I last derived spacetime physics from the string worldsheet, here I shall derive 4-D physics on exotic manifolds in the context of super-string theory. Before proceeding, recall the key steps: since the solution to the Lagrange multiplier equation of motion is

with its Clifford form

for any scalar. Hence, for , we have:

Now, by solving via a metric:

we get the Dp action:

And since in 4-dimensional space-time, the mass of a Dp-brane can be derived as:

by T-dualizing in the

direction and factoring the dilaton, the dual is hence:

By matrix world-volume integral reduction on

the Polyakov action for the string is given as:

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