Exotic Branes,
Double Bubbles,
& Superstrata
Masaki Shigemori
(KMI Nagoya)
Saclay, 15 Nov 2011
with Iosif Bena, Jan de Boer, Stefano Giusto & Nick Warner
1004.2521, 1107.2650, 1110.2781
Claim:
Generic microstates
of black holes involve
exotic branes and
thus are non-geometric.
Exotic branes
3
Exotic branes

“Forgotten” branes in string theory
[9707217 Elitzur+Giveon+Kutasov+Rabinovici]
[9712047 Blau+O’Loughlin]
[9809039 Obers+Pioline]
3
Exotic branes
3

“Forgotten” branes in string theory

Co-dimension 2
codim-2
hypersurface
Exotic branes

“Forgotten” branes in string theory

Co-dimension 2

Charge = U-duality monodromy
Jump by a U-duality
as one goes around it
Generalization of F-theory 7-branes
3
Exotic branes

“Forgotten” branes in string theory

Co-dimension 2

Charge = U-duality monodromy

Non-geometric
Even metric can jump!
“U-fold”
3
Supertube effect — “bubbling”
4
Supertube effect — “bubbling”

Spontaneous polarization phenomenon
[Mateos+Townsend]
puffs up
F1(1)
𝑥
1
D0
D2(1ψ)
𝑥1
𝜓
New dipole
charge created
4
Supertube effect — “bubbling”

Spontaneous polarization phenomenon

Exotic puff-ups
F1 1 + D0 → D2(1𝜓)
U-dual
D4 6789 + D4 4589 → 522 (4567𝜓, 89)
Ordinary branes can
generate exotic ones!
4
standard
brane
exotic
brane
Supertube effect — “bubbling”
4

Spontaneous polarization phenomenon

Exotic puff-ups

Exotic branes: ubiquitous

Important for generic non-perturbative
physics of string theory!

Notable example: black hole
“Single bubbling”

2-charge system (“small” BH)
D1(5)
D5(56789)
KKM(6789𝜓;5)
puff up
𝜓
1-dim curve ∈ ℝ4
geometric microstates
(Lunin-Mathur)
𝑆micro = 𝑆geom
5
“Double bubbling”

3-charge system: real BH
M2(56)
M2(78)
M2(9A)
6
M5(789A𝜓)
M5(569A𝜓)
M5(5678𝜓)
53(789A𝜙,56𝜓)
53(569A𝜙,78𝜓)
53(5678𝜙,9A𝜓)
1-dim curve
“supertube”
2-dim surface ∈ ℝ4
“superstratum”
cf. black ring
non-geometric
microstates
?
𝑆micro = 𝑆nongeom
Endless puffing-up??
⋮
?
⋮
Presumably, a black hole is made of an
extremely complicated structure
(fuzzball) of exotic branes.
7
...Really?
Susy in supertube
[Bena+de Boer+Warner+MS 1107.2650]
supertube
F1+D0
 Preserves
1
1
1
× = susy
2
2
4
F1+D0
+D2+P
1
2
 Locally BPS
1
2
 Which is preserved
depends on local orientation
 Common susy preserved =
1
original susy
4
This is why supertube can be along an arbitrary curve.
8
Susy in superstratum
superstratum
3-charge sys.
 Preserves
1
1
1
1
× × = susy
2
2
2
8
1
2
 Locally BPS
1
 Which is preserved
2
depends on local orientation
 Common susy preserved =
1
original susy
8
If true, superstratum can be along an
arbitrary surface in principle!
9
Example: F1-P  D2
F1
P
Susy preserved by
original config:
Π𝐹1(𝑧) 𝒬 = Π𝑃(𝑧) 𝒬 = 0,
𝑄
𝒬=
𝑄
1
Π𝐹1(𝑧) = 1 + Γ 0𝑧 𝜎3
2
1
Π𝑃(𝑧) = 1 + Γ 0𝑧
2
10
Tilted and boosted F1-P
Projector after puffing up:
1
Π = [1 − 𝑠 𝑐Γ 0𝜓 − 𝑠Γ 01 + 𝑐 𝑐Γ 01 + 𝑠Γ 0𝜓 𝜎3 ]
2
= 𝑐 𝑐 + 𝑠Γ 𝑧𝜓 Π𝐹1
𝑧
𝑐 = cos 𝛼,
+ 𝑠 𝑠 − 𝑐Γ 𝑧𝜓 𝜎3 Π𝑃
𝑠 = sin 𝛼.
Same ¼ susy preserved
𝑧
,
General formula for 12 puff-up
Projectors before puffing up:
1
Π1 = 1 + 𝑃1 ,
2
Projector after puffing up:
1
Π2 = 1 + 𝑃2
2
𝜓
1
Π = [1 + 𝑐 2 𝑃1 + 𝑠 2 𝑃2 − 𝑠𝑐Γ 0𝜓 + 𝑠𝑐Γ 0𝜓 𝑃1 𝑃2 ]
2
= 𝑐 𝑐 − 𝑠Γ 0𝜓 Π1 + 𝑠 𝑠 − 𝑐Γ 0𝜓 Π2 + 2𝑠𝑐Γ 0𝜓 Π1 Π2
11
D1-D5-P (1)
D1
D5
P
Original config.
Infinite straight
supertube
= tilted and
boosted D1-D5
puffs up just like
D1-D5  KKM
(LM geom.)
12
Infinite straight
superstratum
Special case;
superstratum is
purely geometric
D1-D5-P (2)
D1
D5
P
1
1 + Γ 0𝑧 𝜎1
2
1
Π2 = 1 + Γ 01234𝑧 𝜎1
2
1
Π3 = 1 + Γ 0𝑧
2
Π1 =
Π𝑖 =
1
1 + 𝑃𝑖
2
𝑃1 = 𝑐1 𝑐2 Γ 0𝑧 𝜎1 + 𝑠1 𝑠2 Γ 01234𝑧 𝜎1 + 𝑐1 𝑠2 𝛤 0𝜃 − 𝑠1 𝑐2 𝛤 01234𝜃
𝑃2 = 𝑠1 𝑠2 Γ 0𝑧 𝜎1 + 𝑐1 𝑐2 Γ 01234𝑧 𝜎1 − 𝑠1 𝑐2 𝛤 0𝜃 + 𝑐1 𝑠2 𝛤 01234𝜃
Γ 𝑧 = 𝑐3 Γ 𝑧 + 𝑠3 Γ 𝜃 ,
Γ 𝜃 = 𝑐3 Γ 𝜃 − 𝑠3 Γ 𝑧
1
Π = (1 + 𝑠42 𝑃1 + 𝑐42 𝑃2
2
−𝑠4 𝑐4 Γ 0𝜓 + 𝑠4 𝑐4 Γ 0𝜓 𝑃1 𝑃2 )
Same 1/8 susy preserved
13
Toward backreacted strata

Dynamics of superstrata


Arbitrary surface possible?
6D sugra (D1-D5-P)

Linear problem if solved in the right order


[Gutowski+Martelli+Reall] [Cariglia+Mac Conamhna]
[Bena+Giusto+Warner+MS 1110.2781]
𝑥 5 -dep 4D almost HK base, functions & forms on it
Given superstrum data,
should be possible to
find solutions
𝑥 = 𝐹𝑖 𝑡 − 𝑥 5
E.g. D1-D5-Pd1-d5 supertube
14
More general superstrata

Non-geometric (exotic) superstrata

More general superstrata

Locally geometric

Generalize susy sol’n ansatz

Generalized geometry, DFT
[Berman, Hohm, Hull, Perry, Zwiebach, …]
15
Conjecture:
Generic microstates of
black holes involve
non-geometric
superstrata.
Thanks!