Zero-norm states and high-energy symmetries of string theory

Chan, Chuan Tsung; Lee, Jen-Chi

doi:10.1016/j.nuclphysb.2004.04.022

Cited by 52 publications

(192 citation statements)

References 21 publications

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“…On the contrary, for the high energy scatterings of the compactified closed string considered in this paper, one gets more kinematic variables, namely ( m R , 1 2 nR), to cover both GR and MR, so that one can see this interesting transition. Through the observation of this transition, one further confirms that the infinite linear relations obtained in [4,5,6,7,8,9,10,11] are responsible for the UV softer string scattering amplitudes than the field theory scatterings.…”

Section: Discussionsupporting

confidence: 52%

“…This is physically consistent as one expects a m R , 1 2 nR dependent Regge-pole and zero structures in the high energy string scattering amplitudes. In conclusion, in the GR, Presumably, the infinite linear relations obtained above can be reproduced by using the method of high energy ZNS, or high energy Ward identities, adopted in the previous works [4,5,6,7,8,9,10,11]. The existence of Soliton ZNS at arbitrary mass levels was constructed in [22].…”

Section: B the Infinite Linear Relations In The Grmentioning

confidence: 81%

“…Note that, in the GR, one can identify e P with e L as usual [4,5]. However, in the MR, one can not identify e P with e L .…”

Section: High Energy Behaviorsmentioning

confidence: 99%

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Linear relations and their breakdown in high energy massive string scatterings in compact spaces

Lee

Yang

2007

Nuclear Physics B

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We calculate high energy massive scattering amplitudes of closed bosonic string compactified on the torus. For each fixed mass level with given quantized and winding momenta m R , 1 2 nR , we obtain infinite linear relations among high energy scattering amplitudes of different string states.For some kinematic regimes, we discover that linear relations with N R = N L break down and, simultaneously, the amplitudes enhance to power-law behavior instead of the usual expoential falloff behavior at high energies. It is the space-time T-duality symmetry that plays a role here.This result is consistent with the coexistence of the linear relations and the softer exponential fall-off behavior of high energy string scattering amplitudes as we pointed out prevously. It is also reminiscent of our previous work on the power-law behavior of high energy string/domain-wall scatterings. *

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Section: Discussionsupporting

confidence: 52%

Section: B the Infinite Linear Relations In The Grmentioning

confidence: 81%

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Linear relations and their breakdown in high energy massive string scatterings in compact spaces

Lee

Yang

2007

Nuclear Physics B

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“…Recently high-energy, fixed-angle behavior of string scattering amplitudes [1,2,3] was intensively reinvestigated [4,5,6,7,8,9,10]. The motivation was to uncover the long-sought hidden stringy space-time symmetry.…”

Section: Introductionmentioning

confidence: 99%

Notes on high-energy limit of bosonic closed string scattering amplitudes

2006

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We study bosonic closed string scattering amplitudes in the high-energy limit. We find that the methods of decoupling of high-energy zero-norm states and the high-energy Virasoro constraints, which were adopted in the previous works to calculate the ratios among high-energy open string scattering amplitudes of different string states, persist for the case of closed string. However, we clarify the previous saddle-point calculation for high-energy open string scattering amplitudes and claim that only (t, u) channel of the amplitudes is suitable for saddle-point calculation. We then discuss three evidences to show that saddle-point calculation for high-energy closed string scattering amplitudes is not reliable. By using the relation of tree-level closed and open string scattering amplitudes of Kawai, Lewellen and Tye (KLT), we calculate the high-energy closed string scattering amplitudes for arbitrary mass levels. For the case of high-energy closed string four-tachyon amplitude, our result differs from the previous one of Gross and Mende, which is NOT consistent with KLT formula, by an oscillating factor.

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“…However, a simple calculation shows that T 4 LLL = T 4 LT T = T 4 (LL) = 0.So the real leading order amplitudes correspond to E 3 , which appear in eqs. (10), (12) and (14). A simple calculation shows that…”

mentioning

confidence: 99%

Stringy symmetries and their high-energy limits

Chan¹,

Lee

2005

Physics Letters B

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165

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We derive stringy symmetries with conserved charges of arbitrarily high spins from the decoupling of two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string. These symmetries are valid to all energy α ′ and all loop orders χ in string perturbation theory. The high-energy limit α ′ → ∞ of these stringy symmetries can then be used to fix the proportionality constants between scattering amplitudes of different string states algebraically without referring to Gross and Mende's saddle point calculation of high-energy string-loop amplitudes. These proportionality constants are, as conjectured by Gross, independent of the scattering angle φ CM and the order χ of string perturbation theory. However, we also discover some new nonzero components of high-energy amplitudes not found previously by Gross and Manes.These components are essential to preserve massive gauge invariances or decouple massive zeronorm states of string theory. A set of massive scattering amplitudes and their high energy limit are calculated explicitly to justify our results.

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Zero-norm states and high-energy symmetries of string theory

Cited by 52 publications

References 21 publications

Linear relations and their breakdown in high energy massive string scatterings in compact spaces

Linear relations and their breakdown in high energy massive string scatterings in compact spaces

Notes on high-energy limit of bosonic closed string scattering amplitudes

Stringy symmetries and their high-energy limits

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