Low energy effective action of multiple D2-branes with Romans mass O- Kab Kwon

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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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