Classical and Quantum Gravity Effects From Planckian Energy Superstring Collisions

Abstract

We argue that superstring collisions at Planckian energies and small deflection angles are calculable through an evaluation and resummation of string loops in flat space-time. This leads to a systematic expansion of the collision in classical general relativity and quantum string effects. Our results explicitly show how unitarity constraints are recovered through loop corrections and how flat metric calculations reveal the generation of nontrivial geometries by energetic particles. Finite-string-size effects can be evaluated in some regimes and are found to modify classical relativity expectations even at impact parameters much larger than the string scale. Conversely, we find that, through the resummation of large genus contributions, intermediate distance physics provides important classical relativity effects even in the hard, fixed angle regime.

High-energy string-brane scattering: leading eikonal and beyond

“…In [1,2] it was shown that an eikonal resummation of the leading high-energy contributions to the S-matrix leads to results that are fully consistent with general relativity expectations whenever effects due to the finite string size (l s = √ α ) can be neglected. In this particular process the effective geometry turns out to be, to leading order, the wellknown Aichelburg-Sexl (AS) shock-wave metric [11] produced by an energetic pointlike massless particle.…”

Anisotropic modulus stabilisation: strings at LHC scales with micron-sized extra dimensions

“…First, such strong growth would eventually violate the unitarity bound once E ∼ M D , indicating that a fuller string calculation is required at higher energies, where the emission and exchange of string states is no longer negligible [101][102][103][104][105][106][107][108]. Second, it shows that it is the highest energy KK states that dominate in the cross section, and since these also have the shortest wavelength their properties (and the cross section) is largely insensitive to the details of the higher-dimensional geometry [109].…”

A microscopic description of absorption in high-energy string-brane collisions

“…It can be simplified, however, under the assumption that R p , while comparable or even larger than b, is still smaller than the string length parameter l s , enhanced by a square root of the logarithm of the energy, as we will discuss in more detail in the rest of the paper. 1 When this is the case the eikonal resummation of the leading terms (in energy) of the higher-order string amplitudes [4,11,12] should give a correct representation of the dynamics for every value of the impact parameter, all the way down to b = 0. Although in this limit a geometric interpretation of the brane background is lacking, the dynamics of the string-brane system remains extremely rich and interesting.…”

“…The vertex operator for a generic closed string state |ψ can be written as follows: 12) where S andS are labels that identify the little group representations of the left and right part of the closed state, ,¯ the corresponding polarization tensors and 5…”

“…For clarity, in the following we will display explicitly the dependence of the Neumann coefficients on the transverse momentum q, writing N rs kl ( q) and N r k ( q). When the transverse momentum is non zero, the vertex becomes 12) where…”