Questions tagged [wess-zumino-witten]
May use for both 4d phenomenological theories of flavor chiral anomalies, and 2d CFTs involving affine Lie Algebras. Wess–Zumino–Witten (WZW) models describe σ-models with flavor-chiral anomalies, of topological significance. Such terms trivialize the torsional curvature of the respective manifolds, leading to infrared fixed points of the RG.
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Which states contribute to the largest gap for WZW model with $so(16)_1$? [closed]
I was told that the WZW model with $so(16)_1$ occurred at $(c,\bar c )=(8,8)$, and it had a gap, i.e. the smallest state with conformal dimension $\Delta = h+\bar h\neq 0$, and it was said to be $2$.
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On the derivation of Wess-Zumino term
$G$-$\text{WZW}$ model on a Riemann surface $\Sigma$ at the level $k$ is defined as
$${\displaystyle S_{k}(\gamma )=-{\frac {k}{8\pi }}\int _{\Sigma }d^{2}x\,{\mathcal {K}}\left(\gamma ^{-1}\partial ^{...
user394668
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Sugawara construction in $G$-WZW models
Lorenz argues that Virasoro generator $L_n$ admits a mode expansion in terms of conserved currents
$$L_n = \gamma\sum_{\alpha}\sum_{m\in\mathbb{Z}}:J^{a}_{n}J^{a}_{m-n}:\space\space\space \gamma = \...
user361492
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Calculating the Bekenstein-Hawking entropy for 1+1 black hole with dilaton background
According to this paper the Bekenstein-Hawking entropy of a 1+1 black hole which described by the $SL_k(2,\mathbb{R})/U(1)$ WZW cigar geometry is given by the following formula appearing in eq. (5.7):
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How to derive WZW model’s energy-momentum tensor? The result is of course the Sugawara construction
I want to know how to derive WZW’s energy-momentum tensor. We know WZW action is
$$
S_{WZW}[g]=\frac{k}{16\pi}\int d^2x Tr(\partial g^{-1}\partial g) - \frac{ik}{24\pi}
\int_B d^3y \epsilon_{abc} Tr(h^...
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Central Charge Calculation of $SL_k(2,\mathbb{R})$ WZW Model
According to P. Francesco et al. conformal field theory book the central charge of the enveloping Virasoro algebra of the affine Lie algebra $\hat{g}_k$ corresponding with Lie algebra $g$ which ...
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WZW primary fields / correlations in terms of current algebra?
Cross-posted from a Mathoverflow thread! Answer there for a bounty ;)
Given the
$\mathfrak{u}_N$ algebra
with generators $L^a$ and commutation relations
$ [L^a,L^b] = \sum_c f^{a,b}_{c} L^c $ ,
the ...
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What does the WZ term in a WZW action means for string theory on group manifolds?
Let $G$ be a semi-simple Lie group. By Cartan's criterion its Killing form $B(X,Y)$ on $\frak g$ is non-degenerate. We can use it to define an inner product on the whole group by left translation
$${\...
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Holographic derivation of correlations functions in $\text{AdS}_3$/$\text{CFT}_2$
Intro
I am interested in finding the correlations functions $\langle A^{a_1}_z(z_1) \cdots A^{a_k}_z(z_k) \rangle$ in the frame of $\text{AdS}_3$/$\text{CFT}_2$ correspondance for 3D gravity and two ...
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Relation between WZW model and gauge transformation
I came across this question while reading Chapter 15 of Conformal Field Theory by Di Francesco.
So the action of the Weiss-Zumino-Witten(WZW) model is as follows:
$$S = \frac{1}{4a^2}\int d^2x {\rm Tr}...
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Is there a character ring for quantum groups?
It is a well known fact that for any (reasonable) group $G$, the character ring and the representation ring are isomorphic,
$$
\chi_{R_1}(g)\chi_{R_2}(g)=\chi_{R_1\otimes R_2}(g),\qquad g\in G
$$
Is ...
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CFTs that are not modular invariant
Are there any 2d CFTs that do not have modular invariant partition functions? All the examples that I know of, like the free boson, WZW models, etc. have modular invariant partition functions.
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2d CFT and WZW model
I have been using Lorenz Eberhardt's 2019 ESI lecture notes on WZW model. Below Equation 3.5 on Page 8, it is written that the current algebra, which forms a Kac-Moody Algebra, is the main organizing ...
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Conformal dimension of conserved current and Current Algebra in CFT
In the 2019 ESI lecture notes on WZW model, right before equation (3.1) Lorenz Eberhardt claims that any conserved current of a CFT has conformal weight (1,0) or (0,1). Can someone please explain why ...
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String theory in ${\rm AdS}_3$ and the ${\rm SL}{(2,\mathbb{R})}$ WZW model on the worldsheet
The WZW model on the sphere $S^2$ with group $G$ and level $k$ is described by the action for a $G$-valued field $g : S^2\to G$ (see these notes by Lorenz Eberhardt):
$$S[g]=\dfrac{1}{4\lambda^2}\int_{...
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