# Past Courses: 2006/2007

### Title: Black hole production in gravity duals and experimental implications for QCD and RHIC

Horatiu Nastase

**First lecture:** *Formalism for black hole formation in gravitational shockwave collisions and gauge theory results using AdS-CFT.*

Abstract: High energy (high s, fixed t) collisions above the Planck scale in a gravitational theory are approximated by gravitational shockwave collisions. I show how one can find black hole formation in such a collision, and calculate (a lower bound on) the total cross section. I apply this formalism for gravity duals and show how to use AdS-CFT a la Polchinski-Strassler to find results in gauge theories**Second lecture:** *Applications to QCD and the real world; the duality between black holes and hot "fireballs" in QCD.*

Abstract: I continue the description of high energy collisions in gauge theories via AdS-CFT. I apply the results obtained to real world QCD and argue that the analysis continues to be valid. I show that the "fireballs" observed at RHIC are dual to black holes situated on the IR brane in the gravity dual. I show that this can be possible by proving that a simple toy model for the fireball, a scalar field theory solution, the "pionless hole", has the same properties as the dual black hole, including Hawking radiation at a fixed and calculable temperature. I study the properties of the fireballs from the dual black holes and show the differences from the usual finite temperature case of Witten

Schedule: 11, 12 July, 11.00am-1.00pm, Room 410.

### Title: Some Fuzzy geometries in String theoryI introduce some examples of non-commutative and fuzzy geometries, and discuss their applications in string theory.

Sanjaye Ramgoolam

I introduce some examples of non-commutative and fuzzy geometries, and discuss their applications in string theory.

Schedule:

2, 4 May, 11.00am-1.00pm, Room 112.

### Title: Introduction to Topological Strings

Alessandro Tanzini

These lectures are intended to provide a basic introduction to topological strings, with the following tentative programme:

- Lect. 1: N = (2,2) supersymmetric 2d field theories and their twistings
- Lect. 2: Observables of A and B-topological models and mirror symmetry. Geometrical description of the A-model.
- Lect. 3: Gromov-Witten invariants and quantum cohomology. Examples and applications to the effective actions of four-dimensional supersymmetric theories.

Schedule:

7 March, 4.00pm-6.00pm, Room 112,

9 March, 2.00pm-4.00pm, Room 410,

12 March, 4.00pm-6.00pm, Room 112.

### Title: Integrability in gauge theories

Gregory Korchemsky

In these lectures, I shall explain the general phenomenon of integrability in four-dimensional gauge theories choosing as a prime example calculation of the anomalous dimensions of various Wilson operators in Yang-Mills theory and its supersymmetric extensions. I will demonstrate that to lowest order of perturbative expansion the mixing matrix for such operators inherits a conformal symmetry of the classical Lagrangian and, most importantly, it can be mapped into a Hamiltonian of the celebrated Heisenberg spin chain and its generalizations. Finally, a short overview of the Bethe Ansatz approach to calculation of anomalous dimensions will be given.

Schedule:

28 February, 4.00pm-6.00pm, Room 112,

1 March, 2:00-4:00pm Room 112 ,

2 March, 2:00-4:00pm; Place: Room 410.

### Title: Lectures on String Field Theory

Martin Schnabl

Lect. 1: Basic introduction to the ideas and concepts of string field theory. Action, gauge invariance and the star algebra.

Lect. 2: Classical solutions in SFT. Tachyon condensation, Sen's conjectures and rolling tachyons.

Schedule:

20, 22 February, 2.00pm-4.00pm, Room 112.

### Title: Superstring theory in a nutshell

Rodolfo Russo

The aim of this course is to introduce some of the most common technical tools in string theory. The tentative program is as follows:

Lect. 1: Canonical quantization: the string spectrum. Modern covariant quantization.

Lect. 2: Neveu-Schwarz and Ramond models. The GSO projection and the superstring spectrum.

Lect. 3: Bosonization equivalence in 2 dimensions. Spin fields. Lect.

Lect. 4: The one-loop partition function.

Schedule:

1 February, 2.00pm-4.00pm, Room 112,

5, 7 February, 4.00pm-6.00pm, Room 112,

14 February 2007, 11.00am-1.00pm, Room UG4.

### Title: Branes and M-theory

David Berman

This course will cover the theory of extended objects, known as branes. They will be decribed both via a world volume action and as solutions of supergravity. The course will cover the following topics as time allows: world volume solitons; world volume duality and the connection to spacetime duality; kappa symmetry; calibrations; M-theory; dualities in M-theory and the relation to the string theories.

Schedule:

16, 23, 30 November and 7 December 2006, 11.00am-1.00 pm.

Room: UG4

### Title: Duality in Supersymmetric Yang-Mills Theory

These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the qualitative behavior of the simplest illustrative models will be analyzed. These include supersymmetric QCD for N_f < N_c, in which the superpotential is generated nonperturbatively, N=2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effective coupling is described geometrically, and supersymmetric QCD for N_f large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality.

The course will end with one lecture providing an introduction to Instantons in Supersymmetric Yang-Mills Theory.

Andreas Brandhuber

Schedule:

12, 19, 26 October and 2 November 2006, 11.00am-1.00 pm.

Room: UG4

Gabriele Travaglini

Schedule:

3 November 2006, 11.00am-1.00 pm.

Room: 410A

### Title: The BMN limit of the AdS/CFT duality

Rodolfo Russo

The tentative program is the following: Lect.

1: Yang-Mills theory and its symmetries. The N=4 SYM spectrum: primary operators, anomalous dimensions.

Lect. 2: Type IIB string/supergravity. AdS_5 x S^5 and the BPS spectrum of IIB string on this background. The AdS/CFT conjecture.

Lect. 3: The BMN limit of the AdS/CFT duality: the spectrum.

Lect. 4: Beyond the spectrum: the interacting theory.

Schedule:

6, 7, 13 and 14 June 2006, 3.00-5.00 pm.

Room: 609