Direct test of the AdS/CFT correspondence by Monte Carlo studies of $ \mathcal{N}=4 $ super Yang-Mills theory

Abstract

Abstract:We perform nonperturbative studies of N = 4 super Yang-Mills theory by Monte Carlo simulation. In particular, we calculate the correlation functions of chiral primary operators to test the AdS/CFT correspondence. Our results agree with the predictions obtained from the AdS side that the SUSY non-renormalization property is obeyed by the three-point functions but not by the four-point functions investigated in this paper. Instead of the lattice regularization, we use a novel regularization of the theory based on an equivalence in the large-N limit between the N = 4 SU(N ) theory on R × S 3 and a one-dimensional SU(N ) gauge theory known as the plane-wave (BMN) matrix model. The equivalence extends the idea of large-N reduction to a curved space and, at the same time, overcomes the obstacle related to the center symmetry breaking. The adopted regularization for S 3 preserves 16 SUSY, which is crucial in testing the AdS/CFT correspondence with the available computer resources. The only SUSY breaking effects, which come from the momentum cutoff Λ in R direction, are made negligible by using sufficiently large Λ.

N=4supersymmetry on a space-time lattice

“…In addition to monitoring the effects of non-zero µ and κ in the 8 3 × 24 lattice ensembles that are the focus of our current investigations, we can also confirm that Q is indeed restored lim (µ,κ)→(0,0) QO = 0.006 (13). Again, Table I indicates that the remaining Ward identity violations in the (µ, κ) → (0, 0) limit may be attributed to the small 4 4 lattice volume.…”

“…An intriguing alternative method employs the equivalence between this theory in the large-N limit on the manifold R×S 3 and a certain limit of supersymmetric large-N quantum mechanics [9][10][11][12][13][14]. This treats all 16 supercharges on an equal footing, but none of them are exactly preserved at a finite ultraviolet cut-off.…”

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

“…(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.…”

Perturbative and Non-perturbative Approaches to String Sigma-Models in AdS/CFT

“…Alternative numerical, non-lattice approaches include the study of N = 4 SYM on R × S 3 as plane-wave (BMN) matrix model [254][255][256][257][258][259][260].…”