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Stringy KLT Relations on $AdS$

Luis F. Alday, Maria Nocchi, Aurélie Strömholm Sangaré

Abstract

We study the building blocks of open and closed string amplitudes on $AdS$. These are given by two infinite towers of world-sheet integrals generalising the Euler and complex beta functions respectively. We show that the open and closed building blocks are related by an $AdS$ version of the KLT relations, whose Kernel can be computed exactly. We furthermore show that the building blocks for open string amplitudes are given by Aomoto-Gelfand hypergeometric functions, and give their closed form expression up to weight four.

Stringy KLT Relations on $AdS$

Abstract

We study the building blocks of open and closed string amplitudes on . These are given by two infinite towers of world-sheet integrals generalising the Euler and complex beta functions respectively. We show that the open and closed building blocks are related by an version of the KLT relations, whose Kernel can be computed exactly. We furthermore show that the building blocks for open string amplitudes are given by Aomoto-Gelfand hypergeometric functions, and give their closed form expression up to weight four.
Paper Structure (11 sections, 140 equations)

This paper contains 11 sections, 140 equations.

Table of Contents

  1. Motivation and summary
  2. Open string amplitudes on $AdS$ - building blocks
  3. Explicit results
  4. Relation to Aomoto-Gelfand hypergeometric functions
  5. Closed string amplitudes on $AdS$ - building blocks
  6. Explicit results
  7. $AdS$ KLT relations
  8. Conclusions
  9. Conventions
  10. Pole structure
  11. Poincaré duality