Scalar CFTs and Their Large N Limits

We study scalar conformal field theories whose large $N$ spectrum is fixed by the operator dimensions of either Ising model or Lee-Yang edge singularity. Using numerical bootstrap to study CFTs with $S_N\otimes Z_2$ symmetry, we find a series of kinks whose locations approach $(\Delta^{\text{Ising}}_{\sigma},\Delta^{\text{Ising}}_{\epsilon})$ at $N\rightarrow \infty$. Setting $N=4$, we study the cubic anisotropic fixed point with three spin components. As byproducts of our numerical bootstrap work, we discover another series of kinks whose identification with previous known CFTs remains a mystery. We also show that "minimal models" of $\mathcal{W}_3$ algebra saturate the numerical bootstrap bounds of CFTs with $S_3$ symmetry.Comment: 29 pages, 5 figure

Bootstrapping the N=1\mathcal{N}=1 Wess-Zumino models in three dimensions

Using numerical bootstrap method, we determine the critical exponents of the minimal three-dimensional N = 1 Wess-Zumino models with cubic superpotetential $W\sim d_{ijk}\Phi_i\Phi_j\Phi_k$. The tensor $d_{ijk}$ is taken to be the invariant tensor of either permutation group $S_N$, special unitary group $SU(N)$, or a series of groups called F4 family of Lie groups. Due to the equation of motion, at the Wess-Zumino fixed point, the operator $d_{ijk}\Phi_i\Phi_j\Phi_k$ is a (super)descendant of $\Phi_i$ . We observe such super-multiplet recombination in numerical bootstrap, which allows us to determine the scaling dimension of the super-field $\Phi_i$.Comment: 19 pages, 8 figure

Non-Wilson-Fisher kinks of O(N)O(N) numerical bootstrap: from the deconfined phase transition to a putative new family of CFTs

It is well established that the $O(N)$ Wilson-Fisher (WF) CFT sits at a kink of the numerical bounds from bootstrapping four point function of $O(N)$ vector. Moving away from the WF kinks, there indeed exists another family of kinks (dubbed non-WF kinks) on the curve of $O(N)$ numerical bounds. Different from the $O(N)$ WF kinks that exist for arbitary $N$ in $2<d<4$ dimensions, the non-WF kinks exist in arbitrary dimensions but only for a large enough $N>N_c(d)$ in a given dimension $d$. In this paper we have achieved a thorough understanding for few special cases of these non-WF kinks. The first case is the $O(4)$ bootstrap in 2d, where the non-WF kink turns out to be the $SU(2)_1$ Wess-Zumino-Witten (WZW) model, and all the $SU(2)_{k>2}$ WZW models saturate the numerical bound on the left side of the kink. We further carry out dimensional continuation of the 2d $SU(2)_1$ kink towards the 3d $SO(5)$ deconfined phase transition. We find the kink disappears at around $d=2.7$ dimensions indicating the $SO(5)$ deconfined phase transition is weakly first order. The second interesting observation is, the $O(2)$ bootstrap bound does not show any kink in 2d ($N_c=2$), but is surprisingly saturated by the 2d free boson CFT (also called Luttinger liquid) all the way on the numerical curve. The last case is the $N=\infty$ limit, where the non-WF kink sits at $(\Delta_\phi, \Delta_T)=(d-1, 2d)$ in $d$ dimensions. We manage to write down its analytical four point function in arbitrary dimensions, which equals to the subtraction of correlation functions of a free fermion theory and generalized free theory. An important feature of this solution is the existence of a full tower of conserved higher spin current. We speculate that a new family of CFTs will emerge at non-WF kinks for finite $N$, in a similar fashion as $O(N)$ WF CFTs originating from free boson at $N=\infty$.Comment: 14+2 pages; v2 typo correcte

A roadmap for bootstrapping gauge theories: decoupling operators of conformal field theories in d>2d>2 dimensions

We propose a roadmap for bootstrapping conformal field theories (CFTs) described by gauge theories in dimensions $d>2$. In particular, we provide a simple and workable answer to the question of how to detect the gauge group in the bootstrap calculation. Our recipe is based on the notion of decoupling operator, which has a simple (gauge) group theoretical origin, and is reminiscent of the null operator of $2d$ Wess-Zumino-Witten CFTs in higher dimensions. Using the decoupling operator we can efficiently detect the rank (i.e. color number) of gauge groups, e.g., by imposing gap conditions in the CFT spectrum. We also discuss the physics of the equation of motion, which has interesting consequences in the CFT spectrum as well. As an application of our recipes, we study a prototypical gauge theory, namely the scalar QED which has a $U(1)$ gauge field interacting with critical bosons. In $d=2+\epsilon$ dimensions we successfully solve it by obtaining a kink as well as an island of the scalar QED. Further attempt towards the $3d$ scalar QED is also discussed.Comment: 31 pages plus references, 8 figure

Training-Free Semantic Video Composition via Pre-trained Diffusion Model

The video composition task aims to integrate specified foregrounds and backgrounds from different videos into a harmonious composite. Current approaches, predominantly trained on videos with adjusted foreground color and lighting, struggle to address deep semantic disparities beyond superficial adjustments, such as domain gaps. Therefore, we propose a training-free pipeline employing a pre-trained diffusion model imbued with semantic prior knowledge, which can process composite videos with broader semantic disparities. Specifically, we process the video frames in a cascading manner and handle each frame in two processes with the diffusion model. In the inversion process, we propose Balanced Partial Inversion to obtain generation initial points that balance reversibility and modifiability. Then, in the generation process, we further propose Inter-Frame Augmented attention to augment foreground continuity across frames. Experimental results reveal that our pipeline successfully ensures the visual harmony and inter-frame coherence of the outputs, demonstrating efficacy in managing broader semantic disparities

Precision Bootstrap for the N=1\mathcal{N}=1 Super-Ising Model

In this note we report an improved determination of the scaling dimensions and OPE coefficients of the minimal supersymmetric extension of the 3d Ising model using the conformal bootstrap. We also show how this data can be used as input to the Lorentzian inversion formula, finding good agreement between analytic calculations and numerical extremal spectra once mixing effects are resolved.Comment: 32 pages, 6 figure

A unified meson-baryon potential

We study the spectra of mesons and baryons, composed of light quarks, in the framework of a semirelativistic potential model including instanton induced forces. We show how a simple modification of the instanton interaction in the baryon sector allows a good description of the meson and the baryon spectra using an interaction characterized by a unique set of parameters.Comment: 7 figure

Bootstrapping the N \mathcal{N} = 1 Wess-Zumino models in three dimensions

Using numerical bootstrap method, we determine the critical exponents of the minimal three-dimensional $\mathcal{N}$ = 1 Wess-Zumino models with cubic superpotetential $\mathcal{W}\sim {d}_{ijk}{\Phi}^i{\Phi}^j{\Phi}^k$. The tensor d$_{ijk}$ is taken to be the invariant tensor of either permutation group S$_{N}$, special unitary group SU(N), or a series of groups called F$_{4}$ family of Lie groups. Due to the equation of motion, at the Wess-Zumino fixed point, the operator d$_{ijk}$Φ$^{j}$Φ$^{k}$ is a (super)descendant of Φ$^{i}$. We observe such super-multiplet recombination in numerical bootstrap, which allows us to determine the scaling dimension of the super-field ∆$_{Φ}$

Bootstrapping the minimal N \mathcal{N} = 1 superconformal field theory in three dimensions

We develop the numerical bootstrap technique to study the 2 + 1 dimensional $\mathcal{N}$ = 1 superconformal field theories (SCFTs). When applied to the minimal $\mathcal{N}$ = 1 SCFT, it allows us to determine its critical exponents to high precision. This model was argued in [1] to describe a quantum critical point (QCP) at the boundary of a 3 + 1D topological superconductor. More interestingly, this QCP can be reached by tuning a single parameter, where supersymmetry (SUSY) is realized as an emergent symmetry. We show that the emergent SUSY condition also plays an essential role in bootstrapping this SCFT. But performing a “two-sided” Padé re-summation of the large N expansion series, we calculate the critical exponents for Gross-Neveu-Yukawa models at N =4 and N =8