Questions tagged [large-n]
70 questions
49
votes
1 answer
$\operatorname{O}(N)$ sigma model at large $N$
I would like to better understand the main principles of large-$N$ expansion in quantum field theory. To this end, I decided to consider a simple toy model with lagrangian (from Wikipedia)
$
\mathcal{L} = \frac{1}{2}(\partial_{\mu}…
user43283
- 885
12
votes
2 answers
Matrix models and condensed matter physics
I am sending a couple of questions which seem a bit more specific than others on this site, partially to probe if there is a point in doing so. Not sure what is the range of expertise here, and no way to find out without trying. This one is also not…
user566
10
votes
1 answer
What is the physical meaning of the large $N$ expansion?
I know about the $1/N$ expansion for some time. Apart from the fact that as Witten suggests, it can be the correct expansion parameter of QCD Baryons in the $1/N$ Expansion (in a parallel that he draws between QED and QCD coupling constants), I was…
Bastam Tajik
- 1,310
9
votes
2 answers
Large-$N$ Yang Mills
I've bumped into the study of the $SU(N)$ theory in the large-$N$ limit.
I'm wondering in which way the study of this Yang-Mills theory, can give contribution to QCD with gauge group $SU(3)$, i.e. $N=3$ Any suggestion?
popoolmica
- 313
7
votes
0 answers
Correlators at large $N$ and large $N$ factorization
I am having this very basic problem. In e.g Maldacena's AdS/CFT review (https://arxiv.org/abs/hep-th/0309246) (page 5), he has defined operators as $\mathcal{O}=N\,{\rm tr}[f(M)]$ for some matrices $M$ and got the connected correlators as…
user1349
- 2,167
7
votes
1 answer
Isn't AdS/CFT an end to String theory as a fundamental theory?
I start with the Large $N$ QCD paper by 't Hooft.
When 't Hooft published his paper on Large $N$ QCD it was clear why the string theory of hadrons due to Gabriele Veneziano could make sense. But at the same time, it was an end to strings as…
Bastam Tajik
- 1,310
7
votes
2 answers
Exact solution of SU($N$) model in large $N$ limit
There is the statement about $\text{U}(N)$ model:
It is not possible to solve $\text{U}(N)$ model even in large $N$ limit
I do not understand this statement. If I go to large $N$ limit I know that only planar diagrams contribute to correlators.…
Artem Alexandrov
- 2,739
6
votes
1 answer
How can I show that $1/N$ expansion for large $N$ matrix models have a string theoretical perturbation expansion?
While surfing through some further reading suggestions on string theory, I stumbled upon this slide from a talk by Nathan Seiberg. I wanted to derive the main argument by applying a perturbation expansion for this partition function, but I couldn't…
user242231
6
votes
1 answer
A question on large-N limit?
Let's take $SU(N)$ for an example. The Lagrangian is
$$\mathcal{L}=-\frac{1}{4g_{YM}^2}F_{\mu\nu}F^{\mu\nu}.$$
We can define the t'Hooft coupling as
$$\lambda=g_{YM}^2N.$$
Then the large-$N$ limit or the t'Hooft limit is:
$$N\rightarrow\infty,\…
Wein Eld
- 3,791
6
votes
0 answers
Relation between holography and matrix models
Let's consider a 0-dimensional $N \times N$ Hermitean one matrix model.
It is defined by a potential V(M). Its partition function
is
$$Z = \int_{H_{N}} dM e^{-\frac{1}{g}V(M)}$$
where $H_{N}$ is the space of $N \times N$ Hermitean matrices
and g…
user40227
- 194
6
votes
1 answer
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 \psi_i]
\end{equation}
where I have chosen the…
Dan
- 2,757
5
votes
0 answers
Some questions about the large-N Gross-Neveu-Yukawa model
Consider the following action with a fermionic field $\psi$ and a scalar field $\sigma$,
$S = \int d^dx \{ -\bar{\psi}(\gamma^\mu \partial_\mu +\sigma )\psi + \Lambda^{d-4}[ \frac{(\partial_\mu \sigma )^2 + m^2\sigma^2 }{2g^2 } + \frac{\lambda…
user6818
- 4,749
5
votes
2 answers
Mean field theory = large-$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 for mean field theory.
I would like reference(s)…
GuSuku
- 847
5
votes
0 answers
How large is large $N$?
I once heard Lenny Susskind relate the question: "how many particles do you need in a box for the ideal gas law to 'pretty much' hold?" Obviously this question requires a notion of 'pretty much' to formalize. In thermodynamics we usually assume $N…
hulsey
- 472
5
votes
1 answer
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 spin will be suppressed, which is so called…
Merlin Zhang
- 1,692