Abstract
We study the behavior of the effective potential between revolving Dp-branes at all ranges of the distance r, interpolating r » ls and r « ls (ls is the string length). Since the one-loop open string amplitude cannot be calculated exactly, we instead employ an efficient method of partial modular transformation. The method is to perform the modular transformation partially in the moduli parameter and rewrite the amplitude into a sum of contributions from both of the open and closed string massless modes. It is nevertheless free from the double counting and can approximate the open string amplitudes with less than 3% accuracy. From the D-brane effective field theory point of view, this amounts to calculating the one-loop threshold corrections of infinitely many open string massive modes. We show that threshold corrections to the ω2r2 term of the moduli field r cancel among them, where ω is the angular frequency of the revolution and sets the scale of supersymmetry breaking. This cancellation suggests a possibility to solve the hierarchy problem of the Higgs mass in high scale supersymmetry breaking models.
Highlights
Dp-branes are set in a target space-time
We study the behavior of the effective potential between revolving Dp-branes at all ranges of the distance r, interpolating r ls and r ls
We show that threshold corrections to the ω2r2 term of the moduli field r cancel among them, where ω is the angular frequency of the revolution and sets the scale of supersymmetry breaking
Summary
We are interested in interaction potential between D-branes, which are relatively moving in a target space-time. We can obtain the potential by calculating the one-loop partition function of an open string stretched between the D-branes. We can quantize the stretched open strings and determine a closed form of the one-loop effective potential. In many other cases where D-branes are accelerating, it is not possible to write the effective potential in a closed form, since open strings have complicated boundary conditions. We propose an efficient method to obtain the interaction potential between generally moving D-branes, including threshold corrections of massive open string modes. As we will see, it may give sizable contributions to the small R behavior of the potential They are the threshold corrections of infinitely many open string massive modes. The open string one-loop amplitude of the UV region is approximated by using the supergravity calculations with an appropriate cutoff corresponding to t ∈ [0, 1]
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