Scale factor duality for conformal cyclic cosmologies

Conformal scale factor inversion for domain walls and holography

“…factor dualities," in analogy to Veneziano's work [32]. CSFI corresponds to the inversion of the FRW scalefactor in conformal time developed by the present authors in [33][34][35].…”

“…The paradigmatic example of scale factor duality is the one found by Veneziano [32], but other maps between cosmological solutions have also been called by the same apellation, e.g., [33,34,37,48]. The analogous of our map for cosmological spacetimes, in particular, has been called a scale factor duality in [33,34]. In the context of string theory and holography, however, the word "duality" should be used with some care to avoid misinterpretation.…”

“…We have seen that Einstein-frame Liouville models with parameters lying within the range (46a) have a well-defined holographic interpretation via the AdS linear dilaton solution (41) found in the Jordan frame (34). In [22], it was shown that one can obtain the Einstein-frame potentials in a different way: by performing a dimensional reduction of a higher-dimensional pure AdS solution over a torus.…”

“…5 The D6-brane has α ¼ 9 2 , violating (44), hence there is no FG expansion since σ ¼ −1. On the other hand, a D2-brane has α ¼ − 1 6 , which gives a negative kinetic term in (34).…”

“…Finally, let us make a comment about the invariant potential in the Einstein frame, with v ¼ v c . It corresponds to α ¼ AE∞, then the kinetic term of Φ is uniquely normalized to unity in (34) and, with the redefinition Φ → −2Φ, one finds just the bosonic string effective action, but with a constant dilaton potential…”