Seminar S. de Haan

Speaker: 
S. de Haan
Title: 
Integrability in gauge theory
Abstract: 
The mixing matrix of planar N=4 super conformal Yang-Mills theory maps to a spin chain, and the eigen energies of the spin chain correspond to the anomalous dimensions of the theory.  We zoom in at the simplest case,  and explain how the one loop anomalous dimensions of the SU(2) sector map to the Heisenberg  (XXX) spin chain. Then we review the coordinate Bethe ansatz, which can be used to find the eigenstates of this spin chain. If time allows, we use the ansatz to identify a simple but nontrivial eigenstate of the SU(2) mixing matrix at one loop.
 
References
·        J. A. Minahan, K. Zarembo JHEP 0303 (2003) 013
The Bethe-Ansatz for N=4 Super Yang-Mills
·        Joseph A Minahan 2006 J. Phys. A: Math. Gen. 39 12657
A brief introduction to the Bethe ansatz in super-Yang–Mills
·        N Dorey 2009 J. Phys. A: Math. Theor. 42 254001
Notes on integrability in gauge theory and string theory
·        Introduction to the Bethe ansatz I.   
M. Karbach. G. Müller  Computers in Physics 11 (1997), 36-43.
 
Date: 
Tuesday, May 11, 2010 - 13:30 - 14:30