david mateos- supersymmetric black rings and supertubes
TRANSCRIPT
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 1/16
SupersymmetricSupersymmetric BlackBlack RingsRings
S 1
S 2
DavidDavid MateosMateos
andand
SupertubesSupertubes
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 2/16
• Emparan & DM , to appear
• Microscopic Entropy of the Black Ring [hep-th/0411187]M. Cyrier, M. Guica, DM & A. Strominger
•A Supersymmetric Black Ring [hep-th/0407065]H. Elvang, R. Emparan, DM & H. Reall
•Supersymmetric Black Rings and 3-charge Supertubes [hep-th/0408120]H. Elvang, R. Emparan, DM & H. Reall
•Supertubes [hep-th/0103030]DM & P. Townsend
•Supergravity Supertubes [hep-th/0106012]R. Emparan, DM & P. Townsend
•Tachyons, Supertubes and Brane/anti-Brane Systems [hep-th/0112054]DM, S. Ng & P. Townsend
•Supercurves [hep-th/0204062]DM, S. Ng & P. Townsend
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 3/16
Black Ring = Asymptotically Flat,
Stationary Black Hole Solution in 5Dwith Horizon Topology S 1 ×××× S 2
S 1
S 2
×××× flat directions = Black Supertube
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 4/16
Why are Black Rings interesting?
D=4M, J, Q
D=5: Black RingM, Q, J, …
Emparan & Reall
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 5/16
Why are Supersymmetric BRs interesting?
• Establish non-uniqueness in susy sector
• Establish stability of Black Rings
• Implications for microscopic entropy calculation
→→→→ Not only counting BPS states with same charges is not enough,
it is also not right!
• Provide ideal arena to study these issues because:
susy + know microscopic constituents + stability mechanism
• Expose how little we know about gravitational physics in D>4
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 6/16
Plan
2-chargeBasic Mechanism: Supertubes
3-charge
Supergravity DescriptionWV DescriptionMicroscopic EntropyAdS/CFT DescriptionConclusions
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 7/16
2-charge Supertubes: Worldvolume Description DM & Townsend
Supersymmetric Brane Expansion in Flat Space by Angular Momentum
F1
D0
E
BP
Tubular D2/ F1 /D0Bound State
1/4-SUSY preserved
QF1 and QD0 dissolved as fluxesJ generated as integrated PoyntingE = Q F1 + Q D0
Arbitrary Cross-section C CC C in EEEE 8:(and charge densities)
TS-Dualizing = `Helical’ String withLeft-moving wave on it
No net D2-brane chargebut dipole q D2 ∼∼∼∼ n D2
J
¼-SUSY
C CC C
P
J
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 8/16
2-charge Supertubes: Supergravity Description
No net D2 charge, but D2 dipole (and higher) moments:
ψ ψψ ψ
Easily understood ~ D2/anti-D2 pair:
x
Emparan, DM & Townsend
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 9/16
3-charge Supertubes and Supersymmetric Black Rings:Supergravity Description
Elvang, Emparan, DM & ReallBena & WarnerGauntlett & Gutowski
T34 Lift
First, lift 2-charge supertube to M-theory:
Ring solution with regular horizon →→→→ 3 charges
Best microscopic description →→→→ M-theory
T 6 E 4 = E 2 (r, ψ) × E 2 (ρ , φ )
ψ ψψ ψ
φ
r
R
ρρρρ
× time = 5D black ring metric
With 3 charges, each pair expands:
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 10/16
ψ ψψ ψ
φ
r
R
ρρρρNew feature: J φφφφ ≠≠≠≠ 0
7 parameters: R, Q i , q i
5 conserved charges: Q i , J ψ ψψ ψ and J φφφφ
Infinite violation of uniqueness by 2 continuous parameters
Choosing Q i, q i and J ψ ψψ ψ as independent parameters:
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 11/16
Black String Limit
Send R →→→→ ∞∞∞∞ keeping Q i / R and q i fixed
Important: J ψ ψψ ψ →→→→ P ψ ψψ ψ ≠≠≠≠ 0 but J φφφφ →→→→ 0 !
Black string solution of Bena
ψ
S 2
12
M23456 ψ
M5
E B
E ×××× B = 0
12
M23456 ψ
M5
E B
E ×××× B ∝∝∝∝ Q1 q 1 + Q 2 q 2 + Q 3 q 3 – q 1 q 2 q 3
Suggests J φφφφ is Poynting-generated by SUGRA fields J φφφφ ∼∼∼∼ ∫ ∫∫ ∫ T0φφφφ ∼∼∼∼ ∫ ∫∫ ∫ E ×××× B
Components ofD=11 SUGRA F 4
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 12/16
Worldvolume 3-charge Supertubes
Elvang, Emparan, D.M. & Reall
First step: F1/D4/D0 bound state with D2/D6/ NS5 dipoles Bena & Kraus
Gibbons & PapadopoulosGauntlett, Lambert & West
Problematic in openstring description
Circumvented in M-theory:
Single M5-brane =
Holomorphic 2-surface in TTTT 6
7
Turning on H induces M2 charge and allows arbitrary C
C
In summary: Captures 3 dipoles, J φφφφ = 0
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 13/16
Microscopic Entropy Counting
Single M5-brane =
Holomorphic 2-surface in TTTT 6 S 1 RRRR 1,3
4D black hole
Maldacena, Strominger & Witten; Vafa
(0,4) CFT with c left = 6q 1q 2q 3 and left-moving momentum p
M-theory on TTTT 6 ×××× S 1 ×××× RRRR 1,3
p’ = p + M2-induced shift+ zero-point shift
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 14/16
Microscopic Entropy Counting Cyrier, Guica, DM & Strominger
Single M5-brane =
Holomorphic 2-surface inTTTT 6
S1
inRRRR 1,4
5D black ring
(0,4) CFT with c left = 6q 1q 2q 3 and left-moving momentum p = J ψ ψψ ψ
Counts states with J φφφφ=0 !!!
M-theory on TTTT 6 ×××× RRRR 1,4
8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes
http://slidepdf.com/reader/full/david-mateos-supersymmetric-black-rings-and-supertubes 15/16
3-charge Supertubes D1/D5/P System Elvang, Emparan, DM & ReallBena & Kraus
Same CFT describes Black Hole and Black Ring
Decoupling limit: αααα ’ →→→→ 0 , r / αααα ’ fixed, etc.
RG
>