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Low energy effective action of multiple D2-branes with Romans mass O- Kab Kwon. Sungkyunkwan University (SKKU). In collaboration with Gyungchoon Go and Driba Tolla. arXiv:1110.3902, Phys.Rev . D85 026006. YongPyong 2012 Winter Conference Feb. 21, 2012. Outline.

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Low energy effective action of multiple D2-branes with Romans mass O-Kab Kwon Sungkyunkwan University (SKKU) In collaboration with Gyungchoon Go and DribaTolla arXiv:1110.3902, Phys.Rev. D85 026006 YongPyong 2012 Winter Conference Feb. 21, 2012 Outline ABJM theory & GT theory Massive IIA gravity and Romans mass MP Higgsing of the N=3 GT theory Vacuum moduli space and fuzzy funnel solution Brane configuration of N=3 YM CS theory Discussion ABJM theory & GT theory ABJM Theory Aharony-Bergman -Jafferis-Maldacena 2008 Chern-Simons matter(CSM) theory U(N)XU(N) gauge group Chern-Simon levels k and –k (k1+k2=0) effective action of M2-branes on small k dual to M-theory on large k dual to IIA string theory on ABJM theory & GT theory GT Theory Gaiotto-Tomasiello 2009 [Fujita-Li-Ryu-Takayanagi 09] Chern-Simons matter(CSM) theory U(N)XU(N) gauge group Chern-Simon levels k and –k + F0 (k1+k2=F0) no brane interpretation and gravity dual in M-theory , 1 GT theory is dual to massive IIA gravity F0 is identified as the flux of D8-brane [Gaiotto-Tomasiello 2009] (a model of QHE) More about GT theory Gravity dual of N=2,3 GT theories in perturbative level in massive IIA gravity [Gaiotto-TomasielloarXiv:0904.3959] Gravity dual of N=0 GT theory solution in massive IIA gravity : quantitative comparison [Bergman- Lifschytz 10] Calculation of partition function=partition function in massive IIA [Jafferis-Klebanov-Pufu-Safdi, Suyama 11] N=2,3 supersymmetry preserving massive deformation and vacuum solution [OK-Tolla 11] Action of the N=3 GT theory Massive IIA gravity and Romans mass Introducing the cosmological constant in massless IIA gravity Aharony et al arXiv:1007.2451, “Massive type IIA string theory cannot be strongly coupled!!” How about at strong curvature? Flux of D8-brane (Romans mass) [Romans 1986] Motivation The only known result for the N=3 GT theory: dual gravity(large N) Massive IIA gravity N=3 GT for large k How about the case for small N? MP Higgising N=8 SYM N=6 ABJM D2-branes M2-branes on (IIA String theory) (M-theory) Our trial MP Higgising N=8 SYM N=6 ABJM D2-branes M2-branes on (IIA String theory) (M-theory) MP Higgising N=3 YM CS N=3 GT D2-branes on D6- D8-branes background (brane configurations?) (M-theory interpretation?) (massive IIA String theory) Mukhi-Papageorgakis(MP) Higgs mechanism Mukhi-Papageorgakis (MP) Higgsing mechanism is allowed only if the bosonic potential has a flat direction. orbifold identification Mukhi-Papageorgakis(MP) Higgs mechanism Mukhi-Papageorgakis (MP) Higgsing mechanism is allowed only if the bosonic potential has a flat direction. N=6 ABJM theory N=8 super YM theory orbifold identification MP Higgising N=6 ABJM theory N=8 super YM theory N=3 GT theory ??? MP Higgising IR conformal [Kapustin-Willet-Yaakov, 10, Dongmin-Koh-Lee-Park, 11] MP Higgising MP Higgsing of the N=3 GT theory[Go-OK-Tolla 11] Flat directions of GT theory: Redefinition of fields: Chern-Simons level and nonvanishingvev of one scalar field: N=3 super YM CS theory: N=3 super YM CS theory: c.f.) N=3 super YM CS [Kao; Kao-Lee-Lee] Vacuum moduli space and fuzzy funnel solution Moduli space 3 massive field and 4 flat directions N=1 fuzzy funnel solution: expressed by 7 generators of SU(3), excluding Our proposal MP Higgising N=8 SYM N=6 ABJM D2-branes M2-branes on (IIA String theory) (M-theory) MP Higgising N=3 YM CS N=3 GT D2-branes on D6- D8-branes background (brane configurations?) (M-theory interpretation?) (massive IIA String theory) Meaning of MP Higgsing MP Higgising N=8 SYM N=6 ABJM D2-branes M2-branes on (IIA String theory) (M-theory) MP Higgsing = moving far away from the orbifold singularity + T-duality = eliminating the NS5 and (1,k)-branes + T-duality NS5 and (1,k)5-branes Meaning of MP Higgsing MP Higgising N=3 YM CS N= GT [Fujita-Li-Ryu-Takayanagi 09] MP Higgsing= eliminating the NS5 and (1,k)-branes + T-duality Brane configuration of N=3 YM CS theory IIB brane configuration: IIA brane configuration: 2 1,6,7,8,9 N D2 q D6 3,4,5 q D8 Vacuum moduli space and fuzzy funnel solution Moduli space 3 massive field and 4 flat directions N=1 fuzzy funnel solution: expressed by 7 generators of SU(3), excluding Discussion [Gaiottotomosiello 0901] Gravity dual and brane construction: GT theory Gravity dual + perturbation for small F0 Braneconstruction in M-theory? [Gaiottotomosiello 0904] Effective action of multiple D2-branes in the presence of F0 D6 and F0 D8-branes N=3 YM CS (Romans mass) Dual gravity? MP Higgising IR conformal [Kapustin-Willet-Yaakov, 10, Dongmin-Koh-Lee-Park, 11] N=6 ABJM theory N=8 super YM theory N=3 GT theory N=3 YM CS theory N=3 mass-deformed GT gravity dual? Fuzzy funnel type of M9-brane solution in GT theory? MP Higgising IR conformal? [OK-Tolla 11] D7-brane SL(2,Z) monodromy of D7-brane: Wess-Zumino type coupling: N D3-branes Brench cut

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