Autumn 2007: AdS/CFT

Abstracts

Andy O'Bannon
After (very) brief reviews of holography and string theory, I will sketch the original motivation for AdS/CFT, Maldacena's low-energy decoupling limit of very many D3-branes. Minimal familiarity with strings and D-branes is assumed. I end with the precise statement of the correpondence and an explanation for the rationale behind our choice and ordering of topics for the quarter. A good paper to read for today (because it is short), or for Friday, is 0709.1523 Mateos "String Theory and Quantum Chromodynamics", sections 1 - 3.

Steve Paik
The N=4 theory has the maximal amount of supersymmetry for an interacting quantum field theory in four dimensions with massless particles of spin <= 1. The supersymmetry is so restrictive that the theory is specified only by the choice of a gauge group, which we take to be SU(N_c), and a value of the coupling constant. We will discuss the field content of this theory and write down its Lagrangian by dimensionally reducing the N=1 Super Yang-Mills theory in ten dimensions. Then we will discuss the bosonic and fermionic symmetries and sketch the Lie algebra in a way that is easy to remember. Next we will prove that the beta function for the coupling is zero using a nonperturbative argument due to Seiberg, showing that the theory is quantum mechanically conformal. The notion of superconformal primary operators will be explained. Finally, we will show that 2 and 3 point functions are heavily constrained by the conformal symmetry. Refs. D'Hoker and Freedman, pp.16-21; MAGOO, pp.30-36, 70-72

Chris Vermilion
I will begin by discussing the conformal structure of flat (Minkowski) space. I will then introduce (p+2) dimensional Anti-de Sitter space as a hyperboloid surface in (p+3) dimensional flat space with (-,-,+,+,+,...) signature. I will discuss a few useful sets of coordinates and metrics on AdS space, building toward a discussion of the boundary. I will show that the boundary of conformally compactified AdS space is equivalent to a conformally compactified Minkowski space in one fewer dimension. Useful references: MAGOO, pp. 36-45 Witten (hep-th/9802150), pp. 1-5

Kristan Jensen
Our goal today is to understand the spectroscopy of Type IIB SUGRA on AdS5 x S5. We will begin by reviewing the theory in (9+1) dimensions and then compactify to (4+1) dimensions. To map out the spectrum of the compactified theory, we will perform harmonic analysis on the compact space and thereby generate the Kaluza-Klein modes of the theory. We will conclude with a few notes on the masses of propagating fields in AdS. We will emphasize the symmetries of the theory (compact, noncompact) throughout the talk. References: 1. D'Hoker & Freedman: hep-th/0201253 primarily chapter 4. 2. MAGOO. Sensibly, of course. 3. Kim, Romans, van Nieuwenhuizen: PRD, 32, 389 (1985).

Andrew Lytle
Dbranes are objects arising in string theory that have descriptions in terms of gauge theory. Today we will attempt to make this statement more precise, leading us to an understanding of dbrane configurations that can be approximated by N=4 SYM in 3+1 dimensions-- one half of the AdS/CFT correspondence. References: Zwiebach has nice material about Dbranes as classical string boundary conditions. Johnson's book "D-Branes" is what I studied for discussing the Dirac-Born-Infeld action.

Paul Chesler
References: Maldacena's orginal paper: hep-th/9711200 Klebanov TASI lecture: hep-th/0009139

Ethan Thompson
The method of calculating correlation functions in a conformal field theory using AdS/CFT will be developed. The field- operator mapping will be discussed. The calculation of scalar correlation functions in Euclidean space will be demonstrated, and the correspondence between the masses of fields in AdS space and the dimension of operators on the field theory side will be shown. Correlation functions of conserved currents will be briefly touched upon. Time permitting, the differences of working in Lorentz signature spacetime will be outlined. References: Witten, hep-th/9802180. Freedman et al, 9804058. MAGOO, section 3.3.

Chris Spitzer
I'll be talking about UV/IR relations and the renormalization group equation derived from AdS/CFT. I'll be following, roughly, the following two references. Susskind & Witten, "The Holographic Bound in Anti-de Sitter Space" hep-th/9805114 Balasubramanian & Kraus, "Spacetime and the Holographic Renormalization Group" hep-th/9903190

Jon Walsh
The title of my talk is "Calculating the expectation value of Wilson loops using the AdS/CFT correspondence". Useful references are: Maldacena, "Wilson loops in large N field theories", hep-th/9803002 Rey et. al., "Wilson-Polyakov loop at finite temperature in large N gauge theory and AdS supergravity", hep-th/9803135 Brandhuber et. al., "Wilson loops in the large N limit at finite temperature", hep-th/9803137

Rob Schabinger
I'll be discussing the recent results of Alday and Maldacena on four gluon scattering at strong coupling in the AdS/CFT correspondence. Useful references are: J. Maldacena and L. Alday "Gluon Scattering Amplitudes at Strong Coupling" arXiv:0705.0303 Z. Bern, L. Dixon, and V. Smirnov "Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond" hep-th/0505205

Organizers: Andy O'Bannon and Ethan Thompson
Last modified: 11 Jan 2008