Strings, Branes,
Black Holes
and Quantum Field
Theory
Professor Jerome Gauntlett
Two Cornerstones of Theoretical Physics
Quantum Mechanics
Uncertainty Principle
Two Cornerstones of Theoretical Physics
Quantum Mechanics
Uncertainty Principle
Standard Model of Particle Physics:
Quantum Field Theory
Yang-Mills Theory SU(3)xSU(2)xU(1)
Describes 3 of the 4 known forces:
Electromagnetism
Strong nuclear force (quark confinement)
Weak nuclear force (beta decay)
Two Cornerstones of Theoretical Physics
General Relativity
Equivalence Principle
Two Cornerstones of Theoretical Physics
General Relativity
Equivalence Principle
Big Bang cosmology
Black holes
Gravitational waves
Two Cornerstones of Theoretical Physics
Quantum Mechanics
General Relativity
Quantum Gravity
String Theory
A very brief history of string theory
Two Revolutions:
80’s Perturbative string theory:
It’s consistent
It’s quantum gravity
90’s Non-perturbative string theory:
Dualities, branes (extended objects), black holes,
supergravity, quantum field theory,….
History:
Not linear! UK very strong in BIG ideas. Not fashion driven.
Perturbative String Theory
String coupling g << 1
Spectrum of string states:
Infinite number of harmonics
infinite tower of particle
states with different mass
Spectrum includes a massless graviton state
and hence string theory is quantum gravity
Perturbative String Theory
Interactions
The likelihood of splitting or joining is determined by g
Perturbative expansion
g2
g4
Makes sense for g<<1
g6
Perturbative String Theory
Consistency implies
Five perturbative string theories
type I, type IIA, type IIB, HET E8 x E8 , HET SO(32)
Ten spacetime dimensions - wrap up 6 a la Kaluza-Klein
D=6
D=3
GUTs
Supersymmetry
Supersymmetry
All elementary particles are either
Bosons
spin 0, 1, 2, . . .
Fermions
spin 1/2, 3/2, . . .
forces
matter
Supersymmetry is the only symmetry that can combine them
Supersymmetric extensions of the Standard Model may be
seen at the LHC
Low energy approximation to string theory is supergravity
- supersymmetric generalisation of Einstein’s equations of
General Relativity
My recent work has focussed on systematically analysing
supergravity solutions
Non-Perturbative String Theory:
The Duality Revolution
What is the description of string theory when g>>1?
String Theory 1:
g
< >
String Theory 2:
1/g
Non-Perturbative String Theory:
The Duality Revolution
What is the description of string theory when g>>1?
String Theory 1:
g
< >
String Theory 2:
1/g
Key input: Branes (extended objects).
p-brane
p-brane
My first paper (with Achucarro, Itoh and Townsend), 1989:
“Supersymmetry ‘on the brane’: world volume supersymmetry from
space-time supersymmetry of the four-dimensional supermembrane”
p-brane
My first paper (with Achucarro, Itoh and Townsend), 1989:
“Supersymmetry ‘on the brane’: world volume supersymmetry from
space-time supersymmetry of the four-dimensional supermembrane”
1761 papers with brane in the title
Brane Surgery
Brane Scans
Brane Waves
…..
- P. Townsend
- M. Duff
Brane Dynamics
When g<<1 some branes can be described as surfaces on
which strings can end:
Web of interconnected string theories
All five perturbative string theories are connected by dualities.
Also connected to an eleven dimensional theory that at low
energies is described by supergravity.
There are no strings in the eleven dimensional limit.
Strings are not fundamental to M-theory.
Black Holes and Black Rings
Black Holes are key arenas for quantum gravity.
Classically: black holes are black.
Quantum mechanically: black holes are thermal
Hawking radiate at TH
Bekenstein-Hawking entropy: SBH =
1
4
Area
BIG question: can we provide a statistical mechanical
interpretation? i.e. SBH = klnN ?
Black Holes in String Theory
1. Construct a black hole by wrapping branes on the compact space.
The localised blob of energy carries conserved charges (e.g. mass,
angular momentum, electric charge)
D=6
D=3
Black Holes in String Theory
1. Construct a black hole by wrapping branes on the compact space.
The localised blob of energy carries conserved charges (e.g. mass,
angular momentum, electric charge)
D=6
D=3
Black Holes In String Theory
2. g<<1 (small string coupling). Back reaction of branes on the
geometry is small. Can count the number of string states with these
conserved charges
N.
3. g>>1 (large string coupling). The back reaction is large and the
configuration is a black hole with these conserved charges and
entropy SBH.
Find SBH = klnN, exactly.
One of the highlights of string theory!
Subtlety: argument implicitly assumes that the black holes are
uniquely specified by their conserved charges.
For black holes in four dimensions this is true.
In addition they all have event horizons with spherical topology.
Both facts were thought to generalise to higher dimensions.
Both don’t!
In five dimensions:
Supersymmetric black holes with event horizons of spherical topology.
Supersymmetric “Black Rings”, black holes with a ring topology.
Moreover, the black rings violate uniqueness.
(JPG, J. Gutowski)
Currently a very active area of investigation.
Black hole
More generally:
Are black rings the tip of the iceberg?
Can we classify the possibilities?
Black ring
Strings and Quantum Field Theory
Limit 1: (Gravitational back reaction is small)
A quantum field theory living on the branes
Limit 2: (Gravitational back reaction is large)
A curved supergravity background
Maldacena’s AdS/CFT correspondence:
Strings propagating on certain supergravity backgrounds in 10
(or 11) dimensions are equivalent to quantum field theories
So what?
1. Quantum gravity on certain backgrounds is quantum field theory!
2. Quantum field theory is quantum gravity!
3. Quantum field theory in four spacetime dimensions is string
theory in ten or eleven spacetime dimensions!
Many subsequent developments (>3600 citations).
Now have string descriptions of quantum field theories with very
interesting dynamics.
We don’t have a string description of ordinary QCD or the minimal
supersymmetric standard model …. Yet.
String theory is a key tool for understanding quantum field theory.
I am applying my programme of systematically analysing
supersymmetric solutions of supergravity theories to try and
find more examples of the correspondence.
Have elucidated some of the underlying geometrical structures.
Have found infinite classes of new solutions of supergravity
each of which is dual to a quantum field theory that is now
being actively studied.
(JPG, D. Martelli, J. Sparks, D.Waldram)
Beautiful interplay between geometry and physics.
Conclusion
String/M-theory is a sophisticated and beautiful set of
physical and mathematical ideas.
Compelling connections with
black holes
quantum field theory
Clues to the deepest open questions:
What is string/M-theory?
What is the stringy principle?
Is it the theory of quantum gravity?
Thanks
Collaborators
Acharya
Achucarro
Azcarraga
Dabholkar
Dowker
Gibbons
Giddings
Gomis
Gutowski
Harvey
Horowitz
Hull
Itoh
Izquierdo
Kastor
1987 - 1991
1991 - 1994
1994 - 1996
1996 - 2003
2003 -
Koehl
C. Kim
N. Kim
Lambert
K. Lee
S. Lee
Liu
Lowe
A. Mateos
D. Mateos
Martelli
Myers
Pakis
Papadopoulos
Park
Portugues
Reall
Robinson
Sparks
Suryanarayana
Tada
Tong
Townsend
Traschen
Waldram
West
Yastremiz
Yi
Zamaklar
Cambridge (PhD)
- Paul Townsend
Chicago
(Postdoc)
- Jeff Harvey
CALTECH (Postdoc)
- John Schwarz
Queen Mary (Lecturer, Reader, Professor) - Chris Hull
Imperial