Brane world creation from flat or almost flat space in dynamical tension string theories

Eur. Phys. J. C (2022) 82:336 https://doi.org/10.1140/epjc/s10052-022-10320-1 Regular Article - Theoretical Physics Brane world creation from flat or almost flat space in dynamical tension string theories E. I. Guendelman1,2,3,a , J. Portnoy3 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 3 Bahamas Advanced Studies Institute and Conferences, 4A Ocean Heights, Hill View Circle, Stella Maris, Long Island, Bahamas Received: 27 February 2022 / Accepted: 8 April 2022 © The Author(s) 2022 Abstract There is great interest in the construction of brane worlds, where matter and gravity are forced to be effective only in a lower dimensional surface, the brane . How these could appear as a consequence of string theory is a crucial question and this has been widely discussed. Here we will examine a distinct scenario that appears in dynamical tension theories and 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, which is in fact a new type of stringy brane world scenario. The basic formulation for obtaining this scenario consist of assuming two types of strings characterized by a different constant of integration related to the spontaneous string tension generation. These string tension multiplied by the embedding metric define conformally related metrics that both satisfy Einsteins equation. The braneworlds appear very naturally when these two metrics are both flat spaces related by a special conformal transformation. The two types of string tensions are determined and they blow up at two close expanding surfaces. A puzzling aspect appears then: the construction is based on flat spaces, but then there are also strings with very large tension near the boundaries of the braneworld,so can the back reaction from the infinite tension strings destroy the flat space background? Fortunatelly that can be resolved using the mechanism Universe creation from almost flat (or empty) spaces, which incorporates a gas of very large string tensions in a membrane, studied before in 1+1 membranes in a 2+1 embedding space and now is generalized for a 1+(D-2) membrane moving in a 1+(D-1) space. a e-mail: (corresponding author) 0123456789().: V,-vol 1 Introduction In a previous publication [1] we have shown, in the context of theories where the string tension becomes a dynamical variable, using the modified measures formalism, which was previously used for a certain class of modified gravity theories under the names of Two Measures Theories or Non Riemannian Measures Theories, see for example [2–9] Leads to the modified measure approach to string theory [10,11], where rather than to put the string tension by hand it appears dynamically. This approach has been studied in various previous works [12–18]. See also the treatment by Townsend and collaborators for dynamical string tension [19,20]. In [1,21] and references there we have also introduced the tension scalar, which is an additional background field that can be introduced into the theory for the bosonic case (and expected to be well defined for all types of superstrings as well) that changes the value of the tension of the extended object along its world sheet. Before studying issues that are very special of this paper we review some of the material contained in previous papers, first present the string theory with a modified measure and containing also gauge fields that like in the world sheet, the integration of the equation of motion of these gauge fields gives rise to a dynamically generated string tension, this string tension may differ from one string to the other. Then we consider the coupling of gauge fields in the string world sheet to currents in this world sheet, as a consequence this coupling induces variations of the tension along the world sheet of the string. Then we consider a bulk scalar and how this scalar naturally can induce this world sheet current that couples to the internal gauge fields. The integration of the equation of motion of the internal gauge field lead to the remarkably simple equation that the local value of the tension along the string is given by T = eφ+Ti , where e is a coupling 123 336 Page 2 of 5 constant that defines the coupling of the bulk scalar to the world sheet gauge fields and Ti is an integration constant which can be different for each string in the universe. Then each string is considered as an independent system that can be quantized. We take into account the string generation by introducing the tension as a function of the scalar field as a factor inside a Polyakov type action with such string tension, then the metric and the factor gφ + Ti enter together in this effective action, so if there was just one string the factor could be incorporated into the metric and the condition of world sheet conformal invariance will not say very much about the scalar φ , but if many strings are probing the same regions of space time, then considering a background metric gμν , for each string the “string dependent metric“ (φ + Ti )gμν appears and in the absence of othe background fields, like dilaton and antisymmetric tensor fields, Einstein’s equations apply for each of the metrics (φ+Ti )gμν , considering two types of strings with T1= T2 . We call gμν the universal metric. In [1] the metrics (φ + Ti )gμν , for i = 1, 2 are taken to be Minkowski space and Minkowski space after a special conformal transformation. There are then solutions for the tensions of the two types of strings that imply a brane type, where the string tension becomes infinite at two expanding surfaces, so that all matter and gravity are constrained to be between those surfaces. Here we want to discuss how, now from the point of view of of a gravitational theory, this phenomenon of arbitrarily large tensions can be consistent with the existence of flat spaces. 2 Are the flat space backgrounds consistent with the presence of very high tension strings? The whole construction of the braneworld has been based on the conformal mapping between two flat spaces, this conformal mapping then defines the behavior of the string tensions and in principle it represents a vacuum solution where test strings acquire string tensions that diverge at two concentric and expanding surfaces, for details see [1]. Furthermore, as we start to populate the braneworld with actual strings, these strings will have infinite tension at the borders of the braneworld. A natural question one may ask at this point is the following: Are the flat space backgrounds of our construction consistent with the presence of very high Tension Strings or will the backreaction from the very lar (...truncated)