June 25, 2015 ICTS-TIFR Bengaluru, India Strings 2015.
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Transcript of June 25, 2015 ICTS-TIFR Bengaluru, India Strings 2015.
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HABEMUS SUPERSTRATU
M
June 25, 2015
MASAKI SHIGEMORI
(YITP Kyoto)
ICTS-TIFR Bengaluru, IndiaStrings 2015
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MAIN MESSAGES
Black hole microstates involve complicated structure of branes called superstrata
Basic superstrata solutions explicitly constructed in sugra as smooth geometries
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Iosif Bena Jan de Boer
Nick Warner
Stefano Giusto
Rodolfo Russo
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MICROSTATE GEOMETRY PROGRAM:
How much of black hole entropy can be accounted for by smooth, horizonless solutions of classical
gravity?D1-D5-P BH:
no horizon,no singularity
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1915
Einstein: general relativity
1975
Hawking radiation
1996
Strominger-Vafa (field theory counting of 3-charge BH)
2001
Lunin-Mathur geometries (2-charge microstates) fuzzball conjecture, microstate geometry program
2006
Microstate geometries in 5D (3- and 4-charge microstates)
2010
Double bubbling & superstrata (into 6D)
2015
Explicit construction of superstrata
SOME HISTORY
This talk
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DOUBLE BUBBLING(OR MULTIPLE SUPERTUBE TRANSITION)
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7
SUPERTUBE TRANSITION
Spontaneous polarization phenomenon Produces new dipole charge Cross section = arbitrary curve
[Mateos+Townsend ’01]
new dipole charge𝑄2
polarize(“bubble”
)
𝜆arbitrary curve
𝑄1
(cf. Myers effect)
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8
SUPERTUBE: F1-P FRAMEF1 (9 )+P (9 )→F1(𝜆)
To carry momentum, F1 must wiggle in transverse
Projection onto transverse is an arbitrary curve
F1(9)
polarizeP
𝑥9
𝑥1𝑥8…
wiggly F1𝜆
compact
transver
seℝ 8 ℝ 8
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9
SUPERTUBE: D1-D5 FRAMED 1(5)+D 5 (56789 )→KKM (𝜆6789,5)
LM geometries (2-charge microstate geometries)
Arbitrary curve large entropy AdS/CFT dictionary well understood
D5D1polarize(“bubble
”) �⃗�=�⃗� ( 𝜆 )∈ℝ12344
KKM
𝜆arbitrary curve
[Lunin-Mathur ’01]
[Rychkov ’05][Lunin-Mathur ’01]
[Kanitscheider-Skenderis-Taylor ’06, 07]
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10
DOUBLE BUBBLING
BH microstates involve arbitrary surface = superstratum
Exotic and non-geometric in general () Arbitrary surface larger entropy ?
D5D1
P arbitrary curve:
supertube
𝜆arbitrary surface:
“superstratum”
𝜆𝜃
3-charge system: real BH
[de Boer-MS ’10, ’12][Bena-de Boer-MS-Warner ’11]
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ENDLESS BUBBLING?
⋮
A black hole is made of an extremely complicated structure (fuzzball) of
puffed-up branes.7
?
⋮
Courtesy of the National Human Genome Research Institute
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12
EXOTIC BRANES
exoticbrane
U-dualitymonodromy
“Forgotten” branes in string theory
Codimension 2 U-duality monodromy
(“U-fold”) Non-geometric
[de Boer-MS ’10, ’12]
[Elitzur-Giveon-Kutasov-Rabinovici ’97][Blau-O’Loughlin ’97] [Hull ’97][Obers-Pioline ’98]
generalization of F-theory 7-branes
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13
A GEOMETRIC CHANNELK KM ( 𝜆6789 ,𝜃 )
wigglyKKMwiggly
D1wiggly
D5D1
D5P
𝑥5
𝑥1 𝑥4…geometric
superstratum
=
Can use geometric intuition (smoothness) Dependence on is crucial 6 dimensions
[Bena-de Boer -MS-Warner ’11]
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SUMMARY: BH microstates involve double-
bubbled superstrata Geometric superstratum in 6D is
important for microstate geometry program
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EXPLICIT CONSTUCTION OF SUPERSTRATA
[Bena+Giusto+Russo+MS+Warner ’15]
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GOAL:Explicitly construct
“superstrata” = wiggly KKM in 6D
They must depend on functions of two variables:
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SUSY SOLUTIONS IN 6D
17
IIB sugra on Require same susy as preserved by D1-
D5-P[Gutowski+Martelli+Reall ’03] [Cariglia+Mac Conamhna ’04][Bena+Giusto+MS+Warner ’11] [Giusto+Martucci+Petrini+Russo ’13]
)
𝑒2Φ=𝛼𝑍1
𝑍 2
𝐹 1=𝒟( 𝑍4
𝑍 1)+(𝑑𝑣+𝛽 )∧𝜕𝑣( 𝑍 4
𝑍1)
𝛼≡𝑍1𝑍2
𝑍 1𝑍 2−𝑍42 𝒟≡𝑑4− 𝛽∧𝜕𝑣 ❑̇≡𝜕𝑣
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BPS EQUATIONS
18
1st layer
2nd layer
Give 4D base0th layer
□𝐶=𝐴𝐵
Linear if solved in the right order
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0TH LAYER
19
Give 4D base
□𝐶=𝐴𝐵
This is the base for: round LM
geometry(2-charge)
pure
round superstratumwith no wiggle
(yet) 𝑆3
Take flat
¿¿
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1ST LAYER
20
Give 4D base
□𝐶=𝐴𝐵
𝑆3
[Mathur+Saxena+Srivastava ’03]
Mode numbers: ( , )𝑘 𝑚 Take known linear solution
with P
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1ST LAYER (2)
21
Give 4D base
□𝐶=𝐴𝐵
Superpose modes to get function of 2 variables𝐴=∑
𝑘,𝑚𝑎𝑘 ,𝑚𝑌 𝑘 ,𝑚
¿+¿
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NL completi
on
2ND LAYER
22
Give 4D base
□𝐶=𝐴𝐵
Find as non-linear 𝐶solution Do it for pair of modes
Regularity fixes solution
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SUMMARY: Constructive proof of
existence of superstrata! Big step toward general 3-
charge microstate geometries
Most general microstate geometry with known CFT dual
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CFT PICTURE
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BOUNDARY CFT D1-D5 CFT
2D SCFT, , Target space: orbifold
Orbifold CFT Twist sectors represented by
component strings
𝑁………1 1 1 2 2 3 𝑘
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2-CHARGE STATES (1)
Round LM geom
1 1 1 ……… 11 1
NS vacuum
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27
2-CHARGE STATES (2)
General LM geom
Linear fluct around round LM
………1 1 2 3 5
𝑘 1 1 ……… 11 11
“single-trace” chiral primary
general chiral primary
[Lunin-Mathur ’01]
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28
KNOWN 3-CHARGE STATES P-carrying linear fluct around round LM
: momentum number State of a single
supergravitonwith quantum numbers
𝑘 ,𝑚 1 ……… 11 1
descendant of chiral primary
∼¿¿𝑘 ,𝑚
“known linear solution”
[Mathur+Saxena+Srivastava ’03]
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29
SUPERSTRATA General P-carrying fluct around round
LM
Various modes turned on with finite amp.
The most general microstate geometrywith known CFT dual
State of supergraviton gas(D1-D5 1/8-BPS version of LLM) descendant of non-chiral
primary
………
strings strings
𝑘1𝑚1 1𝑘2𝑚2… 𝑘1𝑚1 … … 1𝑘2𝑚2
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TOWARD MORE GENERAL STRATA
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WHAT’S MISSING Does this class of superstrata
reproduce ? Not yet These correspond to supergraviton gas = fluct around .Entropy parametrically smaller.
𝑆3
[de Boer ’98]
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32
MORE GENERAL SUPERSTRATA
Other backgrounds multiple ’s, orbifolds
CFT side: Need higher and fractional
modesof
multi-superstratu
m
𝑆3 𝑆3
𝑆3
𝐽−2+¿𝜎𝑘
++¿ ¿¿𝐽− 1𝑘
+¿ 𝐽− 2𝑘
+¿ 𝜎𝑘++ ¿¿¿ ¿¿¿ →
Next steps:
𝑆3/ℤ𝑘
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CONCLUSIONS
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CONCLUSIONS:Superstratum
Represents a new class of microstate geometries
Depends on functions of two variables Represents the most general
microstate geometry with known CFT dual
More general superstrata out there;Construct them. Can they reproduce ?
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STAY TUNED
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Thanks!