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One-loop Yukawas on Intersecting Branes

S. A. Abel, B. W. Schofield

Abstract

We calculate Yukawa interactions at one-loop on intersecting D6 branes. We demonstrate the non-renormalization theorem in supersymmetric configurations, and show how Yukawa beta functions may be extracted. In addition to the usual logarithmic running, we find the power-law dependence on the infra-red cut-off associated with Kaluza-Klein modes. Our results may also be used to evaluate coupling renormalization in non-supersymmetric cases.

One-loop Yukawas on Intersecting Branes

Abstract

We calculate Yukawa interactions at one-loop on intersecting D6 branes. We demonstrate the non-renormalization theorem in supersymmetric configurations, and show how Yukawa beta functions may be extracted. In addition to the usual logarithmic running, we find the power-law dependence on the infra-red cut-off associated with Kaluza-Klein modes. Our results may also be used to evaluate coupling renormalization in non-supersymmetric cases.

Paper Structure

This paper contains 26 sections, 204 equations.

Table of Contents

  1. Introduction
  2. Elements of the calculation
  3. Vertex operators and $H$-charge
  4. One-loop amplitudes and picture-changing
  5. Bosonic fields
  6. Spin fields
  7. Ghost spin fields
  8. Twist fields
  9. Excited twist fields
  10. The quantum part
  11. The classical action
  12. Limiting cases of the classical action
  13. The partition function limit: $y_{1}\rightarrow y_{2}\rightarrow y_{3}$, $t\rightarrow\infty$
  14. The vertex correction limit: $\left(t-y_{3}\right)\rightarrow\infty$, generic $y_{i}$
  15. The purely twisted loop: $\left(t-y_{3}\right)\rightarrow0$, generic $y_{i}$
  16. ...and 11 more sections