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3
votes
0answers
55 views

Projective superspace: why extra bosonic coordinates

I'm studying the projective superspace formalism for N = 4 supersymmetric $\sigma$-models in two dimensions. My question is: why do we need the extra bosonic coordinates for the manifest action? I ...
4
votes
0answers
66 views

Renormalization of Auxiliary Fields

I have the following non-linear sigma model (the base space $\mathcal{M}$ is Euclidean): $$ \mathcal{L}=\dfrac{1}{2\alpha}\int_{\mathcal{M}}\mathrm{d}^2\sigma\ \partial^2X^{\mu}\partial^2X_{\mu} $$ ...
0
votes
0answers
44 views

How can we see that a 4D N = 2 sigma model will yield a 3D N = 4 sigma model when compactified on a circle?

I have a question about sigma models in 3D. If we have $\mathcal{N}=2$ field theory on $\mathbb{R}^4$ and compactify it on $\mathbb{R}^3 \times S^1_R$ (in which $S^1_R$ is a circle of radius $R$) we ...
2
votes
1answer
126 views

Where does this delta of zero come from?

It is common when evaluating the partition function for a $O(N)$ non-linear sigma model to enforce the confinement to the $N$-sphere with a delta functional, so that $$ Z ~=~ \int d[\pi] d[\sigma] ~ ...
14
votes
0answers
380 views

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} = ...
6
votes
0answers
934 views

Impostor Higgs?

I recently came across this article, published in the respectable European Physical Journal A. (Apparently, there isn't any corresponding arXiv article for this, so I'm sorry if everyone isn't able to ...
2
votes
0answers
99 views

O(N) sigma model renormalization

Does anyone know, is a model with lagrangian $\mathcal{L} = \frac{(\partial_{\mu}\phi_a)^2}{2}-\frac{m^2 \phi_a^2}{2}-\frac{\lambda}{8N}(\phi_a \, \phi_a)^2$ renormalizable? I'm using BPHZ scheme and ...
2
votes
0answers
108 views

Difference of the O(N) Non-linear Sigma model and SO(N) Non-linearSigma model

The Hamiltonian \begin{equation} H=J\sum_{i,j}\vec{n}_i\cdot\vec{n}_j \end{equation} is invariant under a global rotation $\vec{n}_i\rightarrow R\vec{n}_i$, where $\vec{n}$ is a $N$ component rotor ...
12
votes
3answers
396 views

Effect of linear terms on a QFT

I was always told when first learning QFT that linear terms in the Lagrangian are harmless and we can essentially just ignore them. However, I've recently seen in the linear sigma model, ...
3
votes
1answer
84 views

Question about the vacuum bundle on A- and B-model

Let us consider the topological string A- and B-model (twisted SUSY non-linear sigma model on CY 3-manifold $X$). They are realization of $N=2$ SCFT and there are ground-states vector bundle ...
31
votes
0answers
1k views

Linear sigma models and integrable systems

I'm a mathematician who recently became very interested in questions related to mathematical physics but somehow, I already have difficulties in penetrating the literature... I'd highly appreciate any ...
4
votes
1answer
142 views

Parametrization of $U(N)$ non-linear sigma model

The motivation of this question actually comes from this (really old) paper of Weinberg. He considers a theory of massless pions. They have a chiral $SU(2)_{L} \times SU(2)_{R}$ symmetry. The pions ...
5
votes
0answers
98 views

sigma model on $S^1 \times S^3$

In arXiv:1207.3497 - 4D partition function on $S^1 \times S^3$ and 2D Yang-Mills with nonzero area, Yuji Tachikawa explains the partition function for an 4d $\mathcal{N}=2$ sigma model on $S^3 \times ...
5
votes
1answer
70 views

Gravitating sigma models

I am looking for a review or book on sigma models in (super)gravity theories, which arise from dimensional reduction.