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Jen-Chi Lee

Publications and source records attributed to Jen-Chi Lee.

At least 19 recordsLinked to original sources
arXiv2026

Scattering Equations as the lowest order K-identities in the calculation of Stringy Scaling of Hard String Scattering Amplitudes

We prove explicitly the n-point K-identities we proposed previously in the calculation of one tensor hard string scattering amplitudes (HSSA). These K-identities were the key to obtain the stringy scaling behavior in the saddle point calculation of the n-point HSSA and, on the other hand, to consistently match with the calculation of decoupling of zero norm states. Moreover, we introduce a G function to generate an infinite set of generalized K-identities (GKI). The lowest order set of these GKI is the scattering equations (SE) used in the calculation of field theory amplitudes in the CHY formalism. The next to leading order set of these GKI is the K-identities used previously in the calculation of one tensor HSSA. We conjecture that the higher order sets of these GKI can be used to calculate higher order HSSA and/or multi-tensor HSSA.

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arXiv2024

Stringy scaling of multi-tensor hard string scattering amplitudes and the K-identities

We calculate n-point hard string scattering amplitudes (HSSA) with n-2 tachyons and 2 tensor states at arbitrary mass levels. We discover the stringy scaling behavior of these HSSA. It is found that for HSSA with more than 2 transverse directions, the degree of stringy scaling dimM2 decreases comparing to the degree of stringy scaling dimM1 of the n-1 tachyons and 1 tensor HSSA calculated previously. Moreover, we propose a set of K-identities which is the key to demonstrate the stringy scaling behavior of HSSA. We explicitly prove both the diagonal and off-diagonal K-identities for the 4-point HSSA and give numerical proofs of these K-identities for some higher point HSSA.

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arXiv2024

Stringy Scaling

We discover a general stringy scaling behavior for 1. All n-point hard string scattering amplitudes (HSSA) and 2. A class of n-point Regge string scattering amplitudes (RSSA) to all string loop orders. The number of independent kinematics variables is found to be reduced by dim M.

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arXiv2024

The stringy scaling loop expansion and stringy scaling violation

We propose a systematic approximation scheme to calculate general $n$-point $HSSA$ of open bosonic string theory. This stringy scaling loop expansion contains finite number of vacuum diagram terms at each loop order of scattering energy due to a vacuum diagram contraint and a topological graph constraint. In addition, we calculate coefficient and give the vacuum diagram representation and its Feynman rules for each term in the expansion of the $HSSA$. As an application to extending our previous calculation of $n$-point leading order stringy scaling behavior of $HSSA$, we explicitly calculate some examples of $4$-point next to leading order stringy scaling violation terms.

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arXiv2022

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].

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arXiv2022

The exact SL(K+3,C) symmetry of string theory

By using on-shell recursion relation of string scattering amplitudes (SSA), we show that all n-point SSA of the open bosonic string theory can be expressed in terms of the Lauricella functions. This result extends the previous exact SL(K+3,C) symmetry of the 4-point Lauricella SSA (LSSA) of three tachyons and one arbitrary string states to the whole tree-level open bosonic string theory. Moreover, we present three applications of the SL(K+3,C) symmetry on the SSA. They are the solvability of all SSA in terms of one amplitude, the existence of iteration relations among residues of a given SSA so as to soften its hard scattering behavior and finally the re-derivation of infinite linear relations among hard SSA [12].

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arXiv2022

The $SL(K+3,\mathbb{C})$ 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.

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arXiv2021

Residues of bosonic string scattering amplitudes and the Lauricella functions

We calculate explicitly residues of all n-point Koba-Nielsen (KN) amplitudes by using on-shell recursion relation of string scattering amplitudes (SSA). In addition, we show that the residues of all SSA including the KN amplitudes can be expressed in terms of the Lauricella functions. This result demonstrates the exact SL(K+3,C) symmetry of the tree-level open bosonic string theory. Moreover, we derive an iteration relation among the residues of a given SSA. This iteration relation is related to the SL(K+3,C) symmetry and can presumably be used to soften the well-known hard SSA.

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arXiv2021

Comment on "High Energy Symmetry of String Theory"

Following the recent discovery of the Lauricella string scattering amplitudes (LSSA) and their associated exact SL(K+3,C) symmetry, we give a brief comment on Gross conjecture regarding "High energy symmetry of string theory".

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arXiv2021

New bosonic hard string scattering amplitudes and extended Gross conjecture in superstring theory

We discover new hard string scattering amplitudes (HSSA) with polarizations orthogonal to the scattering plane in the NS sector of 10D open superstring theory. The corresponding HSSA in the bosonic string theory are of subleading order in energy. In addition, all HSSA are found to be proportional to each other and the ratios among these HSSA are calculated to justify Gross conjecture in 1988 on high energy symmetry of string theory. Moreover, together with these new HSSA, the total number of HSSA calculated in the first massive level of NS sector are found to agree with those of hard polarized fermion string scattering amplitudes (PFSSA) in the R sector calculated recently.

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arXiv2021

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.

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arXiv2020

Sheaf lines of Yang-Mills Instanton Sheaves

We calculate a sheaf line in CP^3 which is the real line supporting sheaf points on CP^3 of SL(2,C) Yang-Mills instanton (or SU(2) complex Yang-Mills instanton) sheaves for some given ADHM data we obtained previously. We found that this sheaf line is indeed a special jumping line over S^4 spacetime. In addition, we calculate the singularity structure of the connection A and the field strength F at the corresponding singular point on S^4 of this sheaf line. We found that the order of singularity at the singular point on S^4 associated with the sheaf line in CP^3 is higher than those of other singular points associated with normal jumping lines. We conjecture that this is a general feature for sheaf lines among jumping lines.

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arXiv2019

Overview on High energy String Scattering Amplitudes and Symmetries of String Theory

We overview 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 infinite 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 by 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 review 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 maybe crucial to probe spacetime symmetry of string theory.

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arXiv2019

Spin polarization independence of hard polarized fermion string scattering amplitudes

We calculate a class of polarized fermion string scattering amplitudes (PFSSA) at arbitrary mass levels. We discover that, in the hard scattering limit, the functional forms of the non-vanishing PFSSA at each fixed mass level are independent of the choices of spin polarizations. This result justifies and extends Gross conjecture on high energy string scattering amplitudes to the fermionic sector. In addition, this peculiar property of hard PFSSA is to be compared with the usual spin polarization dependence of the hard polarized fermion field theory scatterings.

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arXiv2019

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].

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arXiv2018

Extended Complex Yang-Mills Instanton Sheaves

In the search of 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 [4] or 0 on some points of CP^3 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 [3]. We then show that in the new "extended complex YM instantons" discovered in this paper, rank(beta) can be either 2 on the whole CP^3 (bundle) with some given ADHM data or 1, 0 on some points of CP^3 with other ADHM data (sheaves). These extended SU(2) complex YM instantons have no real instanton counterparts.

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