Black Hole Attractors and Superconformal Quantum Mechanics Davide - - PowerPoint PPT Presentation
Black Hole Attractors and Superconformal Quantum Mechanics Davide Gaiotto dgaiotto@fas.harvard.edu Harvard University joint work with Aaron Simons, Andrew Strominger, Xi Yin hep-th/ 0412322 hep-th/ 0412179 Black Hole Attractors and
Davide Gaiotto
dgaiotto@fas.harvard.edu
Harvard University joint work with Aaron Simons, Andrew Strominger, Xi Yin
hep-th/0412322 hep-th/0412179
Black Hole Attractors and Superconformal Quantum Mechanics – p.
Black Hole Attractors and Superconformal Quantum Mechanics – p.
Black Hole Attractors and Superconformal Quantum Mechanics – p.
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Black Hole Attractors and Superconformal Quantum Mechanics – p.
µ,λi,zi
Black Hole Attractors and Superconformal Quantum Mechanics – p.
µ,λi,zi
Black Hole Attractors and Superconformal Quantum Mechanics – p.
µ,λi,zi
GA
FA
µ,λi,zi
GA
FA
X0
Black Hole Attractors and Superconformal Quantum Mechanics – p.
µ,λi,zi
GA
FA
X0
X0
Black Hole Attractors and Superconformal Quantum Mechanics – p.
Black Hole Attractors and Superconformal Quantum Mechanics – p.
fixed(pA, qA)
Black Hole Attractors and Superconformal Quantum Mechanics – p.
fixed extremizes |Z| = |pAFA − qAXA|
fixed = pA
Black Hole Attractors and Superconformal Quantum Mechanics – p.
fixed extremizes |Z| = |pAFA − qAXA|
fixed = pA
fixed
Black Hole Attractors and Superconformal Quantum Mechanics – p.
qA
Black Hole Attractors and Superconformal Quantum Mechanics – p.
qA
12Dabqaqb
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qA
12Dabqaqb
1 (1−xn)6D
Black Hole Attractors and Superconformal Quantum Mechanics – p.
Black Hole Attractors and Superconformal Quantum Mechanics – p.
Black Hole Attractors and Superconformal Quantum Mechanics – p.
Black Hole Attractors and Superconformal Quantum Mechanics – p.
Black Hole Attractors and Superconformal Quantum Mechanics – p.
Black Hole Attractors and Superconformal Quantum Mechanics – p.
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Black Hole Attractors and Superconformal Quantum Mechanics – p.
σ2 (1− ˙ σ2)−R2( ˙ θ2+sin2 θ ˙ φ2)−2gµν ˙ yµ ˙ yν
Black Hole Attractors and Superconformal Quantum Mechanics – p.
σ2 (1− ˙ σ2)−R2( ˙ θ2+sin2 θ ˙ φ2)−2gµν ˙ yµ ˙ yν
σ + qmR
Black Hole Attractors and Superconformal Quantum Mechanics – p.
σ2 (1− ˙ σ2)−R2( ˙ θ2+sin2 θ ˙ φ2)−2gµν ˙ yµ ˙ yν
σ + qmR
vA
e + q2 m = m2
Black Hole Attractors and Superconformal Quantum Mechanics – p.
8mR ˆ
ξ + 1 2mRˆ ξ2 ˆ
S2 + 1 2mRˆ ξ2 ˆ
Black Hole Attractors and Superconformal Quantum Mechanics – p. 10
8mR ˆ
ξ + 1 2mRˆ ξ2 ˆ
S2 + 1 2mRˆ ξ2 ˆ
2{ˆ
Black Hole Attractors and Superconformal Quantum Mechanics – p. 10
8mR ˆ
ξ + 1 2mRˆ ξ2 ˆ
S2 + 1 2mRˆ ξ2 ˆ
2{ˆ
i
i + ˆ
i
αβ = ˆ
i σi αβ
Black Hole Attractors and Superconformal Quantum Mechanics – p. 10
αΓau + ¯
a αΓ¯ a¯
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αΓau + ¯
a αΓ¯ a¯
α =
¯ λα
Black Hole Attractors and Superconformal Quantum Mechanics – p. 11
αΓau + ¯
a αΓ¯ a¯
α =
¯ λα
α, λB β } = 2ǫABǫαβ
Black Hole Attractors and Superconformal Quantum Mechanics – p. 11
α, ¯
a α partners of ya, ¯
a
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α, ¯
a α partners of ya, ¯
a
α =
α∂a
¯ η¯
a α ¯
∂¯
a
¯ ∂† ∂† ¯ ∂
α, qB β } = ˆ
Black Hole Attractors and Superconformal Quantum Mechanics – p. 12
α, ¯
a α partners of ya, ¯
a
α =
α∂a
¯ η¯
a α ¯
∂¯
a
¯ ∂† ∂† ¯ ∂
α, qB β } = ˆ
Black Hole Attractors and Superconformal Quantum Mechanics – p. 12
α , ˆ
β } = 2ǫABǫαβ ˆ
α = ˆ
α
α, λB β } = 2ǫABǫαβ
Black Hole Attractors and Superconformal Quantum Mechanics – p. 13
α , ˆ
β } = 2ǫABǫαβ ˆ
α = ˆ
α
α, λB β } = 2ǫABǫαβ
α , ˆ
β } = ǫAB(ǫαβ ˆ
αβ)
Black Hole Attractors and Superconformal Quantum Mechanics – p. 13
α = 1 ˆ ξ ˆ
α,CY +
2 ˆ
α − i ˆ ξ(ˆ
αβ + ˆ
αβ + 1 2Lλ αβ)λAβ
Black Hole Attractors and Superconformal Quantum Mechanics – p. 14
α = 1 ˆ ξ ˆ
α,CY +
2 ˆ
α − i ˆ ξ(ˆ
αβ + ˆ
αβ + 1 2Lλ αβ)λAβ
α, ˆ
β } = 2ǫABǫαβ ˆ
1 8mR ˆ
ξ + 1 2mRˆ ξ2 ˆ
tot + m Rˆ ξ2 ˆ
Black Hole Attractors and Superconformal Quantum Mechanics – p. 14
Black Hole Attractors and Superconformal Quantum Mechanics – p. 15
α,± 1
2 =
1 √ 2(QA α ∓ iSA α )
Black Hole Attractors and Superconformal Quantum Mechanics – p. 15
α,± 1
2 =
1 √ 2(QA α ∓ iSA α )
α, 1
2
Black Hole Attractors and Superconformal Quantum Mechanics – p. 15
α,± 1
2 =
1 √ 2(QA α ∓ iSA α )
α, 1
2
+,− 1
2
Black Hole Attractors and Superconformal Quantum Mechanics – p. 15
+
++
α
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+
++
α
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+
++
α
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b = pAαA = Ja¯ b
Black Hole Attractors and Superconformal Quantum Mechanics – p. 18
b = pAαA = Ja¯ b
α
α, qB β } = ˆ
αβ σAB 1
α, QB β }
Black Hole Attractors and Superconformal Quantum Mechanics – p. 18
α = (1 2 ˆ
α − i ˆ ξ(ˆ
αβ + 1 2Lλ αβ))λAβ+
BλB α + 1 ˆ ξ ˆ
α,CY
Black Hole Attractors and Superconformal Quantum Mechanics – p. 19
α = (1 2 ˆ
α − i ˆ ξ(ˆ
αβ + 1 2Lλ αβ))λAβ+
BλB α + 1 ˆ ξ ˆ
α,CY
α, ˆ
β } = 2ǫABǫαβ ˆ
Black Hole Attractors and Superconformal Quantum Mechanics – p. 19
α = (1 2 ˆ
α − i ˆ ξ(ˆ
αβ + 1 2Lλ αβ))λAβ+
BλB α + 1 ˆ ξ ˆ
α,CY
α, ˆ
β } = 2ǫABǫαβ ˆ
α , ˆ
β } = · · · + c(σ1)ABǫαβ
Black Hole Attractors and Superconformal Quantum Mechanics – p. 19
2 only
Black Hole Attractors and Superconformal Quantum Mechanics – p. 20
2 only
Black Hole Attractors and Superconformal Quantum Mechanics – p. 20
2 only
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q Ω(p, q)e−qAφA ≃ |Z|2 top
top is closed string topological partition function at
Black Hole Attractors and Superconformal Quantum Mechanics – p. 22
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Black Hole Attractors and Superconformal Quantum Mechanics – p. 23