N = 4 super Yang-Mills theory from the plane wave matrix model

Self Cite

We consider the commutative limit of matrix geometry described by a large-N sequence of some Hermitian matrices. Under some assumptions, we show that the commutative geometry possesses a Kähler structure. We find an explicit relation between the Kähler structure and the matrix configurations which define the matrix geometry. We also discuss a relation between the matrix configurations and those obtained from the geometric quantization.

Section: Jhep08(2016)042mentioning

confidence: 89%

Kähler structure in the commutative limit of matrix geometry

Ishiki

Matsumoto

Muraki

2016

Self Cite

“…In addition, there has recently been a great deal of other work, both theoretical and numerical, focused on discrete formulations of N = 4 SYM see Refs. [17,18,19,20,21,22,23]. These alternative approaches should be viewed as complementary to the lattice construction described in this paper.…”

Section: Introductionmentioning

confidence: 99%

Perturbative renormalization of lattice $ \mathcal{N} = 4 $ super Yang-Mills theory

Catterall

Dzienkowski

Giedt

et al. 2011

We consider N = 4 super Yang-Mills theory on a four-dimensional lattice. The lattice formulation under consideration retains one exact supersymmetry at non-zero lattice spacing. We show that this feature combined with gauge invariance and the large point group symmetry of the lattice theory ensures that the only counterterms that appear at any order in perturbation theory correspond to renormalizations of existing terms in the bare lattice action. In particular we find that no mass terms are generated at any finite order of perturbation theory. We calculate these renormalizations by examining the fermion and auxiliary boson self energies at one loop and find that they all exhibit a common logarithmic divergence which can be absorbed by a single wavefunction renormalization. This finding implies that at one loop only a fine tuning of the finite parts is required to regain full supersymmetry in the continuum limit.

“…(For alternative approaches see [6][7][8][9][10][11].) One motivation for such efforts is that it is highly desirable to test the AdS/CFT correspondence at a finite number of colors N , and for moderate values of the 't Hooft coupling λ = g 2 N ∼ 1.…”

Section: Introductionmentioning

confidence: 99%

Real space renormalization group for twisted lattice N $$ \mathcal{N} $$ =4 super Yang-Mills

Catterall

Giedt

2014

A necessary ingredient for our previous results on the form of the long distance effective action of the twisted lattice N = 4 super Yang-Mills theory is the existence of a real space renormalization group which preserves the lattice structure, both the symmetries and the geometric interpretation of the fields. In this brief article we provide an explicit example of such a blocking scheme and illustrate its practicality in the context of a small scale Monte Carlo renormalization group calculation. We also discuss the implications of this result, and the possible ways in which to use it in order to obtain further information about the long distance theory.