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0
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1answer
37 views

Fields in the action of the Non-linear Sigma Model (WZW)

I am trying to understand the action of the nonlinear sigma model in the context of understanding WZW-models. On Wikipedia, its action is given as ...
0
votes
1answer
95 views

Reparametrization invariance in scalar QFT: What does it mean, exactly?

In the Cecotti's book "Supersymmetric Field Theories" he wrote " Physical quantities are independent of the fields we use to parametrize the configuration, that is, observables are invariant under ...
9
votes
2answers
225 views

Symmetry of the Polyakov action?

Let us look at the Polyakov action for a string moving in a spacetime with metric $g_{\mu \nu}(X)$:$$S_P = -{1\over{4\pi \alpha'}} \int d^2 \sigma \sqrt{-\gamma} \gamma^{ab} \partial_a X^\mu ...
0
votes
0answers
24 views

What is therelation between nonlinear sigma model, complex projective group?

The O(N) nonlinear sigma model has topological solitons only when N=3 in the planar geometry. There exists a generalization of the O(3) sigma model so that the new model possess topological solitons ...
2
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0answers
71 views

Background independent string theory

I don't really understand what one actually means when one says about doing string theory in a background independent way. Apparently B. Sathiapalan is the only person (as far as I know from ...
1
vote
0answers
63 views

Riemannian generalization/adaption of the Hubbard–Stratonovich transformation

I'd like to write the Hubbard–Stratonovich (HS) transformation of a scalar function on a Riemannian manifold. This transformation is quite simple in Euclidean space. One can consider it as a Fourier ...
3
votes
0answers
79 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
85 views

Renormalization of Auxiliary Fields

I have the following non-linear sigma model (the base space $\mathcal{M}$ is Euclidean): $$ \mathcal{L}=\dfrac{1}{2\alpha}\int_{\mathcal{M}}\mathrm{d}^2\sigma\ \partial^2X^{\mu}\partial^2X_{\mu} $$ ...
1
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0answers
64 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
129 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
447 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} = ...
7
votes
0answers
964 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
136 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
126 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 ...
13
votes
3answers
499 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
94 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 ...
36
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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
158 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
105 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
73 views

Gravitating sigma models

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