#### Bulg. J. Phys. vol.51 no.1 (2024), pp. 021-041

#### Inversion Invariant Volume Element for Strings, Antistrings and Braneworlds

Eduardo Guendelman

go back^{1,2}^{1}*Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel*^{2}*Frankfurt Institute for Advanced Studies, Giersch Science Center, Campus Riedberg, Frankfurt am Main, Germany*Abstract.The specific model studied is in the context of the modified measure formulation the string or branes, where tension appear as an additional dynamical degree of freedom. We then consider the signed reparametrization invariant volume element formulation of dynamical strings and branes and find that the dynamical tension can produce positive tensions or negative tensions, corresponding exactly to strings and branes and antistrings and antibranes respectively. The antistrings are realized when a scalar time that defines the modified measure runs in the opposite direction to the world sheet time. For strings with positive tension, both times run in the same direction. The situation resembles the situation in Relativistic Quantum Mechanics with positive and negative energies, proper time of particles running forward with respect of coordinate time, while for antiparticles proper tome runs opposite of coordinate time. An example, where string antistring pair creation takes place in analogy to the pair creation in an external electric field in QED background field, this time in the presence of a background scalar field that couples to the strings and locally changes the tension, the tension field. 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, there are two different metrics, associated to the different strings. Each of these metrics have to satisfy vacuum Einstein's equations and the consistency of these two Einstein's equations determine the tension scalar. The universal metric, common to both strings generically does not satisfy Einstein's equation. The two string dependent metrics considered here are flat space in Minkowski space and Minkowski space after a special conformal transformation. The limit, where the two string tensions are the same, is studied, it leads to a well defined solution. If the string tension difference between the two types of strings is very small but finite, the approximately homogeneous and isotropic cosmological solution lasts for a long time, inversely proportional to the string tension difference and then the homogeneity and and isotropy of the cosmological disappears and the solution turns into an expanding brane world, where the strings are confined between two expanding bubbles separated by a very small distance at large times.

doi: https://doi.org/10.55318/bgjp.2024.51.1.021