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Register a new userSymmetry and universality of multi-field interactions in $6-epsilon$ dimensions
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We outline a general strategy developed for the analysis of critical models, which we apply to obtain a heuristic classification of all universality classes with up to three field-theoretical scalar order parameters in $d=6-epsilon$ dimensions. As expected by the paradigm of universality, each class is uniquely characterized by its symmetry group and by a set of its scaling properties, neither of which are built-in by the formalism but instead emerge nontrivially as outputs of our computations. For three fields, we find several solutions mostly with discrete symmetries. These are nontrivial conformal field theory candidates in less than six dimensions, one of which is a new perturbatively unitary critical model.
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We study the Blume-Capel universality class in $d=frac{10}{3}-epsilon$ dimensions. The RG flow is extracted by looking at poles in fractional dimension of three loop diagrams using $overline{rm MS}$. The theory is the only nontrivial universality class which admits an expansion to three dimensions with $epsilon=frac{1}{3}<1$. We compute the relevant scaling exponents and estimate some of the OPE coefficients to the leading order. Our findings agree with and complement CFT results. Finally we discuss a family of nonunitary multicritical models which includes the Lee-Yang and Blume-Capel classes as special cases.
We present a trace formula for a Witten type Index for superconformal field theories in d=3,5 and 6 dimensions, generalizing a similar recent construction in d=4. We perform a detailed study of the decomposition of long representations into sums of short representations at the unitarity bound to demonstrate that our trace formula yields the most general index (i.e. quantity that is guaranteed to be protected by superconformal symmetry alone) for the corresponding superalgebras. Using the dual gravitational description, we compute our index for the theory on the world volume of N M2 and M5 branes in the large N limit. We also compute our index for recently constructed Chern Simons theories in three dimensions in the large N limit, and find that, in certain cases, this index undergoes a large N phase transition as a function of chemical potentials.
We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory having an internal U(1) symmetry. We provide analytic expressions for the charged moments corresponding to the resolution of both relative entropies and distances for general integer $n$. For the relative entropies, these formulas are manageable and the analytic continuation to $n=1$ can be worked out in most of the cases. Conversely, for the distances the corresponding charged moments become soon untreatable as $n$ increases. A remarkable result is that relative entropies and distances are the same for all symmetry sectors, i.e. they satisfy entanglement equipartition, like the entropies. Moreover, we exploit the OPE expansion of composite twist fields, to provide very general results when the subsystem is much smaller than the total system. We focus on the massless compact boson and our results are tested against exact numerical calculations in the XX spin chain.
We determine both analytically and numerically the entanglement between chiral degrees of freedom in the ground state of massive perturbations of 1+1 dimensional conformal field theories quantised on a cylinder. Analytic predictions are obtained from a variational Ansatz for the ground state in terms of smeared conformal boundary states recently proposed by J. Cardy, which is validated by numerical results from the Truncated Conformal Space Approach. We also extend the scope of the Ansatz by resolving ground state degeneracies exploiting the operator product expansion. The chiral entanglement entropy is computed both analytically and numerically as a function of the volume. The excellent agreement between the analytic and numerical results provides further validation for Cardys Ansatz. The chiral entanglement entropy contains a universal $O(1)$ term $gamma$ for which an exact analytic result is obtained, and which can distinguish energetically degenerate ground states of gapped systems in 1+1 dimensions.
Boundaries in three-dimensional $mathcal{N}=2$ superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining $2d$ boundary algebra exhibits $mathcal{N}=(0,2)$ or $mathcal{N}=(1,1)$ supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For $mathcal{N}=(1,1)$ supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the $epsilon$-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a supersymmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.
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