Dynamical string tension theories with target space scale invariance leading to 4D

Abstract The string tensions can be dynamical, as we have studied in recent publications, for example in the case when we formulate string theories in the modified measure formalism. Then string and brane tensions appear, but as an additional dynamical degree of freedom. It can be seen, however, that these string or brane tensions may not be universal, but rather each string and each brane generates its own tension, which can have a different value for each string or brane. The case where there are strings that can have different spontaneously generated tensions has been considered in previous publication. To have a real dynamical string tension, we consider new background fields that can couple to the strings, the tension scalar which is capable of changing locally along the world sheet the value of the tension of the extended object. When all string tensions are equal, there is now an unbroken target space scale invariance. By considering possible effective actions of gravity and strings as matter in D dimensions, we determine D by requiring that the effective action be, as the fundamental theory, target space scale invariant, which singles out D=4.