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Questions tagged [large-n]

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48 views

Why do we consider only the tree diagrams in effective field theory?

I have studied Witten's paper entitled in ''BARYONS IN THE 1INEXPANSION''.(Link: https://www.sciencedirect.com/science/article/pii/0550321379902323). I have a question about quark bilinears. About ...
2
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0answers
76 views

Is there confinement in the Gross-Neveu model?

The Gross-Neveu model is a simple quantum field theory in 2 space-time dimensions that is considered a toy model for QCD, in the sense that it realizes asymptotic freedom, chiral symmetry breaking ...
2
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1answer
65 views

How does gauge theory become strongly coupled at large $N$ whether it's coupling is proportional to 1/$\sqrt N$?

At large $N$, gravity theory becomes weakly coupled is correct as we see from its formula that string's coupling is proportional to $1/N^2$. then how could gauge theory become strongly coupled?
3
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1answer
125 views

Manipulations with Traces: Saddle point integration in Large-$N$ model

For reference I am trying to work out the derivation in this paper, in which the partition function for an Ising model is approximated by replacing the Ising variables $\sigma_i$ with $N$ component ...
3
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0answers
91 views

How to get the eigenvalue density contribution $\rho_1(x)$?

I'm studying the $1/N$ expansion beyond the planar limit in matrix models. Currently I'm trying to understand and reproduce the results of: Antisymmetric Wilson loops in $\mathcal N \geq 4$ SYM ...
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0answers
82 views

What physics describes a $SU(N)$ theory with large $N$?

Suppose that we have a system that can be described by $N$ (is a large number!) degree of freedom besides well-known degree of freedom like energy, momentum, spin, etc.. Now scattering processes are ...
0
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1answer
166 views

$1/N$ expansion in $SU(N)$ Yang-Mills theories at large $N$

It is a well-known fact that correlators of $SU(N)$ Yang-Mills theories at large $N$ are expanded in powers of the 't Hooft coupling $g_{YM}^{2}N$ and $1/N$. Is there a reason why an expansion in ...
5
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1answer
184 views

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 ...
3
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0answers
82 views

What is the meaning of the existence of a large $N$ limit in QFT?

Large $N$ limits are present in many different contexts: matrix models, gauge theories in various dimensions, conformal field theories (where $N$ is essentially the central charge). We often hear ...
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0answers
64 views

Non-renormalization theorems at large N

I know of numerous examples of non-renormaliation theorems in theories with SUSY - e.g. the non-renormaliation of the superpotential in 4d theories. However, I've never seen a non-renormaliation ...
2
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1answer
439 views

The logic of large $N$ expansion

I have some understanding of how the large-$N$ expansion works but feel like I'm missing the most important concepts. For example, I understand that in QCD the order of the diagram in $N$ depends ...
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0answers
126 views

Central Charge of large $N$ Gauge theory in 't Hooft limit

It is well known that large N gauge theory in t'Hooft limit has central charge ~ $N^2$ I want to convince myself in this by considering simple example of: 1 flavor(meaning that we have only one ...
1
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1answer
208 views

Relation between $1/N$ and perturbative expansions in QFT

I heard many times phrases like "large $N$ is a clever way to organize the diagrammatic expansion" or "each diagram in the large $N$ expansion contains an infinite number of usual perturbative ...
3
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1answer
243 views

Large $N$ expansion vs AdS/CFT

I'm beginning to learn AdS/CFT and I have an elementary question. It is said that since it is very hard to calculate 4 point and above correlators in a strongly coupled CFT, we can use instead the ...
4
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0answers
177 views

Some questions about QCD [closed]

About QCD, I have two questions. I know I should propose one question one time, but they are actually two steps of the same question: Non-perturbative aspects of QCD. 1, Why do we need to solve QCD ...
33
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0answers
1k views

$\operatorname{O}(N)$ 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 simple toy-model with lagrangian (from Wikipedia) $ \mathcal{L} ...
5
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0answers
222 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 ...
6
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1answer
97 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 \...
8
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2answers
253 views

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=...
1
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0answers
77 views

Large-N critical NLSM (equation 13.115 of Peskin and Schroeder)

Any opinions if the equation 13.115 of Peskin and Schroeder is true on arbitrary manifolds in arbitrary dimensions for the same Lagrangian? I a priori see no problem. The point I also want to ask is -...
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0answers
204 views

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 \...
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2answers
958 views

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 ...