# Questions tagged [large-n]

The tag has no usage guidance.

38 questions
Filter by
Sorted by
Tagged with
43 views

### What's the difference and relations between $SU(N)$ Schwinger boson and $CP(N\!-\!1)$ non-linear sigma model?

There are two ways when dealing with spin system(Heisenberg model): non-linear $\sigma$ model and Schwinger boson. Non-linear $\sigma$ model When taking large $S$ limit, the quantum fluctuation of ...
135 views

84 views

### Besides instantons and large-$N$ what are some other general non-perturbative methods for quantum field theory?

Besides large-$N$, instantons, lattice QFT, what are some other non-perturbative methods that help us better understand QFTs like the large distance dynamics of Yang Mills and QCD?
66 views

### Question about the Dyson-Schwinger equation for 4-point function of the SYK model

In studying the SYK model, I have no idea how to get the kernel $K(t_a,t_b,t_3,t_4)$ and $\Gamma_0(t_1,t_2,t_3,t_4)$ and also ladder diagrams in the Dyson-Schwinger equation for 4 point function of ...
54 views

125 views

### Different purposes for using the Large-$N$ Expansion

I've started studying the Large-$N$ expansion and there seems to be several different reasons for using it. In the context of the SYK model, the limit is useful because it reorganizes the Feynman ...
78 views

295 views

### Relation between holography and matrix models

Let's consider a 0-dimensional $N \times N$ Hermitean one matrix model. It is defined by a potential V(M). Its partition function is $$Z = \int_{H_{N}} dM e^{-\frac{1}{g}V(M)}$$ where $H_{N}$ is the ...
111 views

### Normalization of Source Terms in Large-N Gauge Theory

Typically when you do the counting for large N gauge theory, you rescale fields so that the Lagrangian takes the form \begin{equation} \mathcal{L}=N[-\frac{1}{2g^2}TrF^2+\bar{\psi}_i\gamma^\mu D_\mu \...
321 views

### Large-$N$ factorization of single-trace operators
Does anyone know where I can find a pedagogical explanation of large-$N$ factorization in $SU(N)$ gauge theories or nonlinear $O(N)$ sigma models (in the latter case the trace corresponds to a dot ...
### Mean field theory = large-$N$ approximation?
Wikipedia entry of $1/N$ expansion (or 't Hooft large-N expansion) mentions that It (large-$N$) is also extensively used in condensed matter physics where it can be used to provide a rigorous basis ...