Decoupling of degenerate positive-norm states in Witten’s string field theory

2005

Physics Letters B

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165

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.

“…(9) to represent this energy reduction. Similar rule applies to T LLT in eq (10). For eq(6), we have θ ′µ = e µ L or θ ′µ = e µ T and one gets, in the high energy limit,…”

mentioning

confidence: 93%

mentioning

confidence: 99%

Stringy symmetries and their high-energy limits

Chan¹,

2005

Physics Letters B

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165

“…It was found that the ratios of string scattering amplitudes at each fixed mass level were independent of the scattering energy and the scattering angle, and the ratios can be extracted at each mass level. Alternatively, this infinite number of ratios can be recalculated algebraically by solving linear relations or stringy Ward identities derived from decoupling of two types of zero-norm states [9][10][11] in the string spectrum. These infinite linear relations are so powerful that all fixed angle high energy string scattering amplitudes can be expressed in terms of one amplitude, say, four tachyon amplitude.…”

Section: Introductionmentioning

confidence: 99%

The Appell function F1 and Regge string scattering amplitudes

Yang

2014

Physics Letters B

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We show that each 26D open bosonic Regge string scattering amplitude (RSSA) can be expressed in terms of one single Appell function F 1 in the Regge limit. This result enables us to derive infinite number of recurrence relations among RSSA at arbitrary mass levels, which are conjectured to be related to the known SL(5, C ) dynamical symmetry of F 1 . In addition, we show that these recurrence relations in the Regge limit can be systematically solved so that all RSSA can be expressed in terms of one amplitude. All these results are dual to high energy symmetries of fixed angle string scattering amplitudes discovered previously [4][5][6][7][8].

“…A consistent check of counting of number of zero-norm states by using the background ghost fields in WSFT was given in Ref. 6). Here we go one step further and invent a simplified method to explicitly construct D=26 stringy zero-norm states.…”

Section: §1 Introductionmentioning

confidence: 99%

“…A consistent check of counting of zero-norm states by using background ghost fields in WSFT was given in Ref. 6).…”

Section: §1 Introductionmentioning

confidence: 99%

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

Progress of Theoretical Physics

2005

We give a simplified method to generate two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string. Zero-norm states up to the fourth massive level and general formulas of some zero-norm tensor states at arbitrary mass levels are calculated. On-shell Ward identities generated by zero-norm states and the factorization property of stringy vertex operators can then be used to argue that the string-tree scattering amplitudes of the degenerate lower spin propagating states are fixed by those of higher spin propagating states at each fixed mass level. This decoupling phenomenon is, in contrast to Gross's high-energy symmetries, valid to all energies. As examples, we explicitly demonstrate this stringy phenomenon up to the fourth massive level (spin-five), which justifies the calculation of two other previous approaches based on the massive worldsheet sigma-model and Witten's string field theory (WSFT). §1. IntroductionThe theory of string, as a consistent quantum theory, has no free parameter and an infinite number of states. It is thus conceivable that there exists huge hidden symmetry group which is responsible for the ultraviolet finiteness of the theory. In fact, it was conjectured by Gross 1) more than a decade ago that an infinite broken gauge symmetries get restored at energy much higher than the Planck energy. Moreover, he conjectured that, for the closed string, there existed an infinite number of linear relations among the scattering amplitudes of different string states that are valid order by order and are of the identical form in string perturbation theory as α goes to infinity. As a result, the scattering amplitudes of all string states can be expressed in terms of, say, the dilaton amplitudes. A similar result was presented in Ref.2) for the open string case.Soon after, it was discovered that 3) the equations of motion for massive background fields of the degenerate positive-norm propagating states can be expressed in terms of those of higher spin propagating states at each fixed mass level. This decoupling phenomenon was argued to be arisen from the existence of two types of zero-norm states with the same Young representations as those of the degenerate positive-norm states in the OCFQ spectrum. This was demonstrated by using massive worldsheet sigma-model approach in the lowest order weak field approximation but valid to all orders in α , and thus was, in contrast to Gross's result, valid to all energies. To compare with the usual sigma-model loop (α ) approximation, this result was argued to be a sigma-model n+1 loop result for the n-th massive level * )