Light Like Segment Compactification and Braneworlds with Dynamical String Tension

Braneworld scenarios appear in dynamical string tension theories, where string tension is positive between two surfaces separated by a short distance and at the two surfaces themselves the string tensions become infinite, therefore producing an effective confinement of the strings and therefore of all matter and gravity to the space between these to surfaces. The specific model studied is in the context of the modified measure formulation the string where tension appear as an additional dynamical degree of freedom and these tensions are not universal, but rather each string generates its own tension, which can have a different value for each string. We consider a new background field that can couple to these strings, the tension scalar is capable then of changing locally along the world sheet and then the value of the tension of the string object changes accordingly along the world sheet. Sting tension appears dynamically and each string tension has a characteristic constant of integration that appears as a consequence of the dynamical tension generation . When many types of strings probing the same region of space are considered this tension scalar is constrained by the requirement of quantum conformal invariance. For the case of two types of strings probing the same region of space with different dynamically generated tensions (characterized by different constants of integration) , there are two different metrics, associated to the different strings, that have to satisfy vacuum Einsteins equations and the consistency of these two Einsteins equations determine that the tension field behaves. The two metrics are flat space in Minkowshi space and flat space after a special conformal transformation, then the strings are confined inside a light like Segment or alternatively as expanding Braneworlds where the strings are confined between two expanding bubbles.