed the deformations of the CFT, then we would also understand how string compactifications are "selected".