Jen-Chi Lee

Stringy symmetries and their high-energy limits

Abstract 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 Mendes 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 zero-norm states of string theory. A set of massive scattering amplitudes and their high energy limit are calculated explicitly to justify our results.

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

We study the implication of decoupling zero-norm states in the high-energy limit, for the 26dimensional 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.  2005 Elsevier B.V. All rights reserved.

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

Abstract We derive stringy Ward identities from the decoupling of two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string. These Ward identities are valid to all energy α ′ and all loop orders χ in string perturbation theory. The high-energy limit α ′→∞ of these stringy Ward identities can then be used to fix the proportionality constants between scattering amplitudes of different string states algebraically without referring to Gross and Mendes saddle point calculation of high-energy string-loop amplitudes. As examples, all Ward identities for the mass level M 2 =4,6 are derived, their high-energy limits are calculated and the proportionality constants between scattering amplitudes of different string states are determined. In addition to those identified before, we 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 zero-norm states of string theory. A set of massive scattering amplitudes and their high-energy limits are calculated explicitly for each mass level M 2 =4,6 to justify our results.

Ward identities and high energy scattering amplitudes in string theory

Abstract High-energy limit α ′ → ∞ of stringy Ward identities derived from the decoupling of two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string are used to check the consistency of saddle point calculations of high energy scattering amplitudes of Gross and Mende and Gross and Manes. Some inconsistencies of their saddle point calculations are found even for the string-tree scattering amplitudes of the excited string states. We discuss and calculate the missing terms of the calculation by those authors to recover the stringy Ward identities. In addition, based on the tree-level stringy Ward identities, we give the proof of a general formula, which was proposed previously, of all high energy four-point string-tree amplitudes of arbitrary particles in the string spectrum. In this formula all such scattering amplitudes are expressed in terms of those of tachyons as conjectured by Gross. The formula is extremely simple which manifestly demonstrates the universal high energy behavior of the interactions among all string states.

High-energy zero-norm states and symmetries of string theory

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.

Discrete gauge states and w, charges in c = 1 2D gravity

Abstract We give a general formula for gauge states at the discrete momenta in Liouville theory. These discrete gauge states carry the w ∞ charges. As in the case of the 26D (or 10D) string theory, they are decoupled from the correlation functions and can be considered as the symmetry parameters in the old covariant quantization of the theory.

Patterns of high energy massive string scatterings in the Regge regime

We calculate high energy massive string scattering amplitudes of open bosonic string in the Regge regime (RR). We found that the number of high energy amplitudes for each fixed mass level in the RR is much more numerous than that of Gross regime (GR) calculated previously. Moreover, we discover that the leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind. In particular, based on a summation algorithm for Stirling number identities developed recently, we discover that the ratios calculated previously among scattering amplitudes in the GR can be extracted from this Kummer function in the RR. We conjecture and give evidences that the existence of these GR ratios in the RR persists to subleading orders in the Regge expansion of all string scattering amplitudes. Finally, we demonstrate the universal power-law behavior for all massive string scattering amplitudes in the RR.

Scatterings of massive string states from D-brane and their linear relations at high energies

We study scatterings of bosonic massive closed string states at arbitrary mass levels from D-brane. We discover that all the scattering amplitudes can be expressed in terms of the generalized hypergeometric function F23 with special arguments, which terminates to a finite sum and, as a result, the whole scattering amplitudes consistently reduce to the usual beta function. For the simple case of D-particle, we explicitly calculate high-energy limits of a series of the above scattering amplitudes for arbitrary mass levels, and derive infinite linear relations among them for each fixed mass level. The ratios of these high-energy scattering amplitudes are found to be consistent with the decoupling of high-energy zero-norm states of our previous works.

High energy scattering amplitudes of superstring theory

We use three different methods to calculate the proportionality constants among high-energy scattering amplitudes of different string states with polarizations on the scattering plane. These are the decoupling of high-energy zero-norm states (HZNS), the Virasoro constraints and the saddle-point calculation. These calculations are performed at arbitrary but fixed mass level for the NS sector of 10D open superstring. All three methods give the consistent results, which generalize the previous works on the high-energy 26D open bosonic string theory. In addition, we discover new leading order high-energy scattering amplitudes, which are still proportional to the previous ones, with polarizations orthogonalto the scattering plane. These scattering amplitudes are of subleading order in energy for the case of 26D open bosonic string theory. The existence of these new high-energy scattering amplitudes is due to the worldsheet fermion exchange in the correlation functions and is, presumably, related to the high-energy massive spacetime fermionic scattering amplitudes in the R-sector of the theory.  2006 Elsevier B.V. All rights reserved.

Comments on the high energy limit of bosonic open string theory

In previous works, ratios among four-point scattering amplitudes at the leading order in the high-energy limit were derived for the bosonic open string theory. The derivation was based on Ward identities derived from the decoupling of zero-norm states and was purely algebraic. The only assumption of the derivation was that the momentum polarization can be approximated by the longitudinal polarization at high energies. In this paper, using the decoupling of spurious states, we reduce this assumption to a much weaker one which can be easily verified by simple power counting in most cases. For the special cases which are less obvious, we verify the new assumption for an example by saddle-point approximation. We also provide a new perspective to our previous results in terms of DDF states. In particular, we show that, by using DDF states, one can easily see that there is only one independent high energy scattering amplitude for each fixed mass level.