Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Worldsheet for Generalized Veneziano Amplitudes

Shota Komatsu, Pronobesh Maity

TL;DR

The paper addresses the lack of a worldsheet description for Mandelstam's generalized Veneziano amplitudes beyond the original open-string four-point case. It proposes a worldsheet action based on a chiral composite linear dilaton (CLD) that reproduces the generalized amplitudes parameterized by $b$, $\\lambda$, and $\\delta$, and extends the construction to higher-point open-string and closed-string amplitudes. Key contributions include explicit four-point formulas, a higher-point open-string framework featuring the Mandelstam map and a discriminant $\\Delta(P_n)$, and a closed-string sector described by Appell-type hypergeometric functions with partial crossing symmetry. The work establishes a first-principles worldsheet approach to generalized amplitudes, enabling future studies of unitarity, no-ghost theorems, and the pursuit of fully crossing-symmetric closed-string amplitudes within this framework.

Abstract

We present a worldsheet action that reproduces a class of dual resonance amplitudes discussed in the literature, which generalize the Veneziano amplitude for open strings. Our proposal builds on the chiral composite linear dilaton introduced recently. We further compute higher-point extensions and closed-string analogs, which exhibit partial crossing symmetry.

Worldsheet for Generalized Veneziano Amplitudes

TL;DR

The paper addresses the lack of a worldsheet description for Mandelstam's generalized Veneziano amplitudes beyond the original open-string four-point case. It proposes a worldsheet action based on a chiral composite linear dilaton (CLD) that reproduces the generalized amplitudes parameterized by , , and , and extends the construction to higher-point open-string and closed-string amplitudes. Key contributions include explicit four-point formulas, a higher-point open-string framework featuring the Mandelstam map and a discriminant , and a closed-string sector described by Appell-type hypergeometric functions with partial crossing symmetry. The work establishes a first-principles worldsheet approach to generalized amplitudes, enabling future studies of unitarity, no-ghost theorems, and the pursuit of fully crossing-symmetric closed-string amplitudes within this framework.

Abstract

We present a worldsheet action that reproduces a class of dual resonance amplitudes discussed in the literature, which generalize the Veneziano amplitude for open strings. Our proposal builds on the chiral composite linear dilaton introduced recently. We further compute higher-point extensions and closed-string analogs, which exhibit partial crossing symmetry.

Paper Structure

This paper contains 17 sections, 67 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Generalized Veneziano amplitudes from worldsheet
  3. Extensions
  4. Higher-point amplitudes
  5. Closed string amplitudes
  6. Conclusion
  7. Conformal invariance of our worldsheet action
  8. Mandelstam formula: derivation and conformal property
  9. Derivation of the Mandelstam formula.
  10. Conformal property
  11. Computing the closed string amplitude using KLT-like factorization
  12. $-\infty<\zeta<0$
  13. $0<\zeta<a_{+}$
  14. $a_{+}<\zeta<a_{-}$
  15. $a_{-}<\zeta<1$
  16. ...and 2 more sections

Figures (7)

  • Figure 1: Open strings between D0-branes placed along $\gamma^1$-direction separated by $\pi w_a R$, where $w_a, \;a=1,\cdots,4$ are fractional winding numbers.
  • Figure 2: To regularise CLD action, we excise semi-circular discs from the upper half plane around insertion points $\{ x_k\}_{k=1}^{n}$, interaction points $\{Z_I\}_{I=1}^{n-2}$, and the point at infinity $x_\infty$.
  • Figure 3: Branch points of the $\xi$-integrand for $-\infty<\zeta<0$ and our choice of the $\xi$-contour
  • Figure 4: Branch points of the $\xi$-integrand for $0<\zeta<a_{+}$ and our choice of the $\xi$-contour
  • Figure 5: Branch points of the $\xi$-integrand for $a_{+}<\zeta<a_{-}$ and our choice of the $\xi$-contour
  • ...and 2 more figures