We discover an infinite number of recurrence relations among Regge string scattering amplitudes [10, 23] of different string states at arbitrary mass levels in the open bosonic string theory. As a result, all Regge string scattering amplitudes can be algebraically solved up to multiplicative factors. Instead of decoupling zero-norm states in the fixed angle regime, the calculation is based on recurrence relations and addition theorem of Kummer functions of the second kind. These recurrence relations among Regge string scattering amplitudes are dual to linear relations or symmetries among high-energy fixed angle string scattering amplitudes discovered previously.

We study scattering of higher spin closed string states at arbitrary mass levels from D-particle in the Regge regime. We extract the complete infinite ratios among high-energy amplitudes of different string states in the fixed angle regime from these Regge string scattering amplitudes. In this calculation, we have used an identity proved recently based on a signless Stirling number identity in combinatorial theory. The complete ratios calculated by this indirect method include a subset of ratios calculated previously by direct fixed angle calculation [C. T. Chan, J. C. Lee and Y. Yang, Nucl. Phys. B 764 (2007), 1]. Moreover, we discover that in spite of the non-factorizability of the closed string D-particle scattering amplitudes, the complete ratios derived for the fixed angle regime are found to be factorized. These ratios are consistent with the decoupling of high-energy zero norm states calculated previously.Subject Index: 129 §1. IntroductionRecently high-energy, fixed angle behavior of string scattering amplitudes 1)-3) was intensively investigated for massive higher-spin string states at arbitrary mass levels. 4)-12) The motivation was to uncover the fundamental hidden stringy spacetime symmetry. An important new ingredient of this calculation was the zero-norm states (ZNS) 13)-15) in the old covariant first quantized string spectrum, in particular, the identification of inter-particle symmetries induced by the inter-particle ZNS 13) in the spectrum. An infinite number of linear relations among high-energy fixed angle scattering amplitudes of different string states at each fixed but arbitrary mass levels can be derived. Moreover, these linear relations can be used to fix the ratios among high-energy scattering amplitudes of different string states at each fixed mass level. On the other hand, 2D discrete zero-norm states were also shown 14) to carry the spacetime ω ∞ symmetry charges of toy 2D string theory. Furthermore, in the high-energy limit, these discrete zero-norm states approach 8), 9) the discrete Polyakov positive-norm states which generate the well-known ω ∞ symmetry of the 2D string. 16)-18) This strongly suggests that the linear relations obtained from zeronorm states are indeed related to the hidden symmetry of the 26 dimensional string.

We show that in the near-horizon limit of a Kerr-NUT-AdS black hole, the space of conformal Killing-Yano two-forms does not enhance and remains of dimension two. The same holds for an analogous polar limit in the case of extremal NUT charge. We also derive the conformal Killing-Yano p-form equation for any background in arbitrary dimension in the form of parallel transport.

A new technique is introduced for reducing the estimation errors accompanying component spectra estimated by means of the concentration-spectrum correlation method. Many estimates of the component spectra, given to different errors, are obtained by the nonparametric statistical method called the bootstrap. Among them, there exists a spectrum that has a very small error. This spectrum can be found by searching for the spectrum that has the least entropy, since a parameter of the entropy is correlated positively with the estimation error. Computer-simulation experiments are performed to demonstrate the effectiveness of the present technique for cases involving both unconstrained concentrations and constrained concentrations whose sum for all the components in a sample is unity.