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 Spectrum of string states: Spectrum includes a massless graviton state and hence string theory is quantum gravity Infinite number of harmonics infinite tower of particle states with different mass String coupling g << 1

Perturbative String Theory Interactions g2g2 g4g4 g6g6 Perturbative expansion Makes sense for g<<1 The likelihood of splitting or joining is determined by g

Perturbative String Theory Consistency implies Five perturbative string theories type I, type IIA, type IIB, HET E 8 x E 8, HET SO(32) Ten spacetime dimensions - wrap up 6 a la Kaluza-Klein GUTs Supersymmetry D = 6 D = 3

Supersymmetry All elementary particles are either Bosons spin 0, 1, 2,... forces Fermions spin 1/2, 3/2,... 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? Key input: Branes (extended objects). String Theory 1: g String Theory 2: 1/g

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 - P. Townsend Brane Scans - M. Duff Brane Waves …..

When g<<1 some branes can be described as surfaces on which strings can end: Brane Dynamics

Web of interconnected string theories There are no strings in the eleven dimensional limit. Strings are not fundamental to M-theory. All five perturbative string theories are connected by dualities. Also connected to an eleven dimensional theory that at low energies is described by supergravity.

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 mechanical interpretation? i.e. S BH = klnN ? 1 4

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

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

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 S BH. Find S BH = 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. More generally: Are black rings the tip of the iceberg? Can we classify the possibilities? Black hole Black ring

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 Maldacena’s AdS/CFT correspondence: 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). We don’t have a string description of ordinary QCD or the minimal supersymmetric standard model …. Yet. Now have string descriptions of quantum field theories with very interesting dynamics.

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 Cambridge (PhD) - Paul Townsend Chicago (Postdoc) - Jeff Harvey CALTECH (Postdoc) - John Schwarz Queen Mary (Lecturer, Reader, Professor) - Chris Hull Imperial Collaborators Acharya Achucarro Azcarraga Dabholkar Dowker Gibbons Giddings Gomis Gutowski Harvey Horowitz Hull Itoh Izquierdo Kastor 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