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Emergent Schrodinger geometries from mass-deformed CFT

Hee-Cheol Kim KIAS. Emergent Schrodinger geometries from mass-deformed CFT. Based on. H-C Kim, Seok Kim, Kimyeong Lee & Jaemo Park, JHEP 1108: 111 (2011). References :

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Emergent Schrodinger geometries from mass-deformed CFT

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  1. Hee-Cheol Kim KIAS Emergent Schrodinger geometries from mass-deformed CFT Based on H-C Kim, Seok Kim, Kimyeong Lee & Jaemo Park, JHEP 1108: 111 (2011) References : D. T. Son, Phys. Rev. D 78, 046003 (2008)K. Balasubramanian & J. McGreevy, Phys. Rev. Lett101, 061601 (2008) J. P. Gauntlett, S. Kim, O. Varela & D. Waldram, JHEP 0904, 102 (2009)J. P. Gauntlett, J. Sonner & T. Wiseman, JHEP 1002, 060 (2010) K. M. Lee, S. Lee & S. Lee, JHEP 0909, 030 (2009) E. O Colgain, O. Varela & H. Yavartanoo, JHEP 0907, 081 (2009) N. Lambert & P. Richmond, JHEP 0910, 084 (2009) D. Forcella & A. Zaffaroni, arXiv:1103.0648 [hep-th]

  2. Motivation • NR-CFT possess Schrodinger symmetry, NR version of conformal symmetry, and gravity duals were proposed. • Correct gravity dual solutions should geometrically realize a natural nonrelativistic limit taken in the field theory. • An example is the flow solution from AdS solution in UV to Schrodinger solution in IR • Can we find the geometric realization of this Holographic RG flow?

  3. Nonrelativistic limit of field theory • (2+1) dimensional CFT with mass deformation. • Decompose relativistic fields into nonrelativistic particles and anti-particles. • Discards all anti-particles. • Restore and take the limit . • NR energy is redefined as

  4. Motivation • NR-CFT possess Schrodinger symmetry, NR version of conformal symmetry, and gravity duals were proposed. • Correct gravity dual solutions should geometrically realize a natural nonrelativistic limit taken in the field theory. • An example is the flow solution from AdS solution in UV to Schrodinger solution in IR • Can we find the geometric realization of this Holographic RG flow?

  5. Schrodinger solution • Schrodinger symmetry is an extension of Galilean symmetry with particle number, dilatation, special conformal symmetry. • Geometric realization of Schrodinger algebra • Invariant under Schrodinger symmetry • Dilatation • Particle number symmetry • Focus on 5-dimensional Schrodinger solution. • Dual theory is (2+1)dim NR-CFT with U(1) global symmetry. • This U(1) global symmetry is identified as the shift of

  6. Gravity Ansatz • A consistent KK truncation of D=11 supergravity. • : dual 1-form of Reeb vector where . • shift is dual to U(1) global rotation. • Choose : Skew-whiffing • Anti-M2 branes at the tip of 8-dimensional cone. • Asymptotic to : as • Far infrared : as : Kahler 2-form of Kahler-Einstein base .

  7. Flow solution from AdS to Schrodinger • A solution satisfying the boundary conditions In IR : mass parameter Redefine Take the scaling limit : and

  8. Summary • Mass-deformed CFT has a natural nonrelativistic limit. • We studied the geometric realization of those limit. • We found a very simple class of the flow solutions from in UV to in IR. • We identified UV mass parameters in the dual mass-deformed CFT. • self-dual 4-form flux drives the flow.

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