Strings and Black Holes David Lowe Brown University AAPT/APS Joint Fall Meeting

10/21/00David Lowe, Brown University  Perturbative string theory well- understood  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! Introduction

10/21/00David Lowe, Brown University  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

10/21/00David Lowe, Brown University Black Holes Mass M, radius r, space probe mass m Escape velocity exceeds speed of light!

10/21/00David Lowe, Brown University 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

10/21/00David Lowe, Brown University Paradoxes  Quantum effects  black holes aren’t black event horizon Hawking radiation

10/21/00David Lowe, Brown University  Metric: Imagine virtual particle starts at Proper time to hit event horizon  Virtual partner gets redshifted, so energy at infinity

10/21/00David Lowe, Brown University Black Hole Entropy  Finite temperature  finite entropy  Compare to usual laws of thermodynamics  1 st law  2 nd law  Identify Famous Bekenstein-Hawking entropy formula

10/21/00David Lowe, Brown University Challenge  Challenge for last 25 years  Find the 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

10/21/00David Lowe, Brown University Black Holes in String Theory  Strominger and Vafa: find a black hole that you can describe using perturbative string theory  Make sure it becomes a nonsingular black hole when it becomes macroscopic  Use supersymmetry to prove entropy doesn’t depend on G when written in terms of charges

10/21/00David Lowe, Brown University D-branes  Key ingredient: D-branes Polchinski

10/21/00David Lowe, Brown University Counting black hole microstates  Use D-5branes, D-1branes and Kaluza-Klein momentum to make a charged 5d black hole

10/21/00David Lowe, Brown University  To count black hole microstates- solve a simple counting problem  Have species of massless particles in 1+1d  Want to count number of states with total energy  Answer agrees exactly with Bekenstein-Hawking formula

10/21/00David Lowe, Brown University 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

10/21/00David Lowe, Brown University 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  Dimensional analysis  Get Bekenstein-Hawking entropy right to within an overall factor  To do better requires strong coupling gauge theory calculations

10/21/00David Lowe, Brown University 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

10/21/00David Lowe, Brown University Mean field solution  Comparison of mean field solution to Bekenstein-Hawking result for free energy  Works well in limited range of Hawking temperature

10/21/00David Lowe, Brown University 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