*Post by FearlessFerret*If String Theory is not background-free, and if it subsumes general relativity,

how can the theory 'explain' space-time curvature?

The simplest way is this: all 4-dimensional Lorentzian manifolds are

representable as the limit of manifolds that are Minkowski except on a

submanifold of measure 0.

The measure 0 subset is where the curvature is concentrated at and --

for 4-dimensions -- the singularities are in the most general case

characterized as 2-dimensional. If timelike and compact, they will be

string singularities.

Associated with each singularity is a set of loop invariants that

essentially define the Riemannian tensor as a singular delta-like

function equal to 0 off the source, with loop integrals that give you

non-zero curvature when linking the source.

Thus, you can have your cake and eat it too -- a theory that is

simultaneously strings and loops; simultaneously background-free and

Minkowski background.

This appears the classical level in string theory, where the solution

to the classical 2-dimensional singularity in an otherwise Minkowski

background is a 2-surface closely associated with a lightlike helical

worldline -- i.e., the worldline of a relativistic particle.

This also appears on the classical level in a very closely related

vein, where fermions, themselves, are directly representable as string

singularities:

Kerr-Newman Solution as a Dirac Particle

hep-th/0210103v2

2004 January 19

Arcos and Pereira

(From the abstract)

"For [source mass m, angular momentum a, electric charge q, where m^2 <

a^2 + q^2], the Kerr-Newmann solution of Einstein's equatins reduces to

a naked singularity of circular shape, enclosing a disk across which

the metric components fail to be smooth [which the paper goes on to

describe as a 'looking glass' type wormhole entrance]. By considering

the Hawking and Ellis extended interpretation of the extended

Kerr-Newman spacetime [the looking glass], it is show that, similarly

to the electron-positron system, the solution represents four

inequivalent states. Next, it is shown that due to the topological

structure of the extended Kerr-Newman spacetime, it does admit states

with half-integral angular momentum. This last fact is corroborated by

the fact that, under a rotation of space coordinates, these states

transform into themselves only after a [720 degree] rotation [as is

characteristic of spin 1/2 particles]. As a consequence it becomes

possible to naturally represent them in a Lorentz spinor basis. The

state vector representing the whole Kerr-Newman solution is then

constructed [i.e. the Dirac spinor, itself], and the evolution is shown

to be governed by the Dirac equation. The Kerr-Newman solution can

thus be consistently interpreted as a model for the electron-positron

system, in which the concepts of mass, charge and angular momentum

becomes connected with the spacetime geometry. Some phenomenological

consequences of the model are explored.