A picture book Closed strings and SUGRA Closed string theory in background X Infinite tower of vibrational modes M 2 n ℓ s String interaction through 3vertex g s String length ID: 298981
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Slide1
String Theory
A picture bookSlide2
Closed strings and SUGRA
Closed string theory in background X
Infinite tower of vibrational modes M
2
~ n/
ℓ
s
String interaction through 3-vertex g
s
String length
At
low energies (E « ℓs ): massless closed str. modes behave like gravitons
10D SUGRA
String
coupling
2
-1Slide3
Closed strings and SUGRA
Closed string theory in background X
Infinite tower of vibrational modes M
2
~ n/
ℓ
s
String interaction through 3-vertex g
s
String length
At
low energies (E « ℓs ): massless closed str. modes behave like gravitons
10D SUGRA
String
coupling
2
-1Slide4
Solitonic
&
Dirichlet p-branes
D-branes are objects on
which open strings can
end
[Polchinski]
10-dim SUGRA has
solutions describing
massive & charged
objects localized on p+1 - dim. surfaces.
[black branes]
Branes in string theory ?Slide5
Open strings & gauge theory
At low energies (E«
ℓ
s
):
massless modes of the
open string behave like
gauge bosons + matter
on the world-volume ofD-branes.
p+1- dimensional gauge theory
a .. b N
Aab
-1Slide6
Gauge-String theory dualities
• Closed string in curved 10-dimensional space
•
Gauge theory loop
classical string theory !
Holography
←
Δ
y
→
Depending on Δyone side simpler
Δy << ℓs: gauge th ↔ closed string th
High redshift ↔ soft strings ↔ meson resonancesSlide7
Example: AdS
5
/ CFT4 duality
N=4 4D S Yang-Mills Strings in AdS
5
x S
5
U(N
c) gauge field A; 6 scalars Φ
Gauge theory on stack Strings in their near of Nc D3 - branes horizon geometry
par.:
λ
=g2YM N
c ; N
c R4 / ℓs4
=λ ; gs
=λ/Nc
Gauge inv. operators
Closed string states
Anomalous dimensions
Mass of string mode
…...
…...Slide8
pert.
Gauge
Theory
pert. String Theory
N
c
λ
l
s
/R
g
s
Lattice
Gauge Theory
[‘t Hooft]
[Polyakov, Maldacena]
Map of Physics
Quantum Gravity