Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThermal phase transition in Yang-Mills matrix model
68
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the bosonic matrix model obtained as the high-temperature limit of two-dimensional maximally supersymmetric SU($N$) Yang-Mills theory. So far, no consensus about the order of the deconfinement transition in this theory has been reached and this hinders progress in understanding the nature of the black hole/black string topology change from the gauge/gravity duality perspective. On the one hand, previous works considered the deconfinement transition consistent with two transitions which are of second and third order. On the other hand, evidence for a first order transition was put forward more recently. We perform high-statistics lattice Monte Carlo simulations at large $N$ and small lattice spacing to establish that the transition is really of first order. Our findings flag a warning that the required large-$N$ and continuum limit might not have been reached in earlier publications, and that was the source of the discrepancy. Moreover, our detailed results confirm the existence of a new partially deconfined phase which describes non-uniform black strings via the gauge/gravity duality. This phase exhibits universal features already predicted in quantum field theory.
rate research
Read More
We test the recent claim that supersymmetric matrix quantum mechanics with mass deformation preserving maximal supersymmetry can be used to study N=4 super Yang-Mills theory on RxS^3 in the planar limit. When the mass parameter is large, we can integrate out all the massive fluctuations around a particular classical solution, which corresponds to RxS^3. The resulting effective theory for the gauge field moduli at finite temperature is studied both analytically and numerically, and shown to reproduce the deconfinement phase transition in N=4 super Yang-Mills theory on RxS^3 at weak coupling. This transition was speculated to be a continuation of the conjectured phase transition at strong coupling, which corresponds to the Hawking-Page transition based on the gauge-gravity duality. By choosing a different classical solution of the same model, one can also reproduce results for gauge theories on other space-time such as RxS^3/Z_q and RxS^2. All these theories can be studied at strong coupling by the new simulation method, which was used successfully for supersymmetric matrix quantum mechanics without mass deformation.
We show that twisted reduced models can be interpreted as noncommutative Yang-Mills theory. Based upon this correspondence, we obtain noncommutative Yang-Mills theory with D-brane backgrounds in IIB matrix model. We propose that IIB matrix model with D-brane backgrounds serve as a concrete definition of noncommutative Yang-Mills. We investigate D-instanton solutions as local excitations on D3-branes. When instantons overlap, their interaction can be well described in gauge theory and AdS/CFT correspondence. We show that IIB matrix model gives us the consistent potential with IIB supergravity when they are well separated.
We discuss bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. We begin by finding convergence conditions for the partition and correlation functions. Moving on, we specialise to the SU(N) models with large N. In both the Yang-Mills and cohomological formulations, we find all quantities which are invariant under the supercharges. Finally, we apply the deformation method of Moore, Nekrasov and Shatashvili directly to the Yang-Mills model. We find a deformation of the action which generates mass terms for all the matrix fields whilst preserving some supersymmetry. This allows us to rigorously integrate over a BRST quartet and arrive at the well known formula of MNS.
We consider the partition function and correlation functions in the bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. In the supersymmetric case, we show that the partition function converges when $D=4,6$ and 10, and that correlation functions of degree $k< k_c=2(D-3)$ are convergent independently of the group. In the bosonic case we show that the partition function is convergent when $D geq D_c$, and that correlation functions of degree $k < k_c$ are convergent, and calculate $D_c$ and $k_c$ for each group, thus extending our previous results for SU(N). As a special case these results establish that the partition function and a set of correlation functions in the IKKT IIB string matrix model are convergent.
We prove that SU(N) bosonic Yang-Mills matrix integrals are convergent for dimension (number of matrices) $Dge D_c$. It is already known that $D_c=5$ for N=2; we prove that $D_c=4$ for N=3 and that $D_c=3$ for $Nge 4$. These results are consistent with the numerical evaluations of the integrals by Krauth and Staudacher.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
