Chanyong Park 35 th Johns Hopkins Workshop ( Budapest, 22-24 June 2011 ) Based on Phys. Rev. D 83, 126004 (2011) arXiv : 1104.1896 arXiv : 1105.3279.

Slides:



Advertisements
Similar presentations
Analysis of QCD via Supergravity S. Sugimoto (YITP) based on hep-th/ (T. Ibaraki + S.S.) Windows to new paradigm in particle Sendai.
Advertisements

Martín Schvellinger Instituto de Física de La Plata - CONICET Departamento de Física - UNLP The gauge/gravity duality and Non-Relativistic Quantum Field.
Summing planar diagrams
Yerevan State University / Leibniz Universität Hannover Supersymmetry in Integrable Systems - SIS'10 International Workshop, August 2010, Yerevan,
ASYMPTOTIC STRUCTURE IN HIGHER DIMENSIONS AND ITS CLASSIFICATION KENTARO TANABE (UNIVERSITY OF BARCELONA) based on KT, Kinoshita and Shiromizu PRD
Giant Magnon and Spike Solutions in String Theories Bum-Hoon Lee Center for Quantum SpaceTime(CQUeST)/Physics Dept. Sogang University, Seoul, Korea PAQFT08,
The Giant Magnon and Spike Solution Chanyong Park (CQUeST) Haengdang Workshop ’07, The Giant Magnon and Spike Solution Chanyong Park.
Semi-Classical strings as probes of AdS/CFT M. Kruczenski Purdue University Based on: arXiv: R. Roiban, A. Tirziu, A. Tseytlin, M.K. arXiv:
Holographic three-point functions of semiclassical states Konstantin Zarembo (Nordita) "From sigma models to four-dimensional QFT“, Hamburg, K.Z.,
3rd International Workshop On High Energy Physics In The LHC Era.
The attractor mechanism, C-functions and aspects of holography in Lovelock gravity Mohamed M. Anber November HET bag-lunch.
Spin Chain in Gauge Theory and Holography Yong-Shi Wu Department of Physics, University of Utah, Center for Advanced Study, Tsinghua University, and Shanghai.
Microscopic entropy of the three-dimensional rotating black hole of BHT massive gravity of BHT massive gravity Ricardo Troncoso Ricardo Troncoso In collaboration.
Spiky strings, light-like Wilson loops and a pp-wave anomaly M. Kruczenski Purdue University Based on: arXiv: arXiv: A. Tseytlin, M.K.
Strings in AdS pp-waves M. Kruczenski Purdue University Based on: arXiv: arXiv: A. Tseytlin, M.K. arXiv: arXiv: R. Ishizeki,
Large spin operators in string/gauge theory duality M. Kruczenski Purdue University Based on: arXiv: (L. Freyhult, A. Tirziu, M.K.) Miami 2009.
Shock waves in strongly coupled plasmas M. Kruczenski Purdue University Based on: arXiv: (S. Khlebnikov, G. Michalogiorgakis, M.K.) Quantum Gravity.
Spiky Strings in the SL(2) Bethe Ansatz
Planar diagrams in light-cone gauge hep-th/ M. Kruczenski Purdue University Based on:
Spiky Strings and Giant Magnons on S 5 M. Kruczenski Purdue University Based on: hep-th/ (Russo, Tseytlin, M.K.)
Strings in AdS pp-waves M. Kruczenski Purdue University Based on: arXiv: A. Tseytlin, M.K. arXiv: R. Ishizeki, A. Tirziu, M.K. + work.
Excited QCD 2010, February 3 (Tatra National Park, 2010) Holographic Models for Planar QCD without AdS/CFT Correspondence Sergey Afonin Ruhr-University.
Integrability and Bethe Ansatz in the AdS/CFT correspondence Konstantin Zarembo (Uppsala U.) Nordic Network Meeting Helsinki, Thanks to: Niklas.
Integrability in Superconformal Chern-Simons Theories Konstantin Zarembo Ecole Normale Supérieure “Symposium on Theoretical and Mathematical Physics”,
Constraints on renormalization group flows Based on published and unpublished work with A.Dymarsky,Z.Komargodski,S.Theisen.
Holographic Description of Quantum Black Hole on a Computer Yoshifumi Hyakutake (Ibaraki Univ.) Collaboration with M. Hanada ( YITP, Kyoto ), G. Ishiki.
An introduction to the Gravity/Fluid correspondence and its applications Ya-Peng Hu College of Science, Nanjing University of Aeronautics and Astronautics,
Constraining theories with higher spin symmetry Juan Maldacena Institute for Advanced Study Based on: and by J. M. and A. Zhiboedov.
Exact Results for perturbative partition functions of theories with SU(2|4) symmetry Shinji Shimasaki (Kyoto University) JHEP1302, 148 (2013) (arXiv: [hep-th])
Super Yang Mills Scattering amplitudes at strong coupling Juan Maldacena Based on L. Alday & JM arXiv: [hep-th] & to appear Strings 2007, Madrid.
Integrability of N=6 Super Chern-Simons Theories Dongsu Bak University of Seoul with S. J. Rey and D. Kang (KIAS, 9/24/2008) TexPoint fonts used in EMF.
Constraining theories with higher spin symmetry Juan Maldacena Institute for Advanced Study Based on & to appearhttp://arxiv.org/abs/
Minimal area surfaces in hyperbolic space
Disordered systems and the replica method in AdS/CFT Yasuaki Hikida (KEK) Ref. Fujita, YH, Ryu, Takayanagi, JHEP12(2008)065 April 13,
Finite N Index and Angular Momentum Bound from Gravity “KEK Theory Workshop 2007” Yu Nakayama, 13 th. Mar (University of Tokyo) Based on hep-th/
HIGHER SPIN SUPERGRAVITY DUAL OF KAZAMA-SUZUKI MODEL Yasuaki Hikida (Keio University) Based on JHEP02(2012)109 [arXiv: [hep-th]]; arXiv:
Holographic Superconductors from Gauss-Bonnet Gravity Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences (May 7, 2012) 2012 海峡两岸粒子物理和宇宙学研讨会,
Bethe ansatz in String Theory Konstantin Zarembo (Uppsala U.) Integrable Models and Applications, Lyon,
II Russian-Spanish Congress “Particle and Nuclear Physics at all scales and Cosmology”, Saint Petersburg, Oct. 4, 2013 RECENT ADVANCES IN THE BOTTOM-UP.
Holography of Wilson-loop expectation values with local operator insertions Akitsugu Miwa ( Univ. of Tokyo, Komaba ) work in collaboration with Tamiaki.
Transverse Momentum Broadening of a Fast Quark in a N=4 Yang Mills Plasma Jorge Casalderrey-Solana LBNL Work in collaboration with Derek Teany.
Minkyoo Kim (Wigner Research Centre for Physics) 9th, September, 2013 Seminar in KIAS.
Wilson Loops in AdS/CFT M. Kruczenski Purdue University Miami Based on work in collaboration with Arkady Tseytlin (Imperial College). To appear.
Comments on entanglement entropy in the dS/CFT correspondence Yoshiki Sato ( Kyoto U. ) PRD 91 (2015) 8, [arXiv: ] 9th July.
Numerical Solution of the Spectral Problem and BFKL at Next-to-Next-to-Leading Order in N=4 SYM Fedor Levkovich-Maslyuk King’s College London based on.
Holographic QCD in the medium
Wilsonian approach to Non-linear sigma models Etsuko Itou (YITP, Japan) Progress of Theoretical Physics 109 (2003) 751 Progress of Theoretical Physics.
1 Renormalization Group Treatment of Non-renormalizable Interactions Dmitri Kazakov JINR / ITEP Questions: Can one treat non-renormalizable interactions.
Higher spin AdS 3 holography and superstring theory Yasuaki Hikida (Rikkyo University) Based on collaborations with T. Creutzig (U. of Alberta) & P. B.
Integrability for the Full Spectrum of Planar AdS/CFT Nikolay Gromov DESY/HU/PNPI V.Kazakov and P.Vieira.
Integrability and Bethe Ansatz in the AdS/CFT correspondence Konstantin Zarembo (Uppsala U.) Nordic Network Meeting Helsinki, Thanks to: Niklas.
Supersymmetric three dimensional conformal sigma models Collaborated with Takeshi Higashi and Kiyoshi Higashijima (Osaka U.) Etsuko Itou (Kyoto U. YITP)
The nonperturbative analyses for lower dimensional non-linear sigma models Etsuko Itou (Osaka University) 1.Introduction 2.The WRG equation for NLσM 3.Fixed.
Relating e+e- annihilation to high energy scattering at weak and strong coupling Yoshitaka Hatta (U. Tsukuba) JHEP 11 (2008) 057; arXiv: [hep-ph]
B.-H.L, R. Nayak, K. Panigrahi, C. Park On the giant magnon and spike solutions for strings on AdS(3) x S**3. JHEP 0806:065,2008. arXiv: J. Kluson,
Heavy quark energy loss in finite length SYM plasma Cyrille Marquet Columbia University based on F. Dominguez, C. Marquet, A. Mueller, B. Wu and B.-W.
A Holographic Framework for Eternal Inflation Yasuhiro Sekino (Okayama Institute for Quantum Physics) Collaboration with Ben Freivogel (UC Berkeley), Leonard.
Boundary conditions for SU(2) Yang-Mills on AdS 4 Jae-Hyuk Oh at 2012 workshop for string theory and cosmology, Pusan, Korea. Dileep P. Jatkar and Jae-Hyuk.
Gauge/gravity duality in Einstein-dilaton theory Chanyong Park Workshop on String theory and cosmology (Pusan, ) Ref. S. Kulkarni,
Bum-Hoon Lee Sogang University, Seoul, Korea D-branes in Type IIB Plane Wave Background 15th Mini-Workshop on Particle Physics May 14-15, 2006, Seoul National.
Semiclassical correlation functions in holography Kostya Zarembo “Strings, Gauge Theory and the LHC”, Copenhagen, K.Z.,
Rank-n logarithmic conformal field theory (LCFT) in the BTZ black hole Rank-n logarithmic conformal field theory (LCFT) in the BTZ black hole
Geometric Monte Carlo and Black Janus Geometries
Gauge/String Duality and Integrable Systems
Cyrille Marquet Columbia University
A rotating hairy BH in AdS_3
Giant magnons in TsT-transformed Dmitri Bykov Trinity College Dublin
Quantum properties of supersymmetric gauge theories
Gravity from Entanglement and RG Flow
Gauge invariant computable quantities in Timelike Liouville theory
Presentation transcript:

Chanyong Park 35 th Johns Hopkins Workshop ( Budapest, June 2011 ) Based on Phys. Rev. D 83, (2011) arXiv : arXiv : collaborated with B.H. Lee and X. Bai

Plan 1. Review of the solitonic string 2. Correlation functions of magnon 3. Correlation functions of other solutions 4. Finite size effect on the 3-pt correlation function 5. Conclusion and discussion

Review of magon and spike

4 1.

Magnon in the gauge theory (spin chain model) Consider a gauge invariant (heavy) scalar operator which can be interpreted as a magnon in the spin chain model. The anomalous dimension of magnon In the large ‘t Hooft coupling limit, Magnon [Minahan and Zarembo ’02] 5

In the string theory the magnon operator corresponds to a solitonic string rotating on, which is called the giant magnon. In the string world sheet In the target space Consider the action for string moving in 6

The dispersion relation where & = infinite and =finite Conserved charges (in the infinite size limit ) Giant Magnon [Hofman & Maldacena ’06] and The typical structure of the magnon’s dispersion relation in the infinite size limit is described by This dispersion relation is exactly the same as one in the spin chain model in the large ‘t Hooft coupling limit 7

2) spike ( another solution in the different parameter regime ) Conserved charges The dispersion relation where & = infinite =finite Spike in the target space 8

Notice The conformal field theory (CFT) is usually characterized by the conformal dimension of all primary operators and the structure constant included in the three- point correlation functions, because higher point functions may be determined by using the operator product expansion (OPE). - After finding an integrable structure in N=4 SYM theory, there were great progresses in calculating the spectra (the anomalous dimensions) of various operators. - On the contrary, although the structure constant describing the interaction can be evaluated in the weak coupling limit by computing the Feynman diagrams, at the strong coupling there still remain many things to be done. From now on, we will investigate the three-point correlation function of two heavy operators (magnon or spike) and one light (marginal) operator. 2. Correlation functions of magnon 9

Solitonic string on the Poincare AdS The Euclidean AdS metric in the Poincare patch The string action on is given by 1) AdS part 10

we can find : modular parameter of the cylinder Notice that we do not use the Virasoro constraints. In AdS space, the string propagates as a point particle. 11

The equations of motion are reduced to 1) part where and are two integration constants. Notice that there are two additional integration constants, which determine the position of magnon. Because the dispersion relation is described by the conserved quantities which contain one derivative, these two additional integration constants are irrelevant in determining the dispersion relation. 12

Boundary conditions for fixing two integration constants 1) which plays an important role to determine the size of magnon and spike. In the infinite size limit ( ) 2) which guarantees that even the angle difference is finite while the energy and the angular momentum are infinite. After imposing these boundary conditions, we finally obtain 13

The JSW proposed that ( ) -> the two point correlation function of heavy operator in gauge theory is proportional to the string partition function at the saddle point. I. Two-point function of Magnon ( which is nothing but the Virasoro constraints ) Following the JSW procedure, after convolving the semiclassical propagator with the wave function of the state that we are interested in, we obtain JSW : Janik, Surowka and Wereszczynski, arXiv:

Two-point function Using the definitions of the conserved charges, we can reproduce the dispersion relation of the magnon in the large ‘t Hooft coupling regime Energy of the giant magnon the conformal dim. of magnon 15

Now, calculate the three-point correlation function between two heavy operators and one marginal scalar operator 2. Three-point function of Magnon Following the AdS/CFT correspondence, the SUGRA field dual to the marginal scalar operator is the dilaton (massless scalar). [Costa, Monteiro, Santos, Zoakos, JHEP 1011 (2010) 141 [ arXiv: ] ] 16

17

Finally, we obtain The CFT result is - the powers in the denominator are fixed by the global conformal transformation - the structure constant is not determined by conformal symmetry By comparing above two results, we can determine the structure constant 18

* The structure constant in the gauge theory [Costa, Monteiro, Santos, Zoakos, arXiv: ] From the RG analysis, it was shown that the structure constant of the marginally deformed theory can be determined by : coupling between two op. and one marginal op. : the anomalous dimension of two op. For two heavy op. (magnon) and one marginal op., from the dispersion relation of magnon we can find in the large coupling limit 19

3. Correlation functions of other solutions using the same method, we calculated the correlation functions of various Solitonic strings. 1. Dyonic magnon which is described by the solitonic string rotating on Two-point correlation function Three-point correlation function in the RG analysis 20

2. Single spike which is described by the solitonic string rotating on in the different parameter range Two-point correlation function Three-point correlation function with in the RG analysis 21

4. Finite size effect on the 3-pt correlation function the finite size effect of the giant magnon ~ the wrapping effects in the spin chain model Consider the case of The conserved charges for the giant magnon 22

Two-point correlation function Three-point correlation function for, This result coincides with the RG calculation with 23

4. Conclusion and discussion - Using the [JSW] & (CMSZ) prescription, we calculated the two- and three-point correlation functions of various solitonic string solutions - Checked that these prescriptions are working well. - Showed that the correlation functions in the string and gauge theory are perfectly matched, which is another evidence of the AdS/CFT correspondence. - Calculated the finite size effect on the three-point function of the giant magnon JSW : Janik, Surowka, Wereszczynski CMSZ : Costa, Monteiro, Santos, Zoakos 24

25 Thank you !