Dynamical string tension in string theory with spacetime Weyl invariance

Abstract

The fundamental string length, which is an essential part of string theory, explicitly breaks scale invariance. However, in field theory we demonstrated recently that the gravitational constant, which is directly related to the string length, can be promoted to a dynamical field if the standard model coupled to gravity (SM+GR) is lifted to a locally scale (Weyl) invariant theory. The higher gauge symmetry reveals previously unknown field patches whose inclusion turn the classically conformally invariant SM+GR into a geodesically complete theory with new cosmological and possibly further physical consequences. In this paper this concept is extended to string theory by showing how it can be "Weyl lifted" with a local scale symmetry acting on target space background fields. In this process the string tension (fundamental string length) is promoted to a dynamical field, in agreement with the parallel developments in field theory. We then propose a string theory in a geodesically complete cosmological stringy background which suggests previously unimagined directions in the stringy exploration of the very early universe.

Physical interpretation of antigravity

“…The classical or quantum analysis of this theory is best conducted in a Weyl gauge we called the "γ-gauge" [10][1] [7] which amounts to det (−g) = 1. This allows the Sign(φ 2 − s 2 )…”

“…In the worldsheet formulation of string theory the string tension is promoted to a background field T (φ, s) by connecting it directly to the features of the Weyl invariant low energy string theory [7]. Then the string tension T (φ, s) switches sign together with the corresponding gravitational constant [7].…”

“…In the worldsheet formulation of string theory the string tension is promoted to a background field T (φ, s) by connecting it directly to the features of the Weyl invariant low energy string theory [7]. Then the string tension T (φ, s) switches sign together with the corresponding gravitational constant [7]. Thus the Weyl symmetric (SM+GR) and ST predict that, in the Einstein or string gauges, one should expect a sudden sign switch of the effective Planck mass 1 12 (φ 2 − s 2 ) at certain spacetime points that typically correspond to singularities (e.g.…”

“…Finally we emphasize that the same relative minus sign occurs also in a Weyl invariant reformulation of low energy string theory (ST) but with a different interpretation of s related to the dilaton [7]. Hence the structure (φ 2 − s 2 ) R is ubiquitous, but was overlooked because it was commonly assumed that the gravitational constant, or an effective structure that replaces it, could not or should not become negative .…”

“…In our investigations so far, we discovered that the antigravity sectors are geodesically connected to our own gravity sector at gravitational singularities, like the big bang/crunch or black holes, which occur precisely at the same spacetime points where (φ 2 (x) − s 2 (x)) vanishes or goes to infinity. The related dynamical string tension [7] T (φ, s) ∼ (φ + s)…”