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Str in g s , B ran es ,B lac k Ho les

an d Qu an tum FieldTheory

Professor Jerome Gauntlett

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Two Cornerstones of Theoretical Physics

Quantum Mechanics

Uncertainty Principle

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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:ElectromagnetismStrong nuclear force (quark confinement)Weak nuclear force (beta decay)

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Two Cornerstones of Theoretical Physics

General Relativity Equivalence Principle

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Two Cornerstones of Theoretical Physics

General Relativity Equivalence Principle

Big Bang cosmologyBlack holesGravitational waves

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Two Cornerstones of Theoretical Physics

Quantum Mechanics General Relativity

Quantum Gravity

String Theory

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A very brief history of string theory

Two Revolutions:

80s Perturbative string theory: Its consistent Its quantum gravity

90s 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.

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Perturbative String Theory

Spectrum of string states:

Spectrum includes a massless graviton stateand hence string theory is quantum gravity

Infinite number of harmonics infinite tower of particlestates with different mass

String coupling g

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Perturbative String Theory

Interactions

g2 g4 g6

Perturbative expansion

Makes sense for g

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Perturbative String Theory

Consistency implies

Five perturbative string theoriestype I, type IIA, type IIB, HET E 8 x E8 , HET SO(32)

Ten spacetime dimensions - wrap up 6 a la Kaluza-Klein

GUTs

Supersymmetry

D = 6

D = 3

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Supersymmetry

All elementary particles are eitherBosons spin 0, 1, 2, . . . forcesFermions spin 1/2, 3/2, . . . matter

Supersymmetry is the only symmetry that can combine them

Supersymmetric extensions of the Standard Model may beseen at the LHC

Low energy approximation to string theory is supergravity- supersymmetric generalisation of Einsteins equations of

General Relativity

My recent work has focussed on systematically analysingsupergravity solutions

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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

< >

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Non-Perturbative String Theory:The Duality Revolution

What is the description of string theory when g>>1?

Key input: Branes (extended objects).

String Theory 1:g

String Theory 2:1/g

< >

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p- brane

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p- brane

My first paper (with Achucarro, Itoh and Townsend), 1989:Supersymmetry on the brane: world volume supersymmetry fromspace-time supersymmetry of the four- dimensional supermembrane

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p- brane

My first paper (with Achucarro, Itoh and Townsend), 1989:Supersymmetry on the brane: world volume supersymmetry fromspace-time supersymmetry of the four- dimensional supermembrane

1761 papers with brane in the titleBrane Surgery - P. Townsend Brane Scans - M. Duff Brane Waves..

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When g

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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 T H

Bekenstein-Hawking entropy: S BH = Area

BIG question : can we provide a statistical mechanicalinterpretation? i.e. S BH = klnN ?

14

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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=3

D=6

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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=3

D=6

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Black Holes In String Theory

2. g1 (large string coupling). The back reaction is large and theconfiguration is a black hole with these conserved charges andentropy S BH .

Find S BH = klnN , exactly.

One of the highlights of string theory!

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Subtlety: argument implicitly assumes that the black holes areuniquely 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 dont!

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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.

More generally:

Are black rings the tip of the iceberg?

Can we classify the possibilities?

Black hole Black ring

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Strings and Quantum Field Theory

Strings propagating on certain supergravity backgrounds in 10(or 11) dimensions are equivalent to quantum field theories

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

Maldacenas AdS/CFT correspondence:

So what?

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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 stringtheory in ten or eleven spacetime dimensions!

Many subsequent developments (>3600 citations).

We dont have a string description of ordinary QCD or the minimalsupersymmetric standard model . Yet.

Now have string descriptions of quantum field theories with veryinteresting dynamics.

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String theory is a key tool for understanding quantum field theory.

I am applying my programme of systematically analysingsupersymmetric solutions of supergravity theories to try andfind more examples of the correspondence.

Have elucidated some of the underlying geometrical structures.

Have found infinite classes of new solutions of supergravityeach of which is dual to a quantum field theory that is nowbeing actively studied.

(JPG, D. Martelli, J. Sparks, D.Waldram)

Beautiful interplay between geometry and physics.

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Conclusion

String/M-theory is a sophisticated and beautiful set ofphysical and mathematical ideas.

Compelling connections withblack 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?

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