Calculation of Zero-Norm States and Reduction of Stringy Scattering Amplitudes

Lee, Jen-Chi

doi:10.1143/ptp.114.259

Cited by 14 publications

(19 citation statements)

References 13 publications

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“…(2.72) and (2.73). Thus this inter-particle zero-norm state will generate an inter-particle symmetry transformation in the σ-model calculation considered in [7,13]. Note that, in contrast to the high-energy symmetry of Gross [5], this symmetry is valid to all orders in α ′ .…”

Section: )mentioning

confidence: 96%

“…In this subsection, we are going to do the most general spectrum analysis which naturally includes zero-norm states. We will then solve the Virasoro constraints in the helicity basis and recover the zero-norm states listed above [7,13]. In particular, this analysis will make it clear how D 2 zero-norm state in Eq.…”

Section: B Zero-norm States In the Helicity Basismentioning

confidence: 99%

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Anatomy of zero-norm states in string theory

2005

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We calculate and identify the counterparts of zero-norm states in the old covariant first quantised (OCFQ) spectrum of open bosonic string in two other quantization schemes of string theory, namely the light-cone DDF zero-norm states and the off-shell BRST zero-norm states (with ghost) in the Witten string field theory (WSFT). In particular, special attention is paid to the inter-particle 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 few 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 σ-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.Recently it was discovered that [1, 2] the high-energy limit α ′ → ∞ of stringy Ward identities, derived from the decoupling of two types of zero-norm states in the OCFQ spectrum, imply an infinite number of linear relations among high energy scattering amplitudes of different string states with the same momenta. Moreover, these linear relations can be used to fix the proportionality constants between high energy scattering amplitudes of different string states algebraically at each fixed mass level. Thus there is only one independent component of high energy scattering amplitude at each fixed mass level. For the case of string-tree amplitudes, a general formula can even be given to express all high-energy stringy scattering amplitudes for arbitrary mass levels in terms of those of tachyons [1,3].These zero-norm state calculations are independent of the high-energy saddle-point calculations of Gross and Mende [4], Gross [5] and Gross and Manes [6]. In fact, the results of saddle-point calculations by those authors were found [1-3] to be inconsistent with high energy stringy Ward identities of zero-norm state calculations, and thus could threat the validity of unitarity of string perturbation theory. A corrected saddle-point calculation was given in [3], where the missing terms of the calculations in Refs [4,5,6] were identified to recover the stringy Ward identities.The importance of zero-norm states and their implication on stringy symmetries were first pointed out in the context of massive σ-model approach of string theory [7]. Some implications of the corresponding stringy Ward identities on the scattering amplitudes were discussed in [8]. On the other hand, zero-norm states were also shown [9] to carry the spacetime ω ∞ symmetry [10] charges of 2D string theory [11]. This is in parallel with the work of [12] where the gr...

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Section: )mentioning

confidence: 96%

Section: B Zero-norm States In the Helicity Basismentioning

confidence: 99%

Anatomy of zero-norm states in string theory

2005

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“…Since L † n = L −n , states of the form L −n |χ (18) are orthogonal to all physical states, and they are called spurious states. Zero-norm states are spurious states that are also physical.…”

Section: Linear Relations Among 4-point Functionsmentioning

confidence: 99%

Solving all 4-point correlation functions for bosonic open string theory in the high-energy limit

et al. 2005

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We study the implication of decoupling zero-norm states in the high-energy limit, for the 26 dimensional bosonic open string theory. Infinitely many linear relations among 4-point functions are derived algebraically, and their unique solution is found. Equivalent results are also obtained by taking the high-energy limit of Virasoro constraints, and as an independent check, we compute all 4-point functions of 3 tachyons and an arbitrary massive state by saddle-point approximation.

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“…To further uncover the group theoretical structure of these stringy symmetries, it is important to explicitly calculate the complete set of zero-norm states with arbitrarily high spins in the spectrum. Recently, a simplified method to generate zero-norm states in OCFQ bosonic string was proposed [11]. General formulas of some zero-norm tensor states at an arbitrary mass level were given.…”

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confidence: 99%

Stringy symmetries and their high-energy limits

Chan¹,

Lee

2005

Physics Letters B

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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Calculation of Zero-Norm States and Reduction of Stringy Scattering Amplitudes

Cited by 14 publications

References 13 publications

Anatomy of zero-norm states in string theory

Anatomy of zero-norm states in string theory

Solving all 4-point correlation functions for bosonic open string theory in the high-energy limit

Stringy symmetries and their high-energy limits

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