scholarly journals Recent Developments of the Lauricella String Scattering Amplitudes and Their Exact SL(K + 3,C) Symmetry

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 454 ◽  
Author(s):  
Sheng-Hong Lai ◽  
Jen-Chi Lee ◽  
Yi Yang
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Recurrence Relations ◽  
High Energy ◽  
Infinite Dimensional ◽  
Recent Developments ◽  
New Perspective ◽  
Zero Norm ◽  
Nonrelativistic Scattering ◽  
Infinite Dimensional Representation

In this review, we propose a new perspective to demonstrate the Gross conjecture regarding the high-energy symmetry of string theory. We review the construction of the exact string scattering amplitudes (SSAs) of three tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the 26D open bosonic string theory. These LSSAs 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 LSSAs and express them in terms of one amplitude. As an application in the hard scattering limit, the LSSA can be used to directly prove the Gross conjecture, which was previously corrected and proved by the method of the 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 the associated SL(4,C) symmetry discovered recently.

scholarly journals Overview of High Energy String Scattering Amplitudes and Symmetries of String Theory

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1045 ◽  
Author(s):  
Jen-Chi Lee ◽  
Yi Yang
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Recurrence Relations ◽  
Dynamical Symmetry ◽  
High Energy ◽  
Closed String ◽  
Fixed Angle ◽  
Linear Relations ◽  
Arbitrary Mass ◽  
String Amplitudes

In this paper, we studied symmetries of string scattering amplitudes in the high energy limits of both the fixed angle or Gross regime (GR) and the fixed momentum transfer or Regge regime (RR). We calculated high energy string scattering amplitudes (SSA) at arbitrary mass levels for both regimes. We discovered the infinite linear relations among fixed angle string amplitudes and the ifinite recurrence relations among Regge string amplitudes. The linear relations we obtained in the GR corrected the saddle point calculations by Gross, Gross and Mende. In addition, for the high energy closed string scatterings, our results differ from theirs by an oscillating prefactor which was crucial to recover the KLT relation valid for all energies. We showed that all the high energy string amplitudes can be solved using the linear or recurrence relations, so that all the string amplitudes can be expressed in terms of a single string amplitude. We further found that, at each mass level, the ratios among the fixed angle amplitudes can be extracted from the Regge string scattering amplitudes. Finally, we reviewed the recent developments on the discovery of infinite number of recurrence relations valid for all energies among Lauricella SSA. The symmetries or relations among SSA at various limits obtained previously can be exactly reproduced. It leads us to argue that the known S L ( K + 3 , C ) dynamical symmetry of the Lauricella function may be crucial to probe spacetime symmetry of string theory.

scholarly journals High-Energy Zero-Norm States and Symmetries of String Theory

2006 ◽  
Vol 96 (17) ◽  
Author(s):  
Chuan-Tsung Chan ◽  
Pei-Ming Ho ◽  
Jen-Chi Lee ◽  
Shunsuke Teraguchi ◽  
Yi Yang
Keyword(s):  
String Theory ◽  
High Energy ◽  
Zero Norm

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

2004 ◽  
Vol 690 (1-2) ◽  
pp. 3-20 ◽  
Author(s):  
Chuan-Tsung Chan ◽  
Jen-Chi Lee
Keyword(s):  
String Theory ◽  
High Energy ◽  
Zero Norm

scholarly journals Ward identities and high energy scattering amplitudes in string theory

2005 ◽  
Vol 708 (1-3) ◽  
pp. 99-114 ◽  
Author(s):  
Chuan-Tsung Chan ◽  
Pei-Ming Ho ◽  
Jen-Chi Lee
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
High Energy ◽  
Ward Identities ◽  
Energy Scattering ◽  
High Energy Scattering

scholarly journals Unimodular vs nilpotent superfield approach to pure dS supergravity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sukruti Bansal ◽  
Silvia Nagy ◽  
Antonio Padilla ◽  
Ivonne Zavala
Keyword(s):  
String Theory ◽  
General Framework ◽  
Recent Progress ◽  
High Energy ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
New Approach ◽  
Sitter Spacetime ◽  
Novel Approach ◽  
De Sitter Vacua

Abstract Recent progress in understanding de Sitter spacetime in supergravity and string theory has led to the development of a four dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua, also called de Sitter supergravity. One approach makes use of constrained (nilpotent) superfields, while an alternative one couples supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action. These two approaches have been shown to give rise to the same 4D action. A novel approach to de Sitter vacua in supergravity involves the generalisation of unimodular gravity to supergravity using a super-Stückelberg mechanism. In this paper, we make a connection between this new approach and the previous two which are in the context of nilpotent superfields and the goldstino brane. We show that upon appropriate field redefinitions, the 4D actions match up to the cubic order in the fields. This points at the possible existence of a more general framework to obtain de Sitter spacetimes from high-energy theories.

scholarly journals The Growth of Semiconductor Thin Films Studied by RHEED

1990 ◽  
Vol 43 (5) ◽  
pp. 583
Author(s):  
GL Price
Keyword(s):  
Thin Films ◽  
Surface Science ◽  
High Vacuum ◽  
High Energy ◽  
Ultra High Vacuum ◽  
Large Area ◽  
Growth Modes ◽  
Semiconductor Thin Films ◽  
Wide Range ◽  
Recent Developments

Recent developments in the growth of semiconductor thin films are reviewed. The emphasis is on growth by molecular beam epitaxy (MBE). Results obtained by reflection high energy electron diffraction (RHEED) are employed to describe the different kinds of growth processes and the types of materials which can be constructed. MBE is routinely capable of heterostructure growth to atomic precision with a wide range of materials including III-V, IV, II-VI semiconductors, metals, ceramics such as high Tc materials and organics. As the growth proceeds in ultra high vacuum, MBE can take advantage of surface science techniques such as Auger, RHEED and SIMS. RHEED is the essential in-situ probe since the final crystal quality is strongly dependent on the surface reconstruction during growth. RHEED can also be used to calibrate the growth rate, monitor growth kinetics, and distinguish between various growth modes. A major new area is lattice mismatched growth where attempts are being made to construct heterostructures between materials of different lattice constants such as GaAs on Si. Also described are the new techniques of migration enhanced epitaxy and tilted superlattice growth. Finally some comments are given On the means of preparing large area, thin samples for analysis by other techniques from MBE grown films using capping, etching and liftoff.

scholarly journals Two-parton scattering amplitudes in the Regge limit to high loop orders

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Simon Caron-Huot ◽  
Einan Gardi ◽  
Joscha Reichel ◽  
Leonardo Vernazza
Keyword(s):  
Scattering Amplitudes ◽  
Scattering Amplitude ◽  
Dimensional Regularization ◽  
High Energy ◽  
Logarithmic Order ◽  
Finite Radius ◽  
High Loop ◽  
Parton Scattering ◽  
Infrared Divergences ◽  
Regge Limit

Abstract We study two-to-two parton scattering amplitudes in the high-energy limit of perturbative QCD by iteratively solving the BFKL equation. This allows us to predict the imaginary part of the amplitude to leading-logarithmic order for arbitrary t-channel colour exchange. The corrections we compute correspond to ladder diagrams with any number of rungs formed between two Reggeized gluons. Our approach exploits a separation of the two-Reggeon wavefunction, performed directly in momentum space, between a soft region and a generic (hard) region. The former component of the wavefunction leads to infrared divergences in the amplitude and is therefore computed in dimensional regularization; the latter is computed directly in two transverse dimensions and is expressed in terms of single-valued harmonic polylogarithms of uniform weight. By combining the two we determine exactly both infrared-divergent and finite contributions to the two-to-two scattering amplitude order-by-order in perturbation theory. We study the result numerically to 13 loops and find that finite corrections to the amplitude have a finite radius of convergence which depends on the colour representation of the t-channel exchange.

scholarly journals Towards the Hydrogen Economy—A Review of the Parameters That Influence the Efficiency of Alkaline Water Electrolyzers

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3193
Author(s):  
Ana L. Santos ◽  
Maria-João Cebola ◽  
Diogo M. F. Santos
Keyword(s):  
Energy Content ◽  
Water Electrolysis ◽  
High Energy ◽  
Operating Conditions ◽  
Energy Sources ◽  
Alkaline Water Electrolysis ◽  
Alkaline Water ◽  
New Energy ◽  
Recent Developments ◽  
Cell Components

Environmental issues make the quest for better and cleaner energy sources a priority. Worldwide, researchers and companies are continuously working on this matter, taking one of two approaches: either finding new energy sources or improving the efficiency of existing ones. Hydrogen is a well-known energy carrier due to its high energy content, but a somewhat elusive one for being a gas with low molecular weight. This review examines the current electrolysis processes for obtaining hydrogen, with an emphasis on alkaline water electrolysis. This process is far from being new, but research shows that there is still plenty of room for improvement. The efficiency of an electrolyzer mainly relates to the overpotential and resistances in the cell. This work shows that the path to better electrolyzer efficiency is through the optimization of the cell components and operating conditions. Following a brief introduction to the thermodynamics and kinetics of water electrolysis, the most recent developments on several parameters (e.g., electrocatalysts, electrolyte composition, separator, interelectrode distance) are highlighted.

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

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