Exact Holography Relation in finite N

Transcription

1 Exact Holography Relation in finite N Dongmin Jang Sungkyunkwan University (SKKU) In collaboration with Yoonbai Kim, O-Kab Kwon, D.D. Tolla The 52 nd Workshop on Gravity and Cosmology November 19, 2016 Based on arxiv:

2 Introduction theory ABJM Large N M-theory on

3 Introduction theory ABJM Large N M-theory on mass deformation mabjm theory 3-dim. Gauge theory

4 Introduction theory ABJM Large N M-theory on mass deformation fluctuation mabjm theory Half BPS LLM geometry in 11-dim. SUGRA KK reduction 3-dim. Gauge theory 4-dim. Gravity theory

5 Introduction theory ABJM Large N M-theory on mass deformation fluctuation mabjm theory 3-dim. Gauge theory Gauge/Gravity duality Half BPS LLM geometry in 11-dim. SUGRA KK reduction 4-dim. Gravity theory

6 Introduction theory ABJM Large N M-theory on mass deformation fluctuation mabjm theory 3-dim. Gauge theory vev of CPO with conformal dimension Gauge/Gravity duality Finite Half BPS LLM geometry in 11-dim. SUGRA KK reduction 4-dim. Gravity theory Coefficient of asymptotic expansion of dual scalar field

7 Discrete Higgs vacua of mabjm ABJM theory global sym. SUSY preserving mass deformation mabjm theory sym. [Hosomichi et al 08] [Gomis et al 08]

8 Discrete Higgs vacua of mabjm ABJM theory global sym. SUSY preserving mass deformation mabjm theory sym. [Hosomichi et al 08] [Gomis et al 08] GRVV matrices

9 Discrete Higgs vacua of mabjm ABJM theory global sym. SUSY preserving mass deformation mabjm theory sym. [Hosomichi et al 08] [Gomis et al 08] GRVV matrices Direct sum Discrete Higgs vacua [Gomis et al 08] [Cheon,Kim,Kim 11]

10 Discrete Higgs vacua of mabjm Discrete Higgs vacua (N X N matrices)

11 Discrete Higgs vacua of mabjm Discrete Higgs vacua (N X N matrices) Constraints :,

12 Discrete Higgs vacua of mabjm Discrete Higgs vacua (N X N matrices) Constraints :, Condition for supersymmetric vacua : [Kim,Kim 10] [Cheon,Kim,Kim 11]

13 Discrete Higgs vacua of mabjm Discrete Higgs vacua (N X N matrices) Constraints :, Condition for supersymmetric vacua : Vacua are clarified by occupation number [Kim,Kim 10] [Cheon,Kim,Kim 11]

14 LLM geometry in 11-dim. SUGRA Half-BPS LLM geometry with isometry in 11-dimensional supergravity [Lin,Lunin,Maldacena 04] [Cheon,Kim,Kim 11] This solution is determined by two functions

15 LLM geometry in 11-dim. SUGRA boundary : white strip : black strip Droplet picture

16 LLM geometry in 11-dim. SUGRA boundary : white strip : black strip Discrete torsion Vacuum is identified by the occupation numbers : Droplet picture [Cheon,Kim,Kim 11]

17 LLM geometry in 11-dim. SUGRA boundary : white strip : black strip Discrete torsion Vacuum is identified by the occupation numbers : Droplet picture [Cheon,Kim,Kim 11]

18 LLM geometry in 11-dim. SUGRA For arbitrary Droplet picture Young diagram

19 LLM geometry in 11-dim. SUGRA For arbitrary Droplet picture Young diagram Discrete torsion for arbitrary Discrete torsion for

20 LLM geometry in 11-dim. SUGRA For arbitrary Droplet picture Young diagram Discrete torsion for arbitrary Discrete torsion for

21 vev of CPO with (FT side) CPO with conformal dim. in ABJM theory,

22 vev of CPO with (FT side) CPO with conformal dim. in ABJM theory, vev of CPO with for arbitrary, Discrete Higgs vacua

23 Kaluza-Klein reduction Half BPS LLM geometry in 11-dim. SUGRA KK reduction [Kim et al 85] [Lee et al 98] 4-dim. Gravity theory

24 Kaluza-Klein reduction Half BPS LLM geometry in 11-dim. SUGRA KK reduction 4-dim. Gravity theory Linearlized scalar fields in 4-dim. Gravity theory [Kim et al 85] [Lee et al 98]

25 Kaluza-Klein reduction Half BPS LLM geometry in 11-dim. SUGRA KK reduction 4-dim. Gravity theory Linearlized scalar fields in 4-dim. Gravity theory [Kim et al 85] [Lee et al 98] ( : radius of )

26 Kaluza-Klein reduction Half BPS LLM geometry in 11-dim. SUGRA KK reduction 4-dim. Gravity theory Linearlized scalar fields in 4-dim. Gravity theory [Kim et al 85] [Lee et al 98] ( : radius of ) : :

27 Kaluza-Klein reduction Half BPS LLM geometry in 11-dim. SUGRA KK reduction 4-dim. Gravity theory Linearlized scalar fields in 4-dim. Gravity theory [Kim et al 85] [Lee et al 98] ( : radius of ) : :

28 Kaluza-Klein reduction Half BPS LLM geometry in 11-dim. SUGRA KK reduction 4-dim. Gravity theory Linearlized scalar fields in 4-dim. Gravity theory [Kim et al 85] [Lee et al 98] ( : radius of ) : dual scalar field :

29 Exact holography in finite N Gauge/Gravity mapping (GKP-W relation)

30 Exact holography in finite N Gauge/Gravity mapping (GKP-W relation)

31 Exact holography in finite N Gauge/Gravity mapping (GKP-W relation)

32 Exact holography in finite N Gauge/Gravity mapping (GKP-W relation) Normalization factor :

33 Exact holography in finite N Gauge/Gravity mapping (GKP-W relation) Normalization factor : Exact relation in finite

34 Summary mabjm theory 3-dim. Gauge theory Gauge/Gravity duality Half BPS LLM geometry in 11-dim. SUGRA KK reduction 4-dim. Gravity theory Finite

35 Thank you!