- #1
- 2,810
- 604
I'm reading McGreevy's lecture notes on holographic duality but I have two problems now: (See here!)
1) The author considers a matrix field theory for large N expansion. At first I thought its just a theory considered as a simple example and has nothing to do with the ## \mathcal N=4 ## SYM SU(N) theory which is going to be analyzed later. But if you see the linked pdf, the author says the following just above equation (1):
Also, only SU(N) gauge fields are NxN matrices and not the matter fields. So what is he talking about?
2) In section 3, he considers single-trace operators, defined by equation (4). But I have no idea what kind of an operator this is. The field/operator correspondence in AdS/CFT is supposed to be between quantities like e.g. bulk metric and boundary theory SEM tensor or bulk gauge fields and boundary theory global currents. But what is this single trace operator? Can anyone clarify and give an example?
Thanks
1) The author considers a matrix field theory for large N expansion. At first I thought its just a theory considered as a simple example and has nothing to do with the ## \mathcal N=4 ## SYM SU(N) theory which is going to be analyzed later. But if you see the linked pdf, the author says the following just above equation (1):
Does this mean there is a connection between this matrix field theory and the SYM? What is this connection?we write our theory schematically in terms of one big field ## \Phi ## which we think of as potentially including scalars ## \phi ##, gauge fields ## A_\mu ##, and fermions ## \psi_\alpha ## all of which are N x N matrices.
Also, only SU(N) gauge fields are NxN matrices and not the matter fields. So what is he talking about?
2) In section 3, he considers single-trace operators, defined by equation (4). But I have no idea what kind of an operator this is. The field/operator correspondence in AdS/CFT is supposed to be between quantities like e.g. bulk metric and boundary theory SEM tensor or bulk gauge fields and boundary theory global currents. But what is this single trace operator? Can anyone clarify and give an example?
Thanks