相关论文: O(N) and O(N) and O(N)
A finite size scaling theory for the partition function zeros and thermodynamic functions of O(N) phi^4-theory in four dimensions is derived from renormalization group methods. The leading scaling behaviour is mean-field like with…
We reconsider critical properties of O(N) scalar models with cubic interactions in $d>4$ dimensions using functional renormalization group equations. Working at next-to-leading order in the derivative expansion, we find non-trivial IR fixed…
We discuss general theories of N scalar fields with O(N) symmetry. In addition to the standard case of linearly realized symmetry there are also examples that carry nonlinear realizations, with the topology of a cylinder $R\times S^{N-1}$…
We study the mixing of operators under renormalization group flow in quantum theories, and prove a non-renormalization theorem at non-linear order. It dictates zeros up to a certain number of loops in anomalous dimension tensors that…
We study the sector of large charge operators $\phi^n$ ($\phi$ being the complexified scalar field) in the $O(2)$ Wilson-Fisher fixed point in $4-\epsilon$ dimensions that emerges when the coupling takes the critical value $g\sim \epsilon$.…
In this work, we compute the anomalous dimensions of the $\phi^Q$ operator in six-dimensional cubic scalar theory. The renormalization analysis is carried out within the framework of the Operator Product Expansion method, while the…
We renormalize the six dimensional cubic theory with an $O(N)$ $\times$ $O(m)$ symmetry at three loops in the modified minimal subtraction (MSbar) scheme. The theory lies in the same universality class as the four dimensional…
We investigate $\phi^{2n+1}$ deformations of the generalized free theory in the $\epsilon$ expansion, where the canonical kinetic term is generalized to a higher-derivative version. For $n=1$, we use the conformal multiplet recombination…
We solve analytically the renormalization-group equation for the potential of the O(N)-symmetric scalar theory in the large-N limit and in dimensions 2<d<4, in order to look for nonperturbative fixed points that were found numerically in a…
We examine anomalous dimensions of higher spin currents in the critical O(N) scalar model and the Gross-Neveu model in arbitrary d dimensions. These two models are proposed to be dual to the type A and type B Vasiliev theories,…
We give a detailed account of the theory of position space renormalization using graphical functions in the case of dimensionally regularized $\phi^4$ theory in four dimensions. In this theory we calculate the beta function, the mass gamma…
We perform a global renormalization group study of O(N) symmetric Wess-Zumino theories and their phases in three euclidean dimensions. At infinite N the theory is solved exactly. The phases and phase transitions are worked out for finite…
We summarize the usual implementations of the large $N$ limit of $O(N)$ models and show in detail why and how they can miss some physically important fixed points when they become singular in the limit $N\to\infty$. Using Wilson's…
We use analytic conformal bootstrap methods to determine the anomalous dimensions and OPE coefficients for large spin operators in general conformal field theories in four dimensions containing a scalar operator of conformal dimension…
Anomalous dimensions of Wilson operators with large Lorentz spin scale logarithmically with the spin. Recent multi-loop QCD calculations of twist-two anomalous dimensions revealed the existence of interesting structure of the subleading…
The critical behavior of a non-local scalar field theory is studied. This theory has a non-local quartic interaction term which involves a real power -\beta of the Laplacian. The parameter \beta can be tuned so as to make that interaction…
We present a study of phi-four theory on noncommutative spaces using a combination of the Wilson renormalization group recursion formula and the solution to the zero dimensional vector/matrix models at large $N$. Three fixed points are…
The three dimensional nonlinear sigma model is unrenormalizable in perturbative method. By using the $\beta$ function in the nonperturbative Wilsonian renormalization group method, we argue that ${\cal N}=2$ supersymmetric nonlinear…
We employ the axiomatic framework of Rychkov and Tan to investigate the critical O$(N)$ vector model with a line defect in $(4-\epsilon)$ dimensions. We assume the fixed point is described by defect conformal field theory and show that the…
We formally extend the CFT techniques introduced in arXiv:1505.00963, to $\phi^{\frac{2d_0}{d_0-2}}$ theory in $d=d_0-\epsilon$ dimensions and use it to compute anomalous dimensions near $d_0=3, 4$ in a unified manner. We also do a similar…