The SL(K+3,C) Symmetry of the Bosonic String Scattering Amplitudes

We discover that the exact string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the 26D open bosonic string theory can be expressed in terms of the basis functions in the infinite dimensional representation space of the SL(K+3,C) group. In addition, we find that the K+2 recurrence relations among the LSSA discovered by the present authors previously can be used to reproduce the Cartan subalgebra and simple root system of the SL(K+3,C) group with rank K+2. As a result, the SL(K+3,C) group can be used to solve all the LSSA and express them in terms of one amplitude. As an application in the hard scattering limit, the SL(K+3,C) group can be used to directly prove Gross conjecture [1-3], which was previously corrected and proved by the method of decoupling of zero norm states [4-10].Comment: 19 pages, no figure. v2: 20 pages, typos corrected and Eqs. added. v3: 24 pages, Examples in sec. II added,"Discussion" added, to be published in Nucl.Phys.

String Scattering Amplitudes and Deformed Cubic String Field Theory

We study string scattering amplitudes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. The four-string scattering amplitudes with three tachyons and an arbitrary string state are calculated. The string field theory yields the string scattering amplitudes evaluated on the world sheet of string scattering whereas the coventional method, based on the first quantized theory brings us the string scattering amplitudes defined on the upper half plane. For the highest spin states, generated by the primary operators, both calculations are in perfect agreement. In this case, the string scattering amplitudes are invariant under the conformal transformation, which maps the string world sheet onto the upper half plane. If the external string states are general massive states, generated by non-primary field operators, we need to take into account carefully the conformal transformation between the world sheet and the upper half plane. We show by an explicit calculation that the string scattering amplitudes calculated by using the deformed cubic string field theory transform into those of the first quantized theory on the upper half plane by the conformal transformation, generated by the Schwarz-Christoffel mapping.Comment: 12 pages, 2 figures, references adde

Solving Lauricella String Scattering Amplitudes through Recurrence Relations

We show that there exist infinite number of recurrence relations valid for all energies among the open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA. Moreover, these infinite number of recurrence relations can be used to solve all the Lauricella SSA and express them in terms of one single four tachyon amplitude. These results extend the solvability of SSA at the high energy, fixed angle scattering limit and those at the Regge scattering limit discovered previously.Comment: 19 pages. v2: Fig.1 adde

Cultural Identity and the Making of Modern Taiwanese Painting During the Japanese Colonial Period (1895-1945).

This dissertation addresses the multifaceted aspects of cultural identity as expressed in modern Taiwanese paintings during the Japanese colonial era, from 1895 to 1945. Under Japanese rule, Taiwan was united for the first time by a single official language and a standardized Western-influenced education system. In those circumstances, Taiwan underwent fast-paced modernization that gave rise to challenging new cultural forms and ideologies, and provided space for the gradual development of a new sense of personal and cultural identity. The present study reveals that rather than manifesting a uniform cultural identity or ideological orientation, Western-style paintings of the period demonstrate ambiguity and hybridity, with oscillation between Chinese, Japanese and Western outlooks and signs of an emergent Taiwanese consciousness characterized by a cosmopolitan spirit rooted in love for the land. Chapter One outlines Taiwan’s history and Sino-centric cultural development before the Japanese colonial era. Chapter Two discusses the difficulties confronting aspiring Taiwanese artists during Japanese rule and examines popular new themes, such as the artist’s studio, the self-portrait and the family portrait, which shed light on the fluid construction of new cultural identities. Chapter Three examines artworks and writings by leading expatriate Japanese painters and commentators touching on the question of Taiwan’s cultural distinctiveness. Chapter Four addresses the emergence among the Taiwanese of an ever-maturing consciousness of Taiwan and themselves as a distinctive, integral whole in relation to the colonial mother country, the ancestral motherland and the world. Taiwanese painters of the Japanese colonial period both mirrored and contributed to trends in the evolution of the island’s cultural identity. Through a careful analysis of form and content, this dissertation concludes that while the paintings are less pointed and discursively revealing than were contemporaneous Taiwanese literary works, they provide invaluable testimony to the multivalent complexity of the period’s cross-cultural dynamics and to the individual artists’ search for a vision of Taiwan, Taiwanese-ness, and a broader humanity that lies beyond.Ph.D.History of ArtUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/61650/1/jyl_1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/61650/2/jyl_3.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/61650/3/jyl_2.pd

The SL(K+3,C)SL(K+3,\mathbb{C}) symmetry of string scatterings from D-branes

By using the solvability of Lauricella function $F_{D}^{(K)}\left( \alpha;\beta_{1},...,\beta_{K};\gamma;x_{1},...,x_{K}\right)$ with nonpositive integer $\beta_{J}$, we show that each scattering or decay process of string and D-brane states at \textit{arbitrary} mass levels can be expressed in terms of a single Lauricella function. This result extends the previous exact $SL(K+3,\mathbb{C})$ symmetry of tree-level open bosonic string theory to include the D-brane.Comment: 15 pages, no figure. arXiv admin note: text overlap with arXiv:2108.06326. v2: 18 pages. Final in Nucl.Phys.

Stringy scaling of n-point Regge string scattering amplitudes

We discover a stringy scaling behavior for a class of n-point Regge string scattering amplitudes (RSSA). The number of independent kinematics variables is found to be reduced by dim M.Comment: 33 pages, 1 figur

Recent developments of the Lauricella string scattering amplitudes and their exact SL(K+3,C) Symmetry

In this review we propose a new perspective to demonstrate Gross conjecture on high energy symmetry of string theory. We review the construction of the exact string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the 26D open bosonic string theory. These LSSA form an infinite dimensional representation of the SL(K+3,C) group. Moreover, we show that the SL(K+3,C) group can be used to solve all the LSSA and express them in terms of one amplitude. As an application in the hard scattering limit, the LSSA can be used to directly prove Gross conjecture which was previously corrected and proved by the method of decoupling of zero norm states (ZNS). Finally, the exact LSSA can be used to rederive the recurrence relations of SSA in the Regge scattering limit with associated SL(5,C) symmetry and the extended recurrence relations (including the mass and spin dependent string BCJ relations) in the nonrelativistic scattering limit with associated SL(4,C) symmetry discovered recently.Comment: 54 pages, 1 figure, minor modification, references added. arXiv admin note: text overlap with arXiv:1806.0503

Stringy scaling of n-point hard string scattering amplitudes

Motivated by the recent calculation of the SL(K+3,C) symmetry of n-point Lauricella string scattering amplitudes (SSA) of open bosonic string theory, we calculate ratios of the solvable infinite linear relations of arbitrary n-point hard SSA (HSSA). We discover a general stringy scaling behavior for all n-point HSSA to all string loop orders. For the special case of n=4, the stringy scaling behavior reduces to the infinite linear relations and constant ratios among HSSA conjectured by Gross [8] and later corrected and calculated by the method of decoupling of zero-norm states [11].Comment: 12 pages, no figure. v2: 13 pages, improve calculation in section III without changing result

The initial abundance and distribution of 92Nb in the Solar System

Niobium-92 is an extinct proton-rich nuclide, which decays to 92Zr with a half-life of 37 Ma. This radionuclide potentially offers a unique opportunity to determine the timescales of early Solar System processes and the site(s) of nucleosynthesis for p-nuclei, once its initial abundance and distribution in the Solar System are well established. Here we present internal Nb-Zr isochrons for three basaltic achondrites with known U-Pb ages: the angrite NWA 4590, the eucrite Agoult, and the ungrouped achondrite Ibitira. Our results show that the relative Nb-Zr isochron ages of the three meteorites are consistent with the time intervals obtained from the Pb-Pb chronometer for pyroxene and plagioclase, indicating that 92Nb was homogeneously distributed among their source regions. The Nb-Zr and Pb-Pb data for NWA 4590 yield the most reliable and precise reference point for anchoring the Nb-Zr chronometer to the absolute timescale: an initial 92Nb/93Nb ratio of $(1.4 \pm 0.5) \times 10^{-5}$ at $4557.93 \pm 0.36$ Ma, which corresponds to a 92Nb/93Nb ratio of $(1.7 \pm 0.6) \times 10^{-5}$ at the time of the Solar System formation. On the basis of this new initial ratio, we demonstrate the capability of the Nb-Zr chronometer to date early Solar System objects including troilite and rutile, such as iron and stony-iron meteorites. Furthermore, we estimate a nucleosynthetic production ratio of 92Nb to the p-nucleus 92Mo between 0.0015 and 0.035. This production ratio, together with the solar abundances of other p-nuclei with similar masses, can be best explained if these light p-nuclei were primarily synthesized by photodisintegration reactions in Type Ia supernovae.Comment: Accepted to Earth and Planetary Science Letter