moulting black holes kek, 22 june 2011 masaki shigemori (kmi, nagoya u) iosif bena, borun chowdhury,...
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Moulting Black Holes
KEK, 22 June 2011
Masaki Shigemori(KMI, Nagoya U)
Iosif Bena, Borun Chowdhury, Jan de Boer, Sheer El-Showk
and MS: 103.nnnn
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Introduction
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No hair theorem
Given charges
Black holes have no “hair”
Unique BH solution
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“Moulting” black holes
AdS BH can spit out excessive charges to “hair”and increase entropy
Einstein-Maxwell has BH with charged condensate [Gubser]
AdS5 BH with R-charge [Bhattacharyya+Minwalla+Papadodimas]
“Enigmatic” BHs in 4d N=2 sugra / MSW [Denef+Moore]
“moults” hair
“hair”
— but not under very good control
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AdS3/CFT2: ideal arena
D1-D5 system
Bulk: or
Boundary: D1-D5 CFT
Pivotal role in micro. understanding of BH in
string theory
Strominger-Vafa: the first microscopic explanation
of
BMPV black hole
Under good control
𝐽𝐿
𝐽𝐿≠0 , 𝐽𝑅=0
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What we do
Strategy: find max entropy config for fixed
Results
CFT side: found a novel phase
Gravity side: 2-center solution: “hairy BH” and
BR
But
Implications
Some states lift but some don’t?
A new index?
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Outline
Introduction
Boundary CFT side
Bulk gravity side
Discussion
Conclusion
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Boundary CFT sideof the story
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bulk
Type IIB sugra
with or K3
Strong coupling
D1-branes + D5-branes
boundary
2d SCFT
(D1-D5 CFT)
in the Ramond sector
Sigma model on
with
Weak (zero) coupling
The AdS3/CFT2 correspondence
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Some facts about D1-D5 CFT
Charges: ; R-charges Supersymmetric states:
: momentum; : angular momenta
𝑆=2𝜋 √𝑁𝑃 − 𝐽𝐿2 /4
“Standard lore” phase diagram
Cardy formula
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States of D1-D5 CFT Building blocks: “effective strings”
Has length Carries “base” spin Excitations on it can carry
momentum and angular momenta
States of the CFT is constructed by combining
eff. strings
𝑛
( 𝑗𝐿 , 𝑗𝑅 )base=(+1,−1)
∑𝑖
𝑛𝑖=𝑁
𝑛1 𝑛2 𝑛3 … charges add up
This has entropy
𝑝 , 𝑗𝐿❑
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Example: BMPV ensemble
𝑆CFT=2𝜋√𝑁𝑃 − 𝐽 𝐿2 /4=𝑆BMPV
𝑁
𝑃 , 𝐽 𝐿❑
A single string carries all charges Base spin ignorable
BMPV BH
𝐽𝐿
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The question What’s the max entropy states, for given
Better for to be carried by a long string Making the long string carry reduces entropy It may be better to make some of carried by ‘short’
strings
𝑁− 𝑙 𝑙1 1 1 1 1 1
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Maximizing entropy
𝑆 (𝑙 )=2𝜋 √(𝑁− 𝑙 ) 𝑃− ( 𝐽𝐿− 𝑙)2/4
maximize for
For , max is
,
Always larger than Comes in an multiplet with
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The new CFT phase diagram
P=N/5
Applies for both T4 & K3
old new
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Numerical check
Compare with T4 partition function Can’t use Cardy (which is valid only for )
Use DMVV formula and evaluate by computer
Confirmed!
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Comments
Degeneracy (entropy) index (elliptic genus)
For enigmatic phase, entropy K3 elliptic genus Elliptic genus always gives BMPV entropy:
even outside the Cardy regime [Castro-Murthy]
New phase not captured by elliptic genus
𝑍=Tr BPS [𝑞𝐿0 𝑦 𝐽 𝐿 ] 𝜒=Tr [ (−1 ) 𝐽 𝐿+ 𝐽𝑅𝑞𝐿0 𝑦 𝐽 𝐿 ] Absolute # of
states Not protected
Not absolute # of states
Protected
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Summary — CFT side
Found an “new phase” in non-Cardy regime
Exists even outside the “BMPV parabola”
Dominates over BMPV when coexists
Comes in an multiplet with
Not captured by elliptic genus
Gets lifted at strong coupling?
Zero coupling artifact?
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Bulk sugra sideof the story
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The goal
We found CFT phase with more entropy than BMPV
What’s the bulk dual configuration?
Find max entropy configuration given
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Supersymmetric sugra solutions Assume two isometries reduces to 4d N=2
sugra Most general timelike susy solutions in 4D
known[Bates-Denef] [Gauntlett-Gutowski] [Bena-Warner]
Solution determined given harmonic functions on
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AnsatzCFT states came in an multiplet with
4d angular momentum
2-center configs.𝑉=
1+𝑇𝑟−𝑇Σ
𝐾 𝐼=− 𝑞𝐼
2𝑟−𝑞 ′ 𝐼
2Σ
𝐿𝐼=−𝑄𝐼
4𝑟−𝑄𝐼′
4 Σ
𝑀=𝑚0+𝑚𝑟
+𝑚 ′Σ
𝑟=|�⃗�|,Σ=¿ �⃗�− �⃗�∨¿
Play with parameters and maximize BH entropy
Parameters constrained to give desired total charges
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Result: max-entropy 2-center configs.
P=N/5
¿𝑆CFT
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Bulk phase diagram
2-center configs very barely dominates over BMPV
P=N/5
P=N/5
BM
PV
CFT enigmaticBMPV+tube
BR
BMPV
BMPV+tube
BMPVBM
PV+tube
BR
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Summary — gravity side
Found 2-center configs for
Exists even outside the “BMPV parabola”
Exists in the same region as CFT enigmatic phase does
Dominates over BMPV partly in coexisting region
Entropy strictly smaller than CFT enigmatic phase
gravity CFT
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Discussion
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Discussion Found configs whose entropy is larger than
BMPV BMPV is unstable, in spite of susy
BH configs exist even outside the BMPV parabola!
Elliptic genus doesn’t capture this BH Cf. Matching of CFT and sugra elliptic genera [de Boer]
It was believed that there are no BHs in the gray region,
but there are!
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Partial lifting (1)
Standard lore
𝜆∞0
CFT gravity
contribute to
index
don’t contribute to
index
protected
pairwise lift
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Partial lifting (2)
The reality
𝜆∞0
CFT gravity
contribute to
index
don’t contribute to
index
pairwise lift
protected
don’t lift! “enigmatic” states
Protected for dynamical reasons, not susy?
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Conclusion
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Conclusion
Studied phases of D1-D5 system for given
Found new phases both in CFT & gravity— Controlled example of “hairy” BH
New phases dominate over BMPV
Some states survive strong coupling,although not protected by susy!
— Dynamical protection? A new index??
Further investigation needed
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Thanks!
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A new index?
We are not turning on generic moduli— There may be an index protected only on special loci
𝜆∞0
othermoduli
special locusgeneric locus
moduli space of T4/K3
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Unsolved issues
Black rings (susy)
Microscopics (CFT state) not understood [Bena+Kraus]
Dipole charge?
Multi-center solutions
Zoo of solutions, no organizing principle
Microscopics unclear
Fuzzballs / gravity microstate
𝐽𝐿 , 𝐽𝑅≠0