Moulting Black Holes
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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)
∑𝑖𝑛𝑖=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 entropy𝑆 (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 ′ 𝐼2Σ
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
BMPVP=N/5
P=N/5
BMPV
CFT enigmaticBMPV+tube
BR
BMPV
BMPV+tube
BMPVBMPV+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