Recent Developments in The Black Hole Microstate Geometry Program - - PowerPoint PPT Presentation

Recent Developments in The Black Hole Microstate Geometry Program

Strings and Fields YITP, Kyoto U August 2017

Masaki Shigemori

Based on 1607.03908, 170x.xxxxx with

• I. Bena, S. Giusto, E. Martinec, R. Russo, D.

Turton, N. P. Warner

Microstate geometry program

2

Microstate geometry

horizon smooth, horizonless

BH solution Microstate geometry

 What are the most general microstate geometries?  Can they reproduce area entropy?  What are CFT duals?

Smooth, horizonless solution of classical supergravity with the same asymptotic structure as a given black hole

=

Why microstate geometries?

3

 BH information problem  Sugra does have mechanism to

support horizon-scale structure

[Gibbons, Warner 2013]

Requires non-trivial microstate structure over the horizon scale

[Mathur 2009] [AMPS 2012]  For 1/4-BPS 2-chg sys, all microstates are realized as

microstate geometries

 Real challenge: 1/8-BPS 3-chg sys with finite horizon

[Lunin-Mathur 2001] [Lunin-Maldacena-Maoz 2002] [Rychkov 2005] [Krishnan-Raju 2015]

1975 Hawking radiation 1996 Strominger-Vafa (3-chg BH counting) 2001 Lunin-Mathur geometries (2-chg microstate geom)  fuzzball conjecture, microstate geometry program 2006 Microstate geometries in 5D (some 3-chg geom) 2010 “Superstratum” conjecture (into 6D) 2015 First construction of superstrata (more 3-chg geom) 2016,7 More class of superstrata (still more 3-chg geom)

This talk

Where we are

7

Setup: D1-D5 system

5

Type II superstring in ℝ1,4 × 𝑇1 × 𝑈4

ℝ𝟓 𝑻𝟐 𝑼𝟓 𝑂

1 D1

⋅  ∼ 𝑂5 D5 ⋅  

AdS CFT

String theory / sugra in AdS3 × 𝑇3 × 𝑈4

D1-D5 CFT

decoupling limit

6

Boundary CFT

 D1-D5 CFT

 2D 𝒪 = (4,4) SCFT, 𝑑 = 6𝑂, 𝑂 ≡ 𝑂

1𝑂5

 Target space: orbifold 𝑈4 𝑂/𝑇𝑂

 Symmetry

 𝑇𝑀 2, ℝ 𝑀 × 𝑇𝑉 2 𝑀 × 𝑇𝑀 2, ℝ 𝑆 × 𝑇𝑉 2 𝑆

𝑀𝑜 𝐾𝑜

𝑗=1,2,3

Virasoro R-sym 𝑀0 = 0 Virasoro (unexcited for susy)

7

“Phase diagram”

𝑀0 = 𝑂𝑄 ↔ momentum charge in bulk 𝐾0

3 = 𝐾

↔ angular momentum in bulk

𝐾 = 𝐾0

3

𝑀0 = 𝑂𝑄 𝑃

8

“Phase diagram”

𝑀0 = 𝑂𝑄 ↔ momentum charge in bulk 𝐾0

3 = 𝐾

↔ angular momentum in bulk

𝐾 = 𝐾0

3

𝑀0 = 𝑂𝑄 𝑃 Empty 𝐵𝑒𝑇3 × 𝑇3

9

“Phase diagram”

𝑀0 = 𝑂𝑄 ↔ momentum charge in bulk 𝐾0

3 = 𝐾

↔ angular momentum in bulk

𝐾 = 𝐾0

3

𝑀0 = 𝑂𝑄 𝑃 Empty 𝐵𝑒𝑇3 × 𝑇3 2-chg states

10

“Phase diagram”

𝑀0 = 𝑂𝑄 ↔ momentum charge in bulk 𝐾0

3 = 𝐾

↔ angular momentum in bulk

𝐾 = 𝐾0

3

𝑀0 = 𝑂𝑄 𝑃 Empty 𝐵𝑒𝑇3 × 𝑇3

3-chg BH

𝑇BH = 2𝜌 𝑂𝑂𝑄 2-chg states

11

States of CFT

 T

wist sectors represented by “component strings”

………

1 1 1 2 2 3 𝑙 𝑂

12

States of CFT

 T

wist sectors represented by “component strings” They actually carry 𝑇𝑉 2 𝑀 R-charge (spin)

………

1 1 1 2 2 3 𝑙

+ + + − +

+ 1

2 0 1 + 2 − 2 0 3 …

𝑂

13

Empty 𝐵𝑒𝑇3 × 𝑇3

1

+

1

+

1

+ ………

1

+

1

+

1

+

𝐾 𝑂𝑄

empty 𝐵𝑒𝑇3 × 𝑇3

𝑃

+ 1 𝑂

𝐾 =

𝑂 2

𝑂𝑄 = 0

14

2-charge excitation

𝑙 1 1

………

1 1 1 1 𝐾 𝑂𝑄

+ + + + + +

0 𝑙 ⊗ + 1 𝑂−𝑙

𝐾 =

𝑂−𝑙 2

𝑂𝑄 = 0

2-chg excitation

15

3-charge excitation

𝑙 1 1

………

1 1 1 1

+ + + + + +

𝑀−1 − 𝐾−1

3 𝑜 𝐾−1 + 𝑛 0 𝑙 ⊗

+ 1

𝑂−𝑙

𝑂𝑄

𝐾 =

𝑂−𝑙 2 + 𝑛

𝑂𝑄 = 𝑜 + 𝑛

𝐾 𝑛, 𝑜

3-chg excitation

16

“Supergraviton gas”

𝑗

𝑀−1 − 𝐾−1

3 𝑜𝑗 𝐾−1 + 𝑛𝑗 0 𝑙𝑗 𝑂𝑗 ⊗

+ 1 𝑂0

……

1 1

+ + 𝑙1 𝑛1,𝑜1 𝑂

1

…

 Dual geometry can in principle be

constructed using superstratum technology

𝑙1 𝑛1,𝑜1

……

𝑙2 𝑛2,𝑜2 𝑂

2

𝑙2 𝑛2,𝑜2

……… [Bena, Giusto, Russo, MS, Warner 2015]

 Multi-particle state of supergravitons

17

A family of 3-chg states

𝑀−1 − 𝐾−1

3 𝑜 0 𝑙 𝑂1 ⊗

+ 1

𝑂0

……

1 1 + + 𝑙 𝑛 = 0, 𝑜 𝑂

1

……

 Can go to 3-chg BH regime  Can make 𝐾 as small as we

want (Strominger-Vafa BH)

𝑙 𝑛 = 0, 𝑜 𝑙 𝑛 = 0, 𝑜

𝐾 =

𝑂0 2 , 𝑂𝑄 = 𝑜𝑂 1 𝑂

𝐾 𝑂𝑄

[BGMRSTW 2016,17]

18

Bulk dual: new superstratum

 3-charge microstate  𝐵𝑒𝑇2 throat can be

made arbitrarily deep by making smaller the number of strings

 𝐾 → 0 in the deep

throat limit

[BGMRSTW 2016,17]

𝐵𝑒𝑇3 flat space smooth cap momentum excitations 𝐵𝑒𝑇2 × 𝑇1 throat

+

Explicit expression

19

1 2

20

Significance

 3-charge microstate geometry with smooth cap  Approximates BH with arbitrary precision

(deep throat, scaling)

 𝐾 can be made arbitrarily small

(solves 10-year-old problem in MGP)

 AdS2 region with excitation in it  CFT dual identified

 AdS3/CFT 2 dictionary with AdS2 in it

𝐾

𝑂𝑄

AdS2 AdS3 cap

21

Conclusions

 Making progress toward more 3-charge states  First scaling microstate geom in BH regime with 𝐾 → 0  AdS3/CFT2 dictionary with AdS2 inside

Microstate geometry program: Open issues

 Not yet enough to reproduce 𝑇BH   Need higher & fractional modes: 𝑀−2, 𝑀−3; 𝑀−1/𝑙, …  Multi-center geometries?  Non-geometric states? (cf. Minkyu’s talk right after this)