Theoretical and phenomenological aspects of superstring by Christos Kokorelis
By Christos Kokorelis
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26), we can see that the −b′a lnM 2 (T ) indeed arise. 21) are between −1/2 and 1/2. g (1 − τ12 )1/2 = (1 − (1/2)2)1/2 = (3)/2. 23). Rescaling the τ2 variable in the integral, and using the condition 0 < z < 1 which is necessary for the logarithmic behaviour to be dominant, we get52 4 0 < M 2 (T ) < √ ′ . 001 and ǫ(z) < 2 × 10−7 . 27) Restoring units in the Regge slope parameter a′ . 24) –51– This means that the dominant behaviour of the threshold corrections appears in the form of a √ logarithmic singularity, only when the moduli scalars satisfy the limit M 2 < 4/( 3a′ ).
Corrections to the general theory of relativity(GR) coming from the massless modes of the superstring theory appear in two different forms. One is associated with the use of background field contributions of the infinite tower of massive modes leading to corrections in α′ , while the other corresponds to quantum loop effects. In the first form, the effective lagrangian of the massless modes can be studied in the σ model approach[20]. 1) where Gµν (x), Bµν (x), Φ and the vacuum expectation values of the usual background fields, namely metric, antisymmetric tensor, dilaton and tachyon field respectively[20].
The continuous deformations, of a superstring solution constitute its moduli space. e. e. the value of the β-function remains zero. e they are moduli. i gi d2 zΦi (z, z¯), where the constants –41– the so called target space duality[36, 37, 39, 42, 43, 38, 44] transformations. They change the geometry of the internal space and leave invariant [44] the massive spectrum and interactions. They are of great importance, since by lifting the degeneracy by perturbative string theory [47, 48, 49, 50] or non-perturbative effects31 we will be able to see clearly the effects of string theory on the physical observables.