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

Recent Developments in The Black Hole Microstate Geometry Program Masaki Shigemori Strings and Fields YITP, Kyoto U August 2017 Based on 1607.03908, 170x.xxxxx with I. Bena, S. Giusto, E. Martinec, R. Russo, D. Turton, N. P. Warner

Microstate geometry program Smooth, horizonless solution of classical Microstate = supergravity with the same asymptotic geometry structure as a given black hole smooth, horizonless horizon BH solution Microstate geometry  What are the most general microstate geometries?  Can they reproduce area entropy?  What are CFT duals? 2

Why microstate geometries?  BH information problem Requires non-trivial microstate [Mathur 2009] structure over the horizon scale [AMPS 2012]  Sugra does have mechanism to support horizon-scale structure [Gibbons, Warner 2013]  For 1/4-BPS 2-chg sys, all microstates are realized as microstate geometries [Lunin-Mathur 2001] [Lunin-Maldacena-Maoz 2002] [Rychkov 2005] [Krishnan-Raju 2015]  Real challenge: 1/8-BPS 3-chg sys with finite horizon 3

Where we are 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 7

Setup: D1-D5 system Type II superstring in ℝ 1,4 × 𝑇 1 × 𝑈 4 ℝ 𝟓 𝑻 𝟐 𝑼 𝟓 1 D1  𝑂 ⋅ ∼ 𝑂 5 D5   ⋅ decoupling CFT AdS limit String theory / sugra D1-D5 CFT in AdS 3 × 𝑇 3 × 𝑈 4 5

Boundary CFT  D1-D5 CFT  2D 𝒪 = (4,4) SCFT, 𝑑 = 6𝑂 , 𝑂 ≡ 𝑂 1 𝑂 5  Target space: orbifold 𝑈 4 𝑂 /𝑇 𝑂  Symmetry  𝑇𝑀 2, ℝ 𝑀 × 𝑇𝑉 2 𝑀 × 𝑇𝑀 2, ℝ 𝑆 × 𝑇𝑉 2 𝑆 Virasoro R-sym Virasoro 𝑗=1,2,3 𝑀 𝑜 𝐾 𝑜 𝑀 0 = 0 (unexcited for susy) 6

“Phase diagram” 𝑀 0 = 𝑂 𝑄 ↔ momentum charge in bulk 3 = 𝐾 ↔ angular momentum in bulk 𝐾 0 𝑀 0 = 𝑂 𝑄 3 𝐾 = 𝐾 0 𝑃 7

“Phase diagram” 𝑀 0 = 𝑂 𝑄 ↔ momentum charge in bulk 3 = 𝐾 ↔ angular momentum in bulk 𝐾 0 𝑀 0 = 𝑂 𝑄 3 𝐾 = 𝐾 0 𝑃 Empty 𝐵𝑒𝑇 3 × 𝑇 3 8

“Phase diagram” 𝑀 0 = 𝑂 𝑄 ↔ momentum charge in bulk 3 = 𝐾 ↔ angular momentum in bulk 𝐾 0 𝑀 0 = 𝑂 𝑄 3 𝐾 = 𝐾 0 𝑃 2-chg states Empty 𝐵𝑒𝑇 3 × 𝑇 3 9

“Phase diagram” 𝑀 0 = 𝑂 𝑄 ↔ momentum charge in bulk 3 = 𝐾 ↔ angular momentum in bulk 𝐾 0 3-chg BH 𝑀 0 = 𝑂 𝑄 𝑇 BH = 2𝜌 𝑂𝑂 𝑄 3 𝐾 = 𝐾 0 𝑃 2-chg states Empty 𝐵𝑒𝑇 3 × 𝑇 3 10

States of CFT  T wist sectors represented by “component strings” ……… 1 1 1 2 2 3 𝑙 𝑂 11

States of CFT  T wist sectors represented by “component strings” + + 0 + − 0 + ……… 1 1 1 2 2 3 𝑙 𝑂 They actually carry 𝑇𝑉 2 𝑀 R-charge (spin) 2 0 1 + 2 − 2 0 3 … + 1 12

Empty 𝐵𝑒𝑇 3 × 𝑇 3 + 1 𝑂 ……… + + + + + + 1 1 1 1 1 1 𝑂 𝑄 𝑂 𝐾 = 2 𝑂 𝑄 = 0 𝐾 𝑃 empty 𝐵𝑒𝑇 3 × 𝑇 3 13

2-charge excitation ……… 0 + + + + + + 𝑙 1 1 1 1 1 1 𝑂 𝑄 + 1 𝑂−𝑙 0 𝑙 ⊗ 𝑂−𝑙 𝐾 𝐾 = 2 𝑂 𝑄 = 0 2-chg excitation 14

3-charge excitation 𝑛, 𝑜 ……… 0 + + + + + + 𝑙 1 1 1 1 1 1 𝑜 𝐾 −1 𝑛 0 𝑙 ⊗ 3 + 𝑂−𝑙 𝑀 −1 − 𝐾 −1 + 1 𝑂 𝑄 𝑂−𝑙 𝐾 = 2 + 𝑛 𝑂 𝑄 = 𝑜 + 𝑛 𝐾 3-chg excitation 15

“Supergraviton gas” 𝑛 1 ,𝑜 1 𝑛 1 ,𝑜 1 𝑛 2 ,𝑜 2 𝑛 2 ,𝑜 2 …… …… ……… … 0 0 0 0 + + 𝑙 1 𝑙 1 𝑙 2 𝑙 2 1 1 𝑂 𝑂 1 2 𝑂 𝑗 ⊗ 𝑜 𝑗 𝐾 −1 𝑛 𝑗 0 𝑙 𝑗 3 + + 1 𝑂 0 𝑀 −1 − 𝐾 −1 𝑗  Multi-particle state of supergravitons  Dual geometry can in principle be constructed using superstratum technology [Bena, Giusto, Russo, MS, Warner 2015] 16

[BGMRSTW A family of 3-chg states 2016,17] 𝑛 = 0, 𝑜 𝑛 = 0, 𝑜 𝑛 = 0, 𝑜 …… …… 0 0 0 + + 1 1 𝑙 𝑙 𝑙 𝑂 𝑂 1 0 𝑂 1 ⊗ 𝑜 0 𝑙 3 𝑂 0 𝑀 −1 − 𝐾 −1 + 1 𝑂 0 𝑂 𝑄 𝐾 = 2 , 𝑂 𝑄 = 𝑜𝑂 1  Can go to 3-chg BH regime  Can make 𝐾 as small as we 𝐾 want (Strominger-Vafa BH) 17

Bulk dual: new superstratum [BGMRSTW 2016,17] flat space  3-charge microstate 𝐵𝑒𝑇 3  𝐵𝑒𝑇 2 throat can be made arbitrarily deep 𝐵𝑒𝑇 2 × 𝑇 1 by making smaller the throat number of strings + momentum  𝐾 → 0 in the deep excitations smooth cap throat limit 18

Explicit expression 0 1 2 19

Significance  3-charge microstate geometry with smooth cap 𝑂 𝑄  Approximates BH with arbitrary precision (deep throat, scaling) 𝐾  𝐾 can be made arbitrarily small (solves 10-year-old problem in MGP)  AdS 2 region with excitation in it AdS 3  CFT dual identified 2 dictionary with AdS 2 in it  AdS 3 /CFT AdS 2 cap 20

Conclusions Microstate geometry program:  Making progress toward more 3-charge states  First scaling microstate geom in BH regime with 𝐾 → 0  AdS 3 /CFT 2 dictionary with AdS 2 inside Open issues  Not yet enough to reproduce 𝑇 BH   Need higher & fractional modes: 𝑀 −2 , 𝑀 −3 ; 𝑀 −1/𝑙 , …  Multi-center geometries?  Non-geometric states? (cf. Minkyu’s talk right after this) 21