arXiv subjects

Ning Su

Publications and source records attributed to Ning Su.

33 records · Page 2Linked to original sources

arXiv2021

A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ 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 \emph{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 critical gauge theory, namely the scalar QED which has a $U(1)$ gauge field interacting with critical bosons. We show that the scalar QED can be solved by conformal bootstrap, namely we have obtained its kinks and islands in both $d=3$ and $d=2+ε$ dimensions.

hep-th↗

arXiv2021

Non-Wilson-Fisher kinks of $O(N)$ 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 $2 N_c(d)$ 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 $(Δ_ϕ, Δ_T)=(d-1, 2d)$ 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 $N=\infty$.

hep-th↗

arXiv2020

Topological defects in rotating spin-orbit-coupled dipolar spin-1 Bose-Einstein condensates

We consider the topological defects and spin structures of spin-1 Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) and dipole-dipole interaction (DDI) in a rotating harmonic plus quartic trap. The combined effects of SOC, DDI and rotation on the ground-state phases of the system are analyzed. Our results show that for fixed rotation frequency structural phase transitions can be achieved by adjusting the magnitudes of the SOC and DDI. A ground-state phase diagram is given as a function of the SOC and DDI strengths. It is shown that the system exhibits rich quantum phases including vortex string phase with isolated density peaks (DPs), triangular (square) vortex lattice phase with DPs, checkerboard phase, and stripe phase with hidden vortices and antivortices. For given SOC and DDI strengths, the system can display pentagonal vortex lattice with DPs, vortex necklace with DPs, and exotic topological structure composed of multi-layer visible vortex necklaces, a hidden giant vortex and hidden vortex necklaces, depending on the rotation frequency. In addition, the system sustains fascinating novel spin textures and skyrmion excitations, such as an antiskyrmion pair, antiskyrmion-half-antiskyrmion (antiskyrmion-antimeron) cluster, skyrmion-antiskyrmion lattice, skyrmion-antiskyrmion cluster, skyrmion-antiskyrmion-meron-antimeron lattice, double-layer half-antiskyrmion necklaces, and composite giant-antiskyrmion-antimeron necklaces.

cond-mat.quant-gas↗

arXiv2020

Carving out OPE space and precise $O(2)$ model critical exponents

We develop new tools for isolating CFTs using the numerical bootstrap. A "cutting surface" algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d $O(2)$ model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old $8σ$ discrepancy between theory and experiment.

hep-th↗

arXiv2019

Topological excitations in rotating Bose-Einstein condensates with Rashba-Dresselhaus spin-orbit coupling in a two-dimensional optical lattice

We study the ground-state configurations and spin textures of rotating two-component Bose-Einstein condensates (BECs) with Rashba-Dresselhaus spin-orbit coupling (RD-SOC), which are confined in a two-dimensional (2D) optical lattice plus a 2D harmonic trap. In the absence of rotation, a relatively small isotropic 2D RD-SOC leads to the generation of ghost vortices for initially miscible BECs, while it gives rise to the creation of rectangular vortex-antivortex lattices for initially immiscible BECs. As the strength of the 2D RD-SOC enhances, the visible vortices or the 2D vortex-antivortex chains are created for the former case, whereas the rectangular vortex-antivortex lattices are transformed into vortex-antivortex rings for the later case. For the initially immiscible BECs with fixed 2D RD-SOC strength, the increase of rotation frequency can result in the structural phase transition from square vortex lattice to irregular triangular vortex lattice and the system transition from initial phase separation to phase mixing. In addition, we analyze the combined effects of 1D RD-SOC and rotation on the vortex configurations of the ground states for the case of initial phase separation. The increase of 1D SOC strength, rotation frequency or both of them may result in the formation of vortex chain and phase mixing. Furthermore, the typical spin textures for both the cases of 2D RD-SOC and 1D RD-SOC are discussed. It is shown that the system favors novel spin textures and skyrmion configurations including an exotic skyrmion-half-skyrmion lattice (skyrmion-meron lattice), a complicated meron lattice, a skyrmion chain, and a Bloch domain wall.

cond-mat.quant-gas↗

arXiv2019

Bootstrapping the $\mathcal{N}=1$ 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 $W\sim d_{ijk}Φ_iΦ_jΦ_k$. 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 $d_{ijk}Φ_iΦ_jΦ_k$ 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 $Φ_i$.

hep-th↗

arXiv2018

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

Using numerical bootstrap method, we determine the critical exponents of the minimal three-dimensional $\mathcal{N}=1$ superconformal field theory (SCFT) to be $η_σ=0.168888(60)$ and $ω=0.882(9)$. The model was argued in arXiv:1301.7449 to describe a quantum critical point (QCP) at the boundary a $3+1$D topological superconductor. More interestingly, the QCP can be reached by tuning a single parameter, where supersymmetry (SUSY) is realised as an emergent symmetry. By imposing emergent SUSY in numerical bootstrap, we find that the conformal scaling dimension of the real scalar operator $σ$ is highly restricted. If we further assume the SCFT to have only two time-reversal parity odd relevant operators, $σ$ and $σ'$, we find that allowed region for $Δ_σ$ and $Δ_{σ'}$ becomes an isolated island. The result is obtained by considering not only the four point correlator $\langle σσσσ\rangle$, but also $\langle σεσε\rangle$ and $\langle εεεε\rangle$, with $ε\sim σ^2$ being the superconformal descendant of $σ$.

hep-th↗

arXiv2017

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 $(Δ^{\text{Ising}}_σ,Δ^{\text{Ising}}_ε)$ 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.

hep-th↗

arXiv2017

3D CFT Archipelago from Single Correlator Bootstrap

We show that the scaling dimensions of lowest operators in conformal field theories (CFTs) can be isolated in small and closed regions from single correlator bootstrap. We find the conserved currents play crucial roles in bootstrapping the crossing equation. By imposing a mild gap between the scaling dimensions of the conserved current and its next operator, the scaling dimensions of lowest operators are forced to lie in small isolated regions, i.e., these CFTs can be almost fixed by few lowest operators in certain channels. For CFTs with extended supersymmetry, the single correlator crossing equation involves several conserved or shorted operators and by imposing gaps in these sectors it is possible to isolate different CFTs. Specifically, we bootstrap the isolated regions corresponding to the 3D Ising model, $O(N)$ vector model, $N=1,2$ supersymmetric Ising models by introducing mild gaps in certain sectors with conserved or shorted operators.

hep-th↗

arXiv2016

$ϕ^3$ theory with $F_4$ flavor symmetry in $6-2ε$ dimensions: 3-loop renormalization and conformal bootstrap

We consider $ϕ^3$ theory in $6-2ε$ with $F_4$ global symmetry. The beta function is calculated up to 3 loops, and a stable unitary IR fixed point is observed. The anomalous dimensions of operators quadratic or cubic in $ϕ$ are also computed. We then employ conformal bootstrap technique to study the fixed point predicted from the perturbative approach. For each putative scaling dimension of $ϕ$ ($Δ_ϕ)$, we obtain the corresponding upper bound on the scaling dimension of the second lowest scalar primary in the ${\mathbf 26}$ representation $(Δ^{\rm 2nd}_{\mathbf 26})$ which appears in the OPE of $ϕ\timesϕ$. In $D=5.95$, we observe a sharp peak on the upper bound curve located at $Δ_ϕ$ equal to the value predicted by the 3-loop computation. In $D=5$, we observe a weak kink on the upper bound curve at $(Δ_ϕ,Δ^{\rm 2nd}_{\mathbf 26})$=$(1.6,4)$.

hep-th↗

arXiv2016

Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N) Models

We use the conformal bootstrap approach to explore $5D$ CFTs with $O(N)$ global symmetry, which contain $N$ scalars $ϕ_i$ transforming as $O(N)$ vector. Specifically, we study multiple four-point correlators of the leading $O(N)$ vector $ϕ_i$ and the $O(N)$ singlet $σ$. The crossing symmetry of the four-point functions and the unitarity condition provide nontrivial constraints on the scaling dimensions ($Δ_ϕ$, $Δ_σ$) of $ϕ_i$ and $σ$. With reasonable assumptions on the gaps between scaling dimensions of $ϕ_i$ ($σ$) and the next $O(N)$ vector (singlet) scalar, we are able to isolate the scaling dimensions $(Δ_ϕ$, $Δ_σ)$ in small islands. In particular, for large $N=500$, the isolated region is highly consistent with the result obtained from large $N$ expansion. We also study the interacting $O(N)$ CFTs for $1\leqslant N\leqslant100$. Isolated regions on $(Δ_ϕ,Δ_σ)$ plane are obtained using conformal bootstrap program with lower order of derivatives $Λ$; however, they disappear after increasing $Λ$. We think these islands are corresponding to interacting but nonunitary $O(N)$ CFTs. Our results provide a lower bound on the critical value $N_c>100$, below which the interacting $O(N)$ CFTs turn into nonunitary. The critical value is unexpectedly large comparing with previous estimations.

hep-th↗

arXiv2016

The Most General $4\mathcal{D}$ $\mathcal{N}=1$ Superconformal Blocks for Scalar Operators

We compute the most general superconformal blocks for scalar operators in $4\mathcal{D}$ $\mathcal{N}=1$ superconformal field theories. Specifically we employ the supershadow formalism to study the four-point correlator $\langleΦ_1 Φ_2 Φ_3 Φ_4\rangle$, in which the four scalars $Φ_i$ have arbitrary scaling dimensions and R-charges with the only constraint from R-symmetry invariance of the four-point function. The exchanged operators can have arbitrary R-charges. Our results extend previous studies on $4\mathcal{D}$ $\mathcal{N}=1$ superconmformal blocks to the most general case, which are the essential ingredient for superconformal bootstrap, especially for bootstrapping mixed correlators of scalars with independent scaling dimensions and R-charges.

hep-th↗

arXiv2016

Three-Point Disc Amplitudes in the RNS Formalism

We calculate all tree level string theory vacuum to Dp-brane disc amplitudes involving an arbitrary RR-state and two NS-NS vertex operators. This computation was earlier performed by K. Becker, Guo, and Robbins for the simplest case of a RR-state of type C_{p-3}. Here we use the aid of a computer to calculate all possible three-point amplitudes involving a RR-vertex operator of type C_{p+1+2k}.

hep-th↗

arXiv2014

Finite-temperature three-point function in 2D CFT

We calculate the finite temperature three-point correlation function for primary fields in a 2D conformal field theory in momentum space. This result has applications to any strongly coupled field theory with a 2D CFT dual, as well as to Kerr/CFT.

hep-th↗

arXiv2011

Local strong solution to the compressible magnetohydrodynamic flow with large data

The three-dimensional compressible magnetohydrodynamic (MHD) isentropic flow with zero magnetic diffusivity is studied. The vanishing magnetic diffusivity causes significant difficulties due to the loss of dissipation of the magnetic field. The existence and uniqueness of local in time strong solution with large initial data is established. The strong solution has weaker regularity than the classical solution. A generalized Lax-Milgram theorem and a Schauder-Tychonoff-type fixed point argument are applied with novel techniques and estimates for the strong solution.

math.AP↗