https://cftzoo.net/ 2026-04-17T09:42:50+00:00 https://cftzoo.net/ https://cftzoo.net/lib/tpl/white/images/favicon.ico text/html 2026-04-11T20:39:43+00:00 Ludo Fraser-Taliente (ludo@undisclosed.example.com) https://cftzoo.net/conformal-qed?rev=1775939983&do=diff Conformal QED 3d See <https://arxiv.org/abs/1508.06278> and <https://arxiv.org/abs/1508.06354>. text/html 2026-03-20T15:48:36+00:00 Ludo Fraser-Taliente (ludo@undisclosed.example.com) https://cftzoo.net/ising?rev=1774021716&do=diff Ising model 3d The Ising model is an interacting CFT in three dimensions. For related models in other dimensions, see . The Ising model is the $N=1$ case of the $O(N)$ model. The Ising CFT also goes by the name “Wilson-Fisher fixed point” (in any $d < 4$). Another terminological difficulty: $\sigma$$\epsilon$$$ \Delta_\sigma = 0.5181489(10)\text{ and } \Delta_\epsilon = 1.412625(10)\text. $$$$ \lambda_{\sigma\sigma\epsilon} = 1.0518537(41)\text{ and } \lambda_{\epsilon\epsilon\epsilon} = 1.53… text/html 2026-03-20T15:48:03+00:00 Ludo Fraser-Taliente (ludo@undisclosed.example.com) https://cftzoo.net/on_model?rev=1774021683&do=diff $O(N)$ model 3d holographic The special cases of the $O(2)$ model and $O(3)$ model are particularly well-studied. Higher values of $N$ do come up occasionally, see for instance the $O(4)$ model. The Ising model is the case $N=1$, and the case $N=0$ is covered by self-avoiding walks. This also goes by the name of the “n-vector model”. Its Ginzburg-Landau description is the critical point of an O$(N)$$\phi_i$$\phi^4 =(\phi_i \phi_i)^2$$\sigma$$N-1$$(N)$$N$$N+1$ text/html 2026-03-19T00:31:22+00:00 Ludo Fraser-Taliente (ludo@undisclosed.example.com) https://cftzoo.net/minimal_models?rev=1773880282&do=diff Minimal Models 2d Minimal models are 2d conformal field theories whose spectra consist of a finite number of representations of the Virasoro algebra. Construction The requirement for of a finite number of representations is quite constraining; generically the OPE $ \mathcal{O}_1 \mathcal{O}_2 = \sum_i C_{12i} \mathcal{O}_i$ will contain an infinite number of primaries. In some cases, the right-hand side contains a finite number of operators because the $C_{12i}$$i$$\mathcal{O}_1$$\mathcal{O… text/html 2026-03-19T00:24:06+00:00 Ludo Fraser-Taliente (ludo@undisclosed.example.com) https://cftzoo.net/null_results?rev=1773879846&do=diff Null Results This page is meant to be a resource for informally keeping track of null results, which often are not published but which still may be quite useful to other researchers trying to do the same thing. Minimal models One might want to find the unitary $\mathcal{M}_{m+1,m}$$\frac{1}{2}(\partial \phi)^2 + g \phi^{2(m-1)}$$d=d_c -\epsilon$$d_c = 2(m-1)/(m-2)$$m$$d=2$$d_c$$\epsilon$ text/html 2026-03-19T00:10:55+00:00 Ludo Fraser-Taliente (ludo@undisclosed.example.com) https://cftzoo.net/tag:holographic?rev=1773879055&do=diff Holographic CFTs A holographic CFT is usually described as a CFT which has a weakly coupled gravity dual in the sense of the AdS/CFT correspondence. This typically requires a large number of degrees of freedom in the original CFT, i.e. large-$N$. List of holographic CFTs text/html 2026-03-19T00:09:26+00:00 Ludo Fraser-Taliente (ludo@undisclosed.example.com) https://cftzoo.net/list_of_cfts?rev=1773878966&do=diff List of CFTs Here is a list of CFTs. They are organized by dimension. Note that some CFTs, like the gaussian theories and percolation, can be defined in any number of dimensions. This allows their conformal data to be analytically continued between dimensions, connecting otherwise apparently different CFTs.$T_\mu{}^\mu = 0$$T_{00} = H = 0$$c<1$$c>1$$d>6$$d>6$$d$$d$$d$$p$$(d+1,1)$$S= \int d^d x O(x)$$x$$\phi$$\Delta$$\phi^4$$d$$\Delta \to \Delta_{\phi, \text{Ising}}$$1/8$$d=2$$0.518$$d=3$$T^{\mu… text/html 2026-03-17T19:14:57+00:00 Ludo Fraser-Taliente (ludo@undisclosed.example.com) https://cftzoo.net/tag:largen?rev=1773774897&do=diff Large N CFTs. text/html 2026-03-05T15:57:26+00:00 Ludo Fraser-Taliente (ludo@undisclosed.example.com) https://cftzoo.net/gaussian?rev=1772726246&do=diff Gaussian CFTs are theories with a quadratic action. They can be defined in arbitrary dimension. 'The free scalar' refers to the unique theory in flat space with a scalar field at the unitarity bound, $\Delta_\phi = \frac{d-2}{2}$.