Exotic Branes,Double Bubbles,& Superstrata

Saclay, 15 Nov 2011

Masaki Shigemori(KMI Nagoya)

with Iosif Bena, Jan de Boer, Stefano Giusto & Nick Warner

1004.2521, 1107.2650, 1110.2781

Claim:Generic microstates

of black holes involveexotic branes and

thus are non-geometric.

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Exotic branes

Exotic branes

3

“Forgotten” branes in string

theory[9707217 Elitzur+Giveon+Kutasov+Rabinovici][9712047 Blau+O’Loughlin][9809039 Obers+Pioline]

Exotic branes

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“Forgotten” branes in string

theory

Co-dimension 2

codim-2 hypersurface

Exotic branes

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“Forgotten” branes in string

theory

Co-dimension 2

Charge = U-duality monodromyJump by a U-dualityas one goes around itGeneralization of F-theory 7-branes

Exotic branes

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“Forgotten” branes in string theory

Co-dimension 2

Charge = U-duality monodromy

Non-geometric Even metric can jump!

“U-fold”

Supertube effect — “bubbling”

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Supertube effect — “bubbling”

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Spontaneous polarization

phenomenonD0F1(1

)D2(1ψ)𝜓

puffs up

𝑥1 𝑥1 New dipole

charge created

[Mateos+Townsend]

Supertube effect — “bubbling”

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Spontaneous polarization

phenomenon

Exotic puff-ups

D 4 (6789 )+D 4 (4589 )→522(4567𝜓 ,89)

F1 (1 )+D 0→D 2(1𝜓)

U-dual

Ordinary branes cangenerate exotic ones! standard

braneexotic brane

Supertube effect — “bubbling”

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Spontaneous polarization

phenomenon

Exotic puff-ups

Exotic branes: ubiquitous Important for generic non-

perturbative physics of string theory!

Notable example: black hole

“Single bubbling”

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2-charge system (“small” BH)

puff up

D1(5)D5(56789)

KKM(6789;5)

1-dim curve geometric

microstates(Lunin-Mathur)𝑆micro=𝑆geom

𝜓

“Double bubbling”

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3-charge system: real BHM2(56)M2(78)M2(9A)

cf. black ring

M5(789A)M5(569A)M5(5678)

1-dim curve “supertube”

non-geometricmicrostates

53(789A,56)53(569A,78)53(5678,9A)

2-dim surface “superstratum”

𝑆micro=𝑆nongeom?

Endless puffing-up??

⋮

Presumably, a black hole is made of an extremely

complicated structure (fuzzball) of exotic branes.

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?

⋮

...Really?

Susy in supertube

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F1+D0

Preserves susy

Locally BPS Which is preserved

depends on local orientation

Common susy preserved = original susy

F1+D0+D2+P

supertube

This is why supertube can be along an arbitrary curve.

[Bena+de Boer+Warner+MS 1107.2650]

Susy in superstratum

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3-charge sys.

Preserves susy

Locally BPS Which is preserved

depends on local orientation

Common susy preserved = original susy

superstratum

If true, superstratum can be along an arbitrary surface in principle!

Example: F1-P D2

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F1

P

Susy preserved by original

config:

Tilted and boosted F1-P

Projector after puffing up:

Same ¼ susy preserved

General formula for 12 puff-up

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¿𝑐 (𝑐−𝑠 Γ 0𝜓 )Π 1+𝑠 (𝑠−𝑐 Γ0𝜓 )Π 2+2𝑠𝑐 Γ 0𝜓 Π 1Π 2

Projectors before puffing up:

Π 1=12 (1+𝑃1 ) , Π 2=

12 (1+𝑃2 )

Projector after puffing up: 𝜓

Π=12 [1+𝑐

2 𝑃1+𝑠2𝑃2−𝑠𝑐 Γ 0𝜓+𝑠𝑐 Γ 0𝜓 𝑃1 𝑃2]

D1-D5-P (1)

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D1 PD5

Original config. Infinite straight supertube

= tilted and boosted D1-D5

Infinite straight superstratum

puffs up just likeD1-D5 KKM(LM geom.)

Special case; superstratum is

purely geometric

D1-D5-P (2)

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D1 PD5

,

Same 1/8 susy preserved

Dynamics of superstrata Arbitrary surface possible?

6D sugra (D1-D5-P) Linear problem if solved in the right order

-dep 4D almost HK base, functions & forms on it

Given superstrum data,should be possible tofind solutions

Toward backreacted strata

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�⃗�=�⃗� 𝑖 (𝑡−𝑥5 )

E.g. D1-D5-Pd1-d5 supertube

[Gutowski+Martelli+Reall] [Cariglia+Mac Conamhna][Bena+Giusto+Warner+MS 1110.2781]

Non-geometric (exotic) superstrata More general superstrata Locally geometric Generalize susy sol’n ansatz Generalized geometry, DFT

More general superstrata

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[Berman, Hohm, Hull, Perry, Zwiebach, …]

Conjecture:Generic

microstates of black holes involve non-geometric

superstrata.

Thanks!