By S. P. Novikov (auth.), N. Sánchez, A. Zichichi (eds.)
The modern developments within the quantum unification of all interactions together with gravity inspire this path. the most aim and impression of recent string thought is to supply a constant quantum concept of gravity. This, path is meant to supply an up-to-date knowing of the final advancements and present difficulties of string conception in reference to gravity and the physics on the Planck strength scale. it's also the purpose of this direction to debate basic difficulties of quantum gravity within the present-day context regardless of strings or the other versions. Emphasis is given to the mutual impression of string conception, gravity and cosmology, inside a deep a good outlined programme, which supplies, furthermore, a cautious interdisciplinarity. because the so much proper new physics supplied through strings issues the quantization of gravity, we needs to, a minimum of, comprehend string quantization in curved space-times to begin. Curved space-times, in addition to their glaring relevance m classical gravitation, also are vital at energies of the order of the Planck scale. on the Planck strength, gravitational interactions are no less than as very important because the relaxation and will now not be missed anymore. exact care is taken the following to supply the grounds of different strains of study in pageant (not simply just one approach); this gives a superb chance to profit in regards to the actual nation of the self-discipline, and to benefit it in a serious way.
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Additional info for String Gravity and Physics at the Planck Energy Scale
For the sake of completeness we analyze in sec. IV the effective string equations . These equations have been extensively treated in the literature  and they are not our central aim. It must be noticed that there is no satisfactory derivation of inflation in the context of the effective string equations. This does not mean that string theory is not compatible with inflation, but that the effective string action approach is not enough to describe inflation. The effective string equations are a low energy field theory approximation to string theory containing only the massless string modes.
From now on strings will propagate in the curved (physical) four dimensional space-time. However, we will find instructive to study the case where this curved space-time has dimensionality D, where D may be 2, 3, 4 or arbitrary. B. 1) with respect to the metric GAB at the spacetime point X. 27) where dot and prime stands for B/fh and B/Ba, respectively. 27) is just a spacetime point whereas X(a, T) stands for the string dynamical variables. 27) that TAB (X) vanishes unless 23 X is exactly on the string world-sheet.
1) we have R~ == -(D - l)(H + H2) Rf == -cSf [H + (D - 1) H2] R == -(D - 1)(2 H + D H2). 6) where H == ~ ~ . 3) read iP - (D - l)(H + H2) _ au == ael> e p H + (D-1)H2-H+ au + ~ au == e p .. . ael> au D -loR 2if>+2(D-1)H-2-(D-1)(2H+DH2)-2 a -c+2U==O where dot . 7) can be expressed in a more compact form as iiI - (D _ 1) H2 _ . 12) As is known, under the duality transformation R --+ R- 1 , the dilaton transforms as --+ + (D -1) log R. 1O) is invariant under duality. 14) provided u = d, that is, a duality invariant string source.
String Gravity and Physics at the Planck Energy Scale by S. P. Novikov (auth.), N. Sánchez, A. Zichichi (eds.)