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Register a new userFusion of spin fields in $W_3$ conformal field theories
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In generic conformal field theories with $W_3$ symmetry, we identify a primary field $sigma$ with rational Kac indices, which produces the full $mathbb{Z}_3$ charged and neutral sectors by the fusion processes $sigma times sigma$ and $sigma times sigma^*$, respectively. In this sense, this field generalises the $mathbb{Z}_3$ fundamental spin field of the three-state Potts model. Among the degenerate fields produced by these fusions, we single out a `parafermion field $psi$ and an `energy field $varepsilon$. In analogy with the Virasoro case, the exact curves for conformal dimensions $(h_sigma,h_psi)$ and $(h_sigma,h_varepsilon)$ are expected to give close estimates for the unitarity bounds in the conformal bootstrap analysis.
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We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions, focussing on free fermion models and Wess-Zumino-Witten models. To this end, we utilize a recently introduced operator-algebraic framework for Wilson-Kadanoff renormalization. In this setting, we prove the convergence of the approximation of the Virasoro generators by the Koo-Saleur formula. From this, we deduce the convergence of lattice approximations of conformal correlation functions to their continuum limit. In addition, we show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories.
Higgs fields on gauge-natural prolongations of principal bundles are defined by invariant variational problems and related canonical conservation laws along the kernel of a gauge-natural Jacobi morphism.
We investigate a new property of nets of local algebras over 4-dimensional globally hyperbolic spacetimes, called punctured Haag duality. This property consists in the usual Haag duality for the restriction of the net to the causal complement of a point $p$ of the spacetime. Punctured Haag duality implies Haag duality and local definiteness. Our main result is that, if the theory is locally covariant in the sense of Brunetti, Fredenhagen and Verch, then also the converse holds. The free Klein-Gordon field provides an example in which this property is verified.
In the Lagrangian approach to 2-dimensional sigma models, B-fields and D-branes contribute topological terms to the action of worldsheets of both open and closed strings. We show that these terms naturally fit into a 2-dimensional, smooth open-closed functorial field theory (FFT) in the sense of Atiyah, Segal, and Stolz-Teichner. We give a detailed construction of this smooth FFT, based on the definition of a suitable smooth bordism category. In this bordism category, all manifolds are equipped with a smooth map to a spacetime target manifold. Further, the object manifolds are allowed to have boundaries; these are the endpoints of open strings stretched between D-branes. The values of our FFT are obtained from the B-field and its D-branes via transgression. Our construction generalises work of Bunke-Turner-Willerton to include open strings. At the same time, it generalises work of Moore-Segal about open-closed TQFTs to include target spaces. We provide a number of further features of our FFT: we show that it depends functorially on the B-field and the D-branes, we show that it is thin homotopy invariant, and we show that it comes equipped with a positive reflection structure in the sense of Freed-Hopkins. Finally, we describe how our construction is related to the classification of open-closed TQFTs obtained by Lauda-Pfeiffer.
$CPT$ groups of higher spin fields are defined in the framework of automorphism groups of Clifford algebras associated with the complex representations of the proper orthochronous Lorentz group. Higher spin fields are understood as the fields on the Poincar{e} group which describe orientable (extended) objects. A general method for construction of $CPT$ groups of the fields of any spin is given. $CPT$ groups of the fields of spin-1/2, spin-1 and spin-3/2 are considered in detail. $CPT$ groups of the fields of tensor type are discussed. It is shown that tensor fields correspond to particles of the same spin with different masses.
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