# High-Energy Zero-Norm States and Symmetries of String Theory

## Abstract

High-energy limit of zero-norm states in the old covariant first quantized spectrum of the 26D open bosonic string, together with the assumption of a smooth behavior of string theory in this limit, are used to derive infinitely many linear relations among the leading high-energy, fixed-angle behavior of four-point functions of different string states. As a result, ratios among all high-energy scattering amplitudes of four arbitrary string states can be calculated algebraically and the leading order amplitudes can be expressed in terms of that of four tachyons as conjectured by Gross in 1988. A dual calculation can also be performed and equivalent results are obtained by taking the high-energy limit of Virasoro constraints. Finally, we compute all high-energy scattering amplitudes of three tachyons and one massive state at the leading order by saddle-point approximation to verify our results.

- Authors:

- Physics Division, National Center for Theoretical Sciences, Hsinchu, Taiwan (China)
- Department of Physics, National Taiwan University, Taipei, Taiwan (China)
- Department of Electrophysics, National Chiao-Tung University, Hsinchu, Taiwan (China)
- Physics Division, National Center for Theoretical Sciences, Taipei, Taiwan (China)

- Publication Date:

- OSTI Identifier:
- 20777206

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters; Journal Volume: 96; Journal Issue: 17; Other Information: DOI: 10.1103/PhysRevLett.96.171601; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; APPROXIMATIONS; SADDLE-POINT METHOD; SCATTERING AMPLITUDES; STRING MODELS; SYMMETRY; TACHYONS

### Citation Formats

```
Chan, C.-T., Ho, P.-M., Lee, J.-C., Yang Yi, and Teraguchi, Shunsuke.
```*High-Energy Zero-Norm States and Symmetries of String Theory*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevLett.96.171601.

```
Chan, C.-T., Ho, P.-M., Lee, J.-C., Yang Yi, & Teraguchi, Shunsuke.
```*High-Energy Zero-Norm States and Symmetries of String Theory*. United States. doi:10.1103/PhysRevLett.96.171601.

```
Chan, C.-T., Ho, P.-M., Lee, J.-C., Yang Yi, and Teraguchi, Shunsuke. Fri .
"High-Energy Zero-Norm States and Symmetries of String Theory". United States.
doi:10.1103/PhysRevLett.96.171601.
```

```
@article{osti_20777206,
```

title = {High-Energy Zero-Norm States and Symmetries of String Theory},

author = {Chan, C.-T. and Ho, P.-M. and Lee, J.-C. and Yang Yi and Teraguchi, Shunsuke},

abstractNote = {High-energy limit of zero-norm states in the old covariant first quantized spectrum of the 26D open bosonic string, together with the assumption of a smooth behavior of string theory in this limit, are used to derive infinitely many linear relations among the leading high-energy, fixed-angle behavior of four-point functions of different string states. As a result, ratios among all high-energy scattering amplitudes of four arbitrary string states can be calculated algebraically and the leading order amplitudes can be expressed in terms of that of four tachyons as conjectured by Gross in 1988. A dual calculation can also be performed and equivalent results are obtained by taking the high-energy limit of Virasoro constraints. Finally, we compute all high-energy scattering amplitudes of three tachyons and one massive state at the leading order by saddle-point approximation to verify our results.},

doi = {10.1103/PhysRevLett.96.171601},

journal = {Physical Review Letters},

number = 17,

volume = 96,

place = {United States},

year = {Fri May 05 00:00:00 EDT 2006},

month = {Fri May 05 00:00:00 EDT 2006}

}