Strings and Black Holes
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Transcript Strings and Black Holes
Strings and Black Holes
David Lowe
Brown University
AAPT/APS Joint Fall Meeting
Introduction
Perturbative string theory wellunderstood
Use this to learn about black holes?
Usual string states lead to black
holes with singular and/or
strongly coupled horizons
D-branes
Allow for smooth black holes
Find microstates responsible for
Bekenstein-hawking entropy!
David Lowe, Brown
University
10/21/00
Same circle of ideas
proposals for nonperturbative
formulations of string theory
• Matrix theory
• Maldacena conjecture
large N, SU(N) gauge theory in
various dimensions
Challenge now: learn about string
theory by studying gauge theory
David Lowe, Brown
University
10/21/00
Black Holes
Mass M, radius r,
space probe mass m
1 2 GMm
mv
,
2
r
2GM
need v 2
.
r
2GM
So if r 2
c
Escape velocity exceeds speed of light!
David Lowe, Brown
University
10/21/00
Why Do We Care About
Black Holes?
Astrophysical importance:
supernova remnants
Galactic cores
Binary systems
Theoretical point of view:
testing ground for quantum
gravity
many paradoxes – lead to
important constraints on theory
David Lowe, Brown
University
10/21/00
Paradoxes
Quantum effects black holes
aren’t black
Hawking radiation
event horizon
Et
David Lowe, Brown
University
10/21/00
Metric:
2GM
dr 2
2
ds (1
) dt
2
GM
r
(1
)
r
r 2 (d 2 sin 2 d 2 )
2
Imagine virtual particle starts at
r 2GM
Proper time to hit event horizon
t GM
E
GM
Virtual partner gets redshifted, so
energy at infinity
E E
kT
GM GM
David Lowe, Brown
University
10/21/00
Black Hole Entropy
Finite temperature finite entropy
Compare to usual laws of
thermodynamics
1st law dM dA work
2nd law dA 0
Identify
A
S
4G
Famous Bekenstein-Hawking
entropy formula
David Lowe, Brown
University
10/21/00
Challenge
Challenge for last 25 years
Find the microstates
S k log(# microstates)
Still unsolved problem in general
One of great successes of string
theory
Can describe microstates for BPS
or near BPS black holes
New nonperturbative formulations
of string theory
May lead to complete
understanding
David Lowe, Brown
University
10/21/00
Black Holes in String
Theory
Strominger and Vafa: find a black
hole that you can describe using
perturbative string theory
G0
Make sure it becomes a nonsingular
black hole when it becomes
macroscopic
GM s
Use supersymmetry to prove entropy
doesn’t depend on G when written in
terms of charges
David Lowe, Brown
University
10/21/00
D-branes
Key ingredient: D-branes Polchinski
David Lowe, Brown
University
10/21/00
Counting black hole
microstates
Use D-5branes, D-1branes and
Kaluza-Klein momentum to make a
charged 5d black hole
David Lowe, Brown
University
10/21/00
n5 D - 5branes
n1 D -1branes
nKK Kaluza - Klein momentum
To count black hole microstatessolve a simple counting problem
Have n1n5 species of massless
particles in 1+1d
Want to count number of states
with total energy n KK
Answer agrees exactly with
Bekenstein-Hawking formula
S 2 n1n5 nKK
David Lowe, Brown
University
10/21/00
Nonperturbative String
Theory
Try to formulate nonperturbative
string theory/M-theory by taking N
coincident D-branes and then
adjusting the coupling G so gravity
decouples
Left with QFT on the brane
Argue there is a duality
Large N QFT secretly describes
full string theory that contains
gravity
David Lowe, Brown
University
10/21/00
Maldacena Conjecture
Conjecture: large N SU(N) gauge
theory with 16 SUSY’s is dual to
string theory in a background that is
anti-de Sitter space X sphere
Need to take ‘t Hooft limit
N , GN fixed, but large
Dimensional analysis
Get Bekenstein-Hawking entropy
right to within an overall factor
To do better requires strong coupling
gauge theory calculations
David Lowe, Brown
University
10/21/00
Large N Quantum
Mechanics
0+1 dimensional version of
Maldacena conjecture
SU(N) gauged quantum
mechanics at large N dual to 9+1
dimensional curved spacetime
Simple enough that the conjecture
can be directly tested by doing
quantum mechanics calculations
Kabat, Lifschytz and Lowe: mean
field approximation valid in large N
limit
David Lowe, Brown
University
10/21/00
Mean field solution
Comparison of mean field solution
to Bekenstein-Hawking result for
free energy
T itle:
Creator:
Mathematic a-PSRender
Preview:
T his EPS pic ture was not s aved
with a preview i nc luded i n i t.
Comment:
T his EPS pic ture wi ll pri nt to a
Pos tScri pt printer, but not to
other types of printers.
Works well in limited range of
Hawking temperature
David Lowe, Brown
University
10/21/00
Open Questions
Understanding of microscopic origin
of universal Bekenstein-Hawking
formula still open problem
Have a good chance to understand
this using string theory
Independent of details of vacuum
structure
Dynamical questions
Black hole information problem
David Lowe, Brown
University
10/21/00