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Title: 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:
 [1];  [2]; ;  [3];  [4]
  1. Physics Division, National Center for Theoretical Sciences, Hsinchu, Taiwan (China)
  2. Department of Physics, National Taiwan University, Taipei, Taiwan (China)
  3. Department of Electrophysics, National Chiao-Tung University, Hsinchu, Taiwan (China)
  4. 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}
}
  • We calculate and identify the counterparts of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string in two other quantization schemes of string theory, namely, the light-cone Del Giudice-Di Vecchia-Fubine zero-norm states and the off-shell Becchi-Rouet-Stora-Tyutin (BRST) zero-norm states (with ghost) in the Witten string field theory (WSFT). In particular, special attention is paid to the interparticle zero-norm states in all quantization schemes. For the case of the off-shell BRST zero-norm states, we impose the no-ghost conditions and recover exactly two types of on-shell zero-norm states in the OCFQ string spectrum for the first fewmore » low-lying mass levels. We then show that off-shell gauge transformations of WSFT are identical to the on-shell stringy gauge symmetries generated by two types of zero-norm states in the generalized massive {sigma}-model approach of string theory. The high-energy limit of these stringy gauge symmetries was recently used to calculate the proportionality constants, conjectured by Gross, among high-energy scattering amplitudes of different string states. Based on these zero-norm state calculations, we have thus related gauge symmetry of WSFT to the high-energy stringy symmetry of Gross.« less
  • By means of a recent analysis of the high-energy limit of string scattering, linear relations between string scattering amplitudes are derived. These are shown to hold order by order in perturbation theory. If one assumes that they hold for the full theory, they suggest the existence of an enormous string-broken symmetry which is restored at high energies. Some speculations as to the nature of this symmetry are presented.
  • The spin''-two and scalar physical propagating fields of the third massive level of the open bosonic string are shown to be mere gauge artifacts of the higher- spin'' fields at the same mass level. This is demonstrated by requiring the worldsheet conformal symmetry in the weak-background-field approximation and is argued to be a {sigma}-model four-loop result. It is conjectured that this phenomenon comes from the well-known ambiguity in defining the positive-norm states due to the existence of zero-norm states in the same Young representation.
  • We study 4D low-energy effective field theory, derived from heterotic string theory on the orbifolds. In particular, we study Abelian and non-Abelian discrete symmetries and their anomalies. Furthermore, stringy computations also provide with stringy coupling selection rules.
  • The author studies the high-energy symmetry structure of string theory corresponding to the massive excitations of the string. These enlarged gauge symmetries are closely related to the existence of zero-norm states in the string spectrum. He has derived these symmetries in the framework of the Hamiltonian version of the first-quantized generalized {sigma}-model formalism. It is conjectured that these infinite space-time symmetry structures could shed light on the finiteness of string perturbation theory. Two interesting phenomena were discovered for these massive states symmetries. One is the inter- spin' symmetry for the different spin' states at each fixed mass level. Specifically, themore » four physical propagating states with spins' up to six of the second massive level of the closed bosonic string are found to form a large gauge multiplet. This is demonstrated by the existence of gauge transformations induced by the type II zero-norm states at this mass level. It is argued that this is a {sigma}-model three loop result for the second massive level and is a general feature for higher massive levels at each fixed mass. The other one is the decoupling of some degenerate positive-norm states. As an example, he explicitly demonstrates that the spin' two and scalar physical propagating fields of the third massive level of the open bosonic string are mere gauge artifacts of the higher spin' fields at the same mass level. It is conjectured that this phenomenon comes from the well-known ambiguity in defining the positive-norm states due to the existence of zero-norm states in the same Young representation.« less