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Jen-Chi Lee

Publications and source records attributed to Jen-Chi Lee.

At least 37 records · Page 2Linked to original sources
arXiv2018

Yang-Mills Instanton Sheaves

The SL(2,C) Yang-Mills instanton solutions constructed recently by the biquaternion method were shown to satisfy the complex version of the ADHM equations and the Monad construction. Moreover, we discover that, in addition to the holomorphic vector bundles on CP^3 similar to the case of SU(2) ADHM construction, the SL(2,C) instanton solutions can be used to explicitly construct instanton sheaves on CP^3. Presumably, the existence of these instanton sheaves is related to the singularities of the SL(2,C) instantons on S^4 which do not exist for SU(2) instantons.

hep-th↗
arXiv2017

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.

hep-th↗
arXiv2017

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.

hep-th↗
arXiv2016

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

We review high energy symmetries of string theory at both the fixed angle or Gross regime (GR) and the fixed momentum transfer or Regge regime (RR). We calculated in details high energy string scattering amplitudes at arbitrary mass levels for both regimes. We discovered infinite linear relations among fixed angle string amplitudes conjectured by Gross in 1988 from decoupling of high energy zero-norm states (ZNS), and infinite recurrence relations among Regge string amplitudes from Kummer function U and Appell function F_1. However, the linear relations we obtained in the GR corrected [27-32] the saddle point calculations of Gross, Gross and Mende and Gross and Manes [1-5]. Our results were consistent with the decoupling of high energy ZNS or unitarity of the theory while those of them were not. In addition, for the case of high energy closed string scatterings, our results [36] differ from theirs by an oscillating prefactor which was crucial to recover the KLT relation valid for all energies. In the GR/RR regime, all high energy string amplitudes can be solved by these linear/recurrence relations so that all GR/RR string amplitudes can be expressed in terms of one single GR/RR string amplitude. In addition, we found an interesting link between string amplitudes of the two regimes, and discovered that at each mass level the ratios among fixed angle amplitudes can be extracted from Regge string scattering amplitudes. This result enables us to argue that the known SL(5,C) dynamical symmetry of the Appell function F_1 is crucial to probe high energy spacetime symmetry of string theory.

hep-th↗
arXiv2016

The Lauricella Functions and Exact String Scattering Amplitudes

We discover that the 26D open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state can be expressed in terms of the D-type Lauricella functions with associated SL(K+3,C) symmetry. As a result, SSA and symmetries or relations among SSA of different string states at various limits calculated previously can be rederived. These include the linear relations first conjectured by Gross [1-3] and later corrected and proved in [4-9] in the hard scattering limit, the recurrence relations in the Regge scattering limit with associated SL(5,C) symmetry [19-21] and the extended recurrence relations in the nonrelativistic scattering limit with associated SL(4,C) symmetry [24] discovered recently. Finally, as an application, we calculate a new recurrence relation of SSA which is valid for all energies.

hep-th↗
arXiv2016

The String BCJ Relations Revisited and Extended Recurrence relations of Nonrelativistic String Scattering Amplitudes

We review and extend high energy string BCJ relations in both the fixed angle and Regge regimes. We then give an explicit proof of four point string BCJ relations for all energy. This calculation provides an alternative proof of the one based on monodromy of integration in string amplitude calculation. In addition, we calculate both s-t and t-u channel nonrelativistic low energy string scattering amplitudes of three tachyons and one leading trojectory string state at arbitrary mass levels. We discover that the mass and spin dependent nonrelativistic string BCJ relations can be expressed in terms of Gauss hypergeometry functions. As an application, for each fixed mass level N, we derive extended recurrence relations among nonrelativistic low energy string scattering amplitudes of string states with different spins and different channels.

hep-th↗
arXiv2016

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

We discover that the 26D open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state can be expressed in terms of the D-type Lauricella functions with associated SL(K+3,C) symmetry. As a result, SSA and symmetries or relations among SSA of different string states at various limits calculated previously can be rederived. These include the linear relations conjectured by Gross [1-3] and proved in [4-9] in the hard scattering limit, the recurrence relations in the Regge scattering limit [14-16] and the extended recurrence relations in the nonrelativistic scattering limit [19] discovered recently. Finally, as an application, we calculate a new recurrence relation of SSA which is valid for all energies.

hep-th↗
arXiv2015

Biquaternion Construction of SL(2,C) Yang-Mills Instantons

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.

hep-th↗
arXiv2015

Regge Closed String Scattering and its Implication on Fixed angle Closed String Scattering

We calculate the complete closed string high energy scattering amplitudes (HSA) in the Regge regime for arbitrary mass levels. As an application, we deduce the complete ratios among closed string HSA in the fixed angle regime by using Stirling number identities. These results are in contrast with the incomplete set of closed string HSA in the fixed angle regime calculated previously. The complete forms of the fixed angle amplitudes, and hence the ratios, were not calculable previously without the input of zero-norm state calculation. This is mainly due to the lack of saddle point in the fixed angle closed string calculation.

hep-th↗
arXiv2015

Biquaternions and ADHM Construction of Non-Compact SL(2,C) Yang-Mills Instantons

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 moduli 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 clearify the long standing global singularity problems associated with Backlund transformations of SU(2) instantons.

hep-th↗
arXiv2014

Multi-indexed Extensions of Soliton Potential and Extended Integer Solitons of KdV Equation

We calculate infinite set of initial profiles of higher integer KdV solitons, which are both exactly solvable for the Schrodinger equation and for the Gel'fand-Levitan-Marchenko equation in the inverse scattering transform 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.

quant-ph↗
arXiv2014

The Appell Function $F_1$ and Regge String Scattering Amplitudes

We show that each 26D open bosonic Regge string scattering amplitude (RSSA) can be expressed in terms of one single Appell function $F_1$ in the Regge limit. This result enables us to derive infinite number of recurrence relations among RSSA at arbitrary mass levels, which are conjectured to be related to the known SL(5,C) dynamical symmetry of $F_1$. In addition, we show that these recurrence relations in the Regge limit can be systematically solved so that all RSSA can be expressed in terms of one amplitude. All these results are dual to high energy symmetries of fixed angle string scattering amplitudes discovered previously [4-8].

hep-th↗
arXiv2013

BCFW Deformation and Regge Limit

BCFW deformation has served as an extremely useful tool in providing a recursive approach in studying color-ordered gauge amplitudes. This procedure has also been generalized to the study of graviton scattering. An important ingredient of this approach is the ability to identify amplitudes satisfying convergent dispersion relation when the BCFW parameter, z, is treated as a complex variable. In a modified BCFW treatment, we show in what sense the BCFW deformation in the large-z limit can be understood as the Regge limit. We also discuss how the issue of convergent dispersion integral for amplitudes involving external spins relates to the study of super-convergence relation which served as the precursor to the s-t duality relation for flat space string amplitudes.

hep-th↗
arXiv2013

Recurrence Relations of Higher Spin BPST Vertex Operators for Open String

We calculate higher spin BPST vertex operators for open bosonic string and express these operstors in terms of Kummer function of the second kind. We derive 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.

hep-th↗
arXiv2013

Recurrence relations of Kummer functions and Regge string scattering amplitudes

We discover an infinite number of recurrence relations among Regge string scattering amplitudes \cite{bosonic,RRsusy} 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.

hep-th↗
arXiv2013

A note on on-shell recursion relation of string amplitudes

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.

hep-th↗
arXiv2012

Exponential fall-off Behavior of Regge Scatterings in Compactified Open String Theory

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 (Lee and Yang, 2007, and Lee, Takimi, and Yang, 2008) 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 Lee, Yan, and Yang to link fixed angle and Regge 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 in complementary with a kenematic regime discovered previously (Lee, Takimi, and Yang, 2008), which shows the unusual power-law behavior in the high-energy fixed angle compactified string scatterings. Key words: Regge string scatterings; High-energy String

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