Our discussion of closed strings when a "compact" dimension like a circle is small led to some fascinating results, but when we try to study the same scenario with open strings it seems at first like a much less interesting story. Open strings can never be "stuck" wrapped around the circle, so there is no conserved "winding number" that contributes to their total energy.
This is directly related to the behavior of the open string's endpoints. Point particles do not see the new "winding direction" from T-duality, and when R is very small it costs a great deal of energy to move around the circle at all. Thus, the string endpoints are effectively prevented from moving around the circle, so they move in one less dimension than before.
On the other hand, we have already seen that the interior of the open string acts just like a closed string; it can even "pinch off" new closed string loops! So we would expect that the "body" of an open string would see the new "winding direction" from T-duality! But what could it mean for the "body" of a string to move in 26 dimensions (10 for the superstring) while its endpints move in just 25 (or 9, respectively)?
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Copyright © 2004 by Steuard Jensen.