Browsing by Author "Lee, Jen-Chi"

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A note on on-shell recursion relation of string amplitudes
(2013-02-01)
Chang, Yung-Yeh
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Feng, Bo
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Fu, Chih-Hao
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Lee, Jen-Chi
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Wang, Yihong
In the application of on-shell recursion relation to string amplitudes, one challenge is the sum over infinite intermediate on-shell string states. In this note, we show how to sum these infinite states explicitly by including unphysical states to make complete Fock space.
Biquaternion Construction of SL(2,C) Yang-Mills Instantons
(2016-01-01)
Lee, Jen-Chi
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電子物理學系
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Department of Electrophysics
We use biquaternion to construct SL(2,C) ADHM Yang-Mills instantons. The solutions contain 16k-6 moduli parameters for the kth homotopy class, and include as a subset the SL(2,C) (M,N) instanton solutions constructed previously. In constrast to the SU(2) instantons, the SL(2,C) instantons inhereit jumping lines or singulariries which are not gauge artifacts and can not be gauged away.
Biquaternions and ADHM construction of non-compact SL(2, C) Yang-Mills instantons
(2015-10-01)
Lai, Sheng-Hong
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Lee, Jen-Chi
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Tsai, I-Hsun
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電子物理學系
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Department of Electrophysics
We extend quaternion calculation in the ADHM construction of Sp(1) (=SU(2)) self-dual Yang-Mills (SDYM) instantons to the case of biquaternion. We use the biconjugate operation of biquaternion first introduced by Hamilton to construct the non-compact SL(2, C) k-instantons. The number of parameters of this construction for SL(2, C) k-instantons is found to be twice of that of Sp(1), 16k-6. These new SL(2, C) instanton solutions contain the SL(2, C) (M, N) instanton solutions constructed previously as a subset. The structures of singularities or jumping lines of the complete SL(2, C) k = 1, 2, 3 instantons with 10, 26, 42 moduli parameters are particularly investigated. The existence of singular structures of the SL(2, C) k-instantons is mathematically consistent with recent results of solutions of complex ADHM equations. It may also help to clarify the long standing global singularity problems associated with Backlund transformations of SU(2) instantons. (C) 2015 Elsevier Inc. All rights reserved.
Comments on the high energy limit of bosonic open string theory
(2006-08-14)
Chan, Chuan-Tsung
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Ho, Pei-Ming
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Lee, Jen-Chi
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Teraguchi, Shunsuke
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Yang, Yi
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. (c) 2006 Elsevier B.V. All rights reserved.
Exponential Fall-Off Behavior of Regge Scatterings in Compactified Open String Theory
(2012-11-01)
He, Song
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Lee, Jen-Chi
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Yang, Yi
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電子物理學系
;
Department of Electrophysics
We calculate massive string scattering amplitudes of compactified open string 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. The complete ratios calculated by this indirect method include and extend the subset of ratios calculated previously [J. C. Lee and Y. Yang, Nucl. Phys. B 784 (2007), 22; J. C. Lee, T. Takimi and Y. Yang, Nucl. Phys. B 804 (2008), 250] by the more difficult direct fixed angle calculation. In this calculation of compactified open string scattering, we discover a realization of arbitrary real values L in the identity Eq. (4.18), rather than integer value only in all previous high-energy string scattering amplitude calculations. The identity in Eq. (4-18) was explicitly proved recently in [J. C. Lee, C. H. Yan and Y. Yang, SIGMA 8 (2012), 045, arXiv:1012.5225] to link fixed angle and Rogge string scattering amplitudes. In addition, we discover a kinematic regime with stringy highly winding modes, which shows the unusual exponential fall-off behavior in the Regge string scattering. This is complimentary with a kinematic regime discovered previously [J. C. Lee, T. Takimi and Y. Yang, Nucl. Phys. B 804 (2008), 2501 which shows the unusual power-law behavior in the high-energy fixed angle compactified string scatterings.
Extended complex Yang-Mills instanton sheaves
(2020-03-01)
Lai, Sheng-Hong
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Lee, Jen-Chi
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Tsai, I-Hsun
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電子物理學系
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Department of Electrophysics
In the search of Yang-Mills (YM) instanton sheaves with topological charge two, the rank of beta matrix in the monad construction can be dropped from the bundle case with rank beta = 2 to either rank beta = 1 [S. H. Lai, J. C. Lee and I. H. Tsai, Yang Mills instanton sheaves, Ann. Phys. 377 (2017) 446] or 0 on some points of CP3 of the sheaf cases. In this paper, we first show that the sheaf case with rank beta = 0 does not exist for the previous construction of SU(2) complex YM instantons [S. H. Lai, J. C. Lee and I. H. Tsai, Biquaternions and ADHM construction of concompact SL(2, C) Yang-Mills instantons, Ann. Phys. 361 (2015) 14]. We then show that in the new "extended complex YM instantons" discovered in this paper, rank beta can be either 2 on the whole CP3 (bundle) with some given ADHM data or 1, 0 on some points of CP3 with other ADHM data (sheaves). These extended SU(2) complex YM instantons have no real instanton counterparts. Finally, the potential applications to real physics systems are noted in the end of the paper.
High-energy massive string scatterings from orientifold planes
(2008-07-21)
Lee, Jen-Chi
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Yang, Yi
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電子物理學系
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Department of Electrophysics
We calculate bosonic massive closed string states at arbitrary mass levels scattered from orientifold planes in the high-energy, fixed angle limit. For the case of O-particle scatterings, we obtain infinite linear relations among high-energy scattering amplitudes of different string states. We also confirm that there exist only closed string Regge poles in the form factor of the O-particle amplitudes as expected. For the case of O-domain-wall scatterings, we find that, like the well-known D-instanton scatterings, the amplitudes behave like field theory scatterings, namely UV power-law without infinite Regge poles. In addition, we discover that there exist only finite number of t-channel closed string poles in the form factor of O-domain-wall scatterings, and the masses of the poles are bounded by the masses of the external legs. We thus confirm that all massive closed string states do couple to the O-domain-wall. (c) 2008 Elsevier B.V. All rights reserved.
High-Energy String Scattering Amplitudes and Signless Stirling Number Identity
(2012)
Lee, Jen-Chi
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Yan, Catherine H.
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Yang, Yi
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電子物理學系
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Department of Electrophysics
"We give a complete proof of a set of identities (7) proposed recently from calculation of high-energy string scattering amplitudes. These identities allow one to extract ratios among high-energy string scattering amplitudes in the fixed angle regime from high-energy amplitudes in the Regge regime. The proof is based on a signless Stirling number identity in combinatorial theory. The results are valid for arbitrary real values L rather than only for L = 0,1 proved previously. The identities for non-integer real value L were recently shown to be realized in high-energy compactified string scattering amplitudes [He S., Lee J.C., Yang Y., arXiv:1012.3158]. The parameter L is related to the mass level of an excited string state and can take non-integer values for Kaluza-Klein modes."
High-energy string scatterings of compactified open string
(2008-11-21)
Lee, Jen-Chi
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Takimi, Tomohisa
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Yang, Yi
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電子物理學系
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Department of Electrophysics
We calculate high-energy massive string scattering amplitudes of compactified open string. We derive infinite linear relations, or stringy symmetries, among soft high-energy string scattering amplitudes of different string states in the Gross kinematic regime (GR). In addition, we systematically analyze all hard power-law and soft exponential fall-off regimes of high-energy compactified open string scatterings by comparing the scatterings with their 26D noncompactified counterparts. In particular, we discover the existence of a power-law regime at fixed angle and an exponential fall-off regime at small angle for high-energy compactified open string scatterings. The linear relations break down as expected in all power-law regimes. The analysis can be extended to the high-energy scatterings of the compactified closed string, which corrects and extends the previous results in [J.C. Lee, Y. Yang. Linear relations and their breakdown in high energy massive string scatterings in compact spaces, Nucl. Phys. B 784 (2007) 22]. (C) 2008 Published by Elsevier B.V.
Higher Spin String States Scattered from D-Particle in the Regge Regime and Factorized Ratios of Fixed Angle Scatterings
(2011-09-01)
Lee, Jen-Chi
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Mitsuka, Yoshihiro
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Yang, Yi
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電子物理學系
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Department of Electrophysics
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.
Linear relations and their breakdown in high energy massive string scatterings in compact spaces
(2007-11-12)
Lee, Jen-Chi
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Yang, Yi
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電子物理學系
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Department of Electrophysics
We calculate high energy massive scattering amplitudes of closed bosonic string compactified on the torus. For each fixed mass level with given quantized and winding momenta (m/R ,1/2 nR), we obtain infinite R linear relations among high energy scattering amplitudes of different string states. For some kinematic regimes, we discover that linear relations with N-R = N-L break down and, simultaneously, the amplitudes enhance to power-law behavior instead of the usual exponential fall-off behavior at high energies. It is the space-time T-duality symmetry that plays a role here. This result is consistent with the coexistence of the linear relations and the softer exponential fall-off behavior of high energy string scattering amplitudes as we pointed out previously. It is also reminiscent of our previous work on the power-law behavior of high energy string/domain-wall scatterings. (c) 2007 Elsevier B.V. All rights reserved.
Linear relations of high energy absorption/emission amplitudes of D-brane
(2007-03-08)
Lee, Jen-Chi
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Yang, Yi
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電子物理學系
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Department of Electrophysics
We calculate the absorption amplitudes of a closed string state at arbitrary mass level leading to two open string states on the D-brane at high energies. As in the case of Domain-wall scattering we studied previously, this process contains only one kinematic variable. However, in contrast to the power-law behavior of Domain-wall scattering, its form factor behaves as exponential fall-off in the high energy limit. After identifying the geometric parameter of the kinematic, we derive the linear relations (of the kinematic variable) and ratios among the high energy amplitudes corresponding to absorption of different closed string states for each fixed mass level by D-brane. This result is consistent with the coexistence of the linear relations and exponential fall-off behavior of high energy string/D-brane amplitudes. (c) 2007 Elsevier B.V. All rights reserved.
Massive superstring scatterings in the Regge regime
(2011-03-31)
He, Song
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Lee, Jen-Chi
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Takahashi, Keijiro
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Yang, Yi
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電子物理學系
We calculate four classes of high-energy massive string scattering amplitudes of fermionic string theory at arbitrary mass levels in the Regge regime (RR). We show that all four leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind. Based on the summation algorithm of a set of extended signed Stirling number identities, we show that all four ratios calculated previously by the method of decoupling of zero-norm states among scattering amplitudes in the Gross regime can be extracted from this Kummer function in the RR. Finally, we conjecture and give evidence that the existence of these four Gross regime ratios in the RR persists to subleading orders in the Regge expansion of all high-energy fermionic string scattering amplitudes.
Multi-indexed extensions of soliton potential and extended integer solitons of KdV equation
(2015-08-10)
Ho, Choon-Lin
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Lee, Jen-Chi
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電子物理學系
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Department of Electrophysics
We calculate infinite set of initial profiles of higher integer Korteweg-de Vries (KdV) solitons, which are both exactly solvable for the Schrodinger equation and for the Gel\'fand-Levitan-Marchenko (GLM) equation in the inverse scattering transform (IST) method of KdV equation. The calculation of these higher integer soliton solutions is based on the recently developed multi-indexed extensions of the reflectionless soliton potential.
Notes on high-energy limit of bosonic closed string scattering amplitudes
(2006-08-14)
Chan, Chuan-Tsung
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Lee, Jen-Chi
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Yang, Yi
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電子物理學系
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Department of Electrophysics
We study bosonic closed string scattering amplitudes in the high-energy limit. We find that the methods of decoupling of high-energy zero-norm states and the high-energy Virasoto constraints, which were adopted in the previous works to calculate the ratios among high-energy open string scattering amplitudes of different string states, persist for the case of closed string. However, we clarify the previous saddle-point calculation for high-energy open string scattering amplitudes and claim that only (t, u) channel of the amplitudes is suitable for saddle-point calculation. We then discuss three evidences to show that saddle-point calculation for high-energy closed string scattering amplitudes is not reliable. By using the relation of tree-level closed and open string scattering amplitudes of Kawai, Lewellen and Tye (KLT), we calculate the high-energy closed string scattering amplitudes for arbitrary mass levels. For the case of high-energy closed string four-tachyon amplitude, our result differs from the previous one of Gross and Mende, which is NOT consistent with KLT formula, by an oscillating factor. (c) 2006 Elsevier B.V. All rights reserved.
Overview of High Energy String Scattering Amplitudes and Symmetries of String Theory
(2019-08-01)
Lee, Jen-Chi
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Yang, Yi
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電子物理學系
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Department of Electrophysics
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 SL(K+3,C) dynamical symmetry of the Lauricella function may be crucial to probe spacetime symmetry of string theory.
Patterns of high energy massive string scatterings in the Regge regime
(2009-06-01)
Ko, Sheng-Lan
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Lee, Jen-Chi
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Yang, Yi
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電子物理學系
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Department of Electrophysics
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.
Power-law Behavior of High Energy String Scatterings in Compact Spaces
(2008)
Lee, Jen-Chi
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Yang, Yi
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電子物理學系
;
Department of Electrophysics
We calculate high energy massive scattering amplitudes of closed bosonic string compactified on the torus. We obtain infinite linear relations among high energy scattering amplitudes. For some kinematic regimes, we discover that some linear relations break down and, simultaneously, the amplitudes enhance to power-law behavior due to the space-time T-duality symmetry in the compact direction. This result is consistent with the coexistence of the linear relations and the softer exponential fall-off behavior of high energy string scattering amplitudes as we pointed out prevously. It is also reminiscent of hard (power-law) string scatterings in warped spacetime proposed by Polchinski and Strassler.
Recurrence relations of higher spin BPST vertex operators for open strings
(2013-08-19)
Fu, Chih-Hao
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Lee, Jen-Chi
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Tan, Chung-I
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Yang, Yi
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電子物理學系
We calculate higher-spin Brower-Polchinski-Strassler-Tan (BPST) vertex operators for an open bosonic string and express these operators in terms of a Kummer function of the second kind. We derive an infinite number of recurrence relations among BPST vertex operators of different string states. These recurrence relations among BPST vertex operators lead to the recurrence relations among Regge string scattering amplitudes discovered recently.
Recurrence relations of Kummer functions and Regge string scattering amplitudes
(2013-04-01)
Lee, Jen-Chi
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Mitsuka, Yoshihiro
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電子物理學系
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Department of Electrophysics
We discover an infinite number of recurrence relations among Regge string scattering amplitudes [11, 30] 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.