# The large N limit of SU(N) integrals in lattice models

@article{Borisenko2020TheLN, title={The large N limit of SU(N) integrals in lattice models}, author={O. A. Borisenko and Vladimir Chelnokov and Semen Voloshyn}, journal={Nuclear Physics}, year={2020}, volume={960}, pages={115177} }

Abstract The standard U ( N ) and S U ( N ) integrals are calculated in the large N limit. Our main finding is that for an important class of integrals this limit is different for two groups. We describe the critical behaviour of S U ( N ) models and discuss implications of our results for the large N behaviour of S U ( N ) lattice gauge theories at finite temperatures and non-zero baryon chemical potential. The key ingredients of our approach are 1) expansion of the integrals into a sum over…

## 3 Citations

Polyakov loop models in the large
N
limit: Phase diagram at finite density

- PhysicsPhysical Review D
- 2022

The ’t Hooft-Veneziano limit of various U(N) and SU(N) Polyakov loop models is constructed at finite temperature and non-zero baryon chemical potential. In this paper we calculate the free energy,…

Strong coupling methods in QCD thermodynamics

- PhysicsIndian Journal of Physics
- 2021

For a long time, strong coupling expansions have not been applied systematically in lattice QCD thermodynamics, in view of the success of numerical Monte Carlo studies. The persistent sign problem at…

Polyakov loop eigenvalues in the presence of baryon chemical potential

- 2020

The eigenvalues of the Polyakov loop are calculated in the strong coupled lattice QCD at finite tempera ture. This is done both in the pure gauge theory and in the theory with heavy quarks at finite…

## References

SHOWING 1-10 OF 49 REFERENCES

1/N expansion in two‐dimensional lattice gauge theory

- Physics
- 1980

We use the method of orthonormal polynomials to investigate the large N limit of the two‐dimensional lattice gauge theory. The 1/N2 and 1/N4 corrections to the vacuum energy and the expectation value…

The weak coupling phase of lattice spin and gauge models

- Physics
- 1984

We analyze the lattice weak-coupling (w.c.) expansion of O(N), CPN−1 and chiral spin models, and of large-N reduced chiral and gauge models.
We find that the w.c. expansion always agrees with mean…

Chiral models: Their implication for gauge theories and large N

- Physics
- 1981

Abstract Two-dimensional chiral models are investigated from a strong coupling viewpoint, with the ultimate objective of understanding the phase structure of gauge theories. Predictions for the…

Phase transitions in U(N) and SU(N) lattice gauge theories

- Physics
- 1983

Abstract The transition regions between strong and weak coupling for U(N) and SU(N) lattice gauge theories (2 ⩽ N ⩽ 6) are investigated with the mean field approximation including gaussian…

Approaching the large-N limit: A renormalization group approach to large-N field theories

- Physics
- 1984

Abstract A technique is developed for finding recursive solutions to field theories that take values in SU( N ). The approach can be used as a method of solving the large- N limit as well as…

Possible Third Order Phase Transition in the Large N Lattice Gauge Theory

- Physics
- 1980

The large-$N$ limit of the two-dimensional $\mathrm{U}(N)$ (Wilson) lattice gauge theory is explicitly evaluated for all fixed $\ensuremath{\lambda}={g}^{2}N$ by steepest-descent methods. The…

The external field problem for QCD

- Physics
- 1981

In lattice gauge theory, many computations such as the strong coupling expansions, mean field theory, or the few plaquette models require the evaluation of the one-link integral in the presence of an…

The external field problem in the large N limit of QCD

- Physics
- 1980

Abstract Several problems in lattice gauge theories such as mean field theory or the few plaquette problem lead to the evaluation of the properties of one link in an external matrix source. This…

Improved mean field studies of SU(N) chiral models and comparison with numerical simulations

- Physics
- 1984

Abstract SU( N ) × SU( N ) matrix models are investigated using a systematic expansion around the classical mean field result. One-loop corrections for N = 2−5, and ∞ are computed for the two-,…

N = ∞ phase transition in a class of exactly soluble model lattice gauge theories

- Physics
- 1980

Abstract An exactly soluble class of model U ( N ) lattice gauge theories is considered. The ground state is discussed as a separable N -fermion problem solved by mathieu functions. Some exact…