## Outcomes Research

**A. High energy string scatterings**

1. We use three different methods to derive infinite linear relations among high energy scattering amplitudes for string states at arbitrary mass levels in the fixed angle regime. All three methods give the consistent result.

2. We derive an infinite number of ratios among string scattering amplitudes of different string states and, FOR THE FIRST TIME, complete the proof of the famous conjectures of Gross in 1988 on high energy symmetry of string theory.

3. We discover an infinite number of recurrence relations among Regge string scattering amplitudes of different string states at arbitrary mass levels.

4. We extract ratios among high-energy string scattering amplitudes in the fixed angle regime from high-energy amplitudes in the Regge regime. The calculation is based on a signless Stirling number identity in combinatorial theory.

5. In the application of BCFW on-shell recursion relation to string amplitudes, one challenge is the sum over infinite intermediate on-shell string states. We show how to sum these infinite states explicitly by including unphysical states to make complete Fock space.

**B. AdS/QCD&CMT duality**

1. We studied the thermodynamics of RN black hole and found a new phase at high temperature.

2. We built a holographic QCD model by using AdS/CFT duality. We studied Einstein-Maxwell-Dilaton system analytically and interpreted its dual field theory as heavy quarks in QCD. The phase diagram we obtained is consistent with lattice QCD.

3. We study the transport coefficients in a Lifshitz black brane and find some novel scaling behavior of optical conductivity which can be found in various condensed matter systems.

4. We study a bulk dipole coupling for a probe fermion in a charged dilatonic black hole, and find some Mott-like gap dynamically generated as the strength of dipole coupling is increasing.

5. We construct a holographic two-band superconductor and find the phase diagram, optical conductivity and thermal conductivity are qualitatively consistent with experiments. Our model might be useful as a toy model to study the physical properties of current widely studied new high temperature superconductor – iron-based superconductor.

**C. Gauge theory scattering amplitudes**

1. Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion technique:

From on-shell relation we proved the conjectured color KLT relation inspired by heterotic string amplitude relation. In addition the on-shell technique reproduced a tachyonic recursion relation previously observed was reproduced, providing an explanation to the apparently missing higher-spin structure.

2. Color-kinematic duality:

It was observed by Bern Carrasco and Johansson (BCJ) that kinematic dependence of Yang-Mills amplitude respects the same algebraic identity as its color dependence. We presented an algebraic construction of the BCJ numerator and derived the color-kinematic dual of the Del Duca-Dixon-Maltoni half ladder formula and the familiar color-ordered formulation of Yang-Mills and gravity amplitude.

3. MHV formulation:

Inspired by twistor string theory, Cachazo, Svrcek and Witten (CSW) prescribed a systematic construction of gluon amplitude using MHV (maximally helicity violating) amplitudes as building blocks. We showed that anomolous contributions to CSW rules can be recovered from MHV lagrangian formulation. In particular the standard language used in supersymmetric N=4 super Yang-Mills and N=8 super gravity amplitudes can be derived from chiral action.

**D. Recent Publications (since 2012)**

[1] C. H. Fu, J.C. Lee, C.I. Tan and Y. Yang, “Recurrence relations of higher spin BPST operators for open string”, arXiv 1304.6948 (2013).

[2] Yi-Jian Du, Bo Feng, Chih-Hao Fu , “The Construction of Dual-trace Factor in Yang-Mills Theory”, e-Print: arXiv:1304.2978 (2013).

[3] J.C. Lee and Y. Mitsuka, “Recurrence relations of Kummer functions and Regge string scattering amplitudes”, JHEP 1304,082 (2013). (Impact Factor=IF=5.831)

[4] Yung-Yeh Chang, Bo Feng, Chih-Hao Fu, J.C. Lee, Yihong Wang and Y. Yang, “A note on on-shell recursion relation of string amplitudes”, JHEP 02 (2013) 028. (IF=5.831)

[5] Song He, Shang-Yu Wu, Y.Y., Pei-Hung Yuan, “Phase Structure in a Dynamical Soft-Wall Holographic QCD Model”, JHEP 04 (2013) 093. (IF=5.831)

[6] Chih-Hao Fu, Yi-Jian Du, Bo Feng, “An algebraic approach to BCJ numerators “, JHEP 1303 (2013) 050. (IF=5.831)

[7] Yi-Jian Du, Bo Feng, Chih-Hao Fu, “Note on Cyclic Sum and Combination Sum of Color-ordered Gluon Amplitudes”, JHEP 1203 (2012) 016. (IF=5.831)

[8] Y.D. Tsai, X.N. Wu and Y.Y., “Phase structure of the Kerr-AdS Black Hole”, Phys.Rev. D85, 044005 (2012). (IF=4.964)

[9] Jia-Rui Sun, Shang-Yu Wu, Hai-Qing Zhang, “Novel Features of the Transport Coefficients in Lifshitz Black Branes,” Phys. Rev. D. 87, 086005 (2013) (IF=4.964)

[10] Wen-Yu Wen, Shang-Yu Wu_, “Dipole Coupling Effect of Holographic Fermion in Charged Dilatonic Gravity,“ Phys.Lett. B 712(2012) 266-271. (IF=3.955)

[11] Yi-Jian Du, Bo Feng, Chih-Hao Fu, “Note on Permutation Sum of Color-ordered Gluon Amplitudes”, Phys.Lett. B706 (2012) 490-494. (IF=3.955)

[12] J.C. Lee, C.H. Yan and Y.Y., “High-energy String Scattering Amplitudes and Signless Stirling Number Identity”, SIGMA 8 (2012), 045. (IF=1.071)

[13] S. He, J.C. Lee and Y.Y., “Exponential fall-off Behavior of Regge Scatterings in Compactified Open String Theory”, Prog. Theor. Phys. 128, No. 5 (2012). (IF=2.294)