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Register a new userCharging the $O(N)$ model
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We determine, for the first time, the scaling dimensions of a family of fixed-charge operators stemming from the critical $O(N)$ model in 4-$epsilon$ dimensions to the leading and next to leading order terms in the charge expansion but to all-orders in the coupling. We test our results to the maximum known order in perturbation theory while determining higher order terms.
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We study dual strong coupling description of integrability-preserving deformation of the $O(N)$ sigma model. Dual theory is described by a coupled theory of Dirac fermions with four-fermion interaction and bosonic fields with exponential interactions. We claim that both theories share the same integrable structure and coincide as quantum field theories. We construct a solution of Ricci flow equation which behaves in the UV as a free theory perturbed by graviton operators and show that it coincides with the metric of the $eta-$deformed $O(N)$ sigma-model after $T-$duality transformation.
We apply a semi-classical method to compute the conformal field theory (CFT) data for the U(N)xU(N) non-abelian Higgs theory in four minus epsilon dimensions at its complex fixed point. The theory features more than one coupling and walking dynamics. Given our charge configuration, we identify a family of corresponding operators and compute their scaling dimensions which remarkably agree with available results from conventional perturbation theory validating the use of the state-operator correspondence for a complex CFT.
We study the double scaling limit of the $O(N)^3$-invariant tensor model, initially introduced in Carrozza and Tanasa, Lett. Math. Phys. (2016). This model has an interacting part containing two types of quartic invariants, the tetrahedric and the pillow one. For the 2-point function, we rewrite the sum over Feynman graphs at each order in the $1/N$ expansion as a emph{finite} sum, where the summand is a function of the generating series of melons and chains (a.k.a. ladders). The graphs which are the most singular in the continuum limit are characterized at each order in the $1/N$ expansion. This leads to a double scaling limit which picks up contributions from all orders in the $1/N$ expansion. In contrast with matrix models, but similarly to previous double scaling limits in tensor models, this double scaling limit is summable. The tools used in order to prove our results are combinatorial, namely a thorough diagrammatic analysis of Feynman graphs, as well as an analysis of the singularities of the relevant generating series.
Three related analyses of $phi^4$ theory with $O(N)$ symmetry are presented. In the first, we review the $O(N)$ model over the $p$-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking in an ultrametric context. We demonstrate the existence of a Wilson-Fisher fixed point using an $epsilon$ expansion, and we show how to obtain leading order results for the anomalous dimensions of low dimension operators near the fixed point. Along the way, we note an important aspect of ultrametric field theories, which is a non-renormalization theorem for kinetic terms. In the second analysis, we employ large $N$ methods to establish formulas for anomalous dimensions which are valid equally for field theories over the $p$-adic numbers and field theories on $mathbb{R}^n$. Results for anomalous dimensions agree between the first and second analyses when they can be meaningfully compared. In the third analysis, we consider higher derivativ
In this article we explore a certain definition of alternate quantization for the critical O(N) model. We elaborate on a prescription to evaluate the Renyi entropy of alternately quantized critical O(N) model. We show that there exists new saddles of the q-Renyi free energy functional corresponding to putting certain combinations of the Kaluza-Klein modes into alternate quantization. This leads us to an analysis of trying to determine the true state of the theory by trying to ascertain the global minima among these saddle points.
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