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AdS4/CFT3 correspondence and Chern-Simons gauge theories Jaemo Park (Postech ) Yong Pyong 2010. 02.25 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A A A A A AA

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Outline 1.Motivation and some history 2. N=4 theories via N=1 Formalism 3. N=2 formalism and M2 Theories for generic toric singulraities 5. Monopole solutions of ABJM and nonperturbative tests of M2 theory 6. BPS spectrum and monopole operators 7. Future directions

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Construction of N=4 theories

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Possible configurations

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N=2(4 supercharges) formalism

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4d-3d correspondence

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Evidences of AdS4/CFT3 Moduli space index computation (Bhattacharaya, Minwalla N=6; Choi, Lee, Song N=5,4, Kim N=6) Graviton exchange with nonzero angular momentum Matching BPS operators and spectrum

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Monopole solutions in ABJM and nonperturbative test of M2 brane theory

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Monopole amplitude matches with the graviton exchange with nonzero angular momentum (Analogue of Polchinski, Pouliot of membrane scattering in matrix theory) It is interesting to work out the prefactor as well. (cf. Baek, Hyun, Jang, Yi)

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BPS operators In Chern-Simons matter theory, this involves the monopole operator These operators in field theory could describe nonperturbative objects (e.g. giant gravitons, D2-D0 bound states)

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D4 brane ~ dibaryon oprator det (due to subtle quantization condition)

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Conclusions and Future Directions Construct various CS gauge theories which can describe M2 brane theories and provide several evidences for them Should provide more evidences for AdS4/CFT3 Algorithm of constructing N=2 theories for M2 branes in an arbitrary CY4 singularities Wilson loop evaluation Beyond the chiral rings for N=2 theories Integrability structures?

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