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Contact interactions in D-brane models

I. Antoniadis, K. Benakli, A. Laugier

TL;DR

This work analyzes tree-level four-fermion amplitudes in Type I D-brane models where matter resides at brane intersections (notably D3/D7 setups), showing that massless exchanges mix KK modes, winding states, and string oscillator excitations to generate dimension-six contact operators. Compared to the DD-string case, ND configurations produce dominant dimension-six contributions, with oscillator exchanges providing the leading coefficients (approximately 0.59) and volume/Wilson-line effects producing exponential suppressions and phase factors. By subtracting massless exchanges, the authors derive effective four-fermion operators and quantify their dependence on internal radii, brane separations, and the number of brane sets, yielding model-independent bounds on the string scale $M_s$ from LEP and low-energy data (roughly 2–3 TeV, depending on the setup). The study highlights the distinct phenomenology of brane intersections, including enhanced sensitivity to geometric data (radii, separations) and a framework for translating stringy contact interactions into experimental limits relevant for TeV-scale string scenarios.

Abstract

We compute the tree-level four-point scattering amplitudes in string models where matter fields live on D-brane intersections. Extracting the contribution of massless modes, we are left with dimension-six four-fermion operators which in general receive contributions from three different sources: exchange of massive Kaluza--Klein excitations, winding modes and string oscillator states. We compute their coefficients and extract new bounds on the string scale in the brane-world scenario. This is contrasted with the situation where matter fields arise from open strings with both ends confined on the same collection of D-branes, in which case the exchange of massive string modes leads to dimension-eight operators that have been studied in the past. When matter fields live on brane intersections, the presence of dimension-six operators increases the lower bound on the string scale to 2--3 TeV, independently of the number of large extra dimensions.

Contact interactions in D-brane models

TL;DR

This work analyzes tree-level four-fermion amplitudes in Type I D-brane models where matter resides at brane intersections (notably D3/D7 setups), showing that massless exchanges mix KK modes, winding states, and string oscillator excitations to generate dimension-six contact operators. Compared to the DD-string case, ND configurations produce dominant dimension-six contributions, with oscillator exchanges providing the leading coefficients (approximately 0.59) and volume/Wilson-line effects producing exponential suppressions and phase factors. By subtracting massless exchanges, the authors derive effective four-fermion operators and quantify their dependence on internal radii, brane separations, and the number of brane sets, yielding model-independent bounds on the string scale from LEP and low-energy data (roughly 2–3 TeV, depending on the setup). The study highlights the distinct phenomenology of brane intersections, including enhanced sensitivity to geometric data (radii, separations) and a framework for translating stringy contact interactions into experimental limits relevant for TeV-scale string scenarios.

Abstract

We compute the tree-level four-point scattering amplitudes in string models where matter fields live on D-brane intersections. Extracting the contribution of massless modes, we are left with dimension-six four-fermion operators which in general receive contributions from three different sources: exchange of massive Kaluza--Klein excitations, winding modes and string oscillator states. We compute their coefficients and extract new bounds on the string scale in the brane-world scenario. This is contrasted with the situation where matter fields arise from open strings with both ends confined on the same collection of D-branes, in which case the exchange of massive string modes leads to dimension-eight operators that have been studied in the past. When matter fields live on brane intersections, the presence of dimension-six operators increases the lower bound on the string scale to 2--3 TeV, independently of the number of large extra dimensions.

Paper Structure

This paper contains 14 sections, 55 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. The D-brane model
  3. Four-fermion scattering amplitudes
  4. Four fermions from DD open strings
  5. Four ND fermions from two sets of branes
  6. Four ND fermions from three sets of branes
  7. Two ND and two DD fermions
  8. Effective four-fermion contact interactions
  9. Two sets of branes: the infinite transverse volume case
  10. Two sets of branes: generalization to arbitrary internal radii
  11. Three sets of branes
  12. Summary of the effective field theory results
  13. Experimental bounds from contact terms
  14. Four-scalar scattering amplitudes from ND open strings

Figures (1)

  • Figure 1: Radius dependence of the four-fermion contact terms for two (solid line) and three (dashed line) sets of branes.