# 2d conformal field theory

Then the scalar product endows the space of states with the structure of a Hilbert space. In this chapter the 2d Wess-Zumino-Novikov-Witten (WZNW) models (as the NLSM in field theory) are discussed from the viewpoint of 2d Conformai Field Theory (CFT) [45]. Moreover, they provide the foundation upon which the quantisation of string theory is built. We also consider supersymmetric generalizations of the WZNW models and gauging of their symmetries. Responsible Officer: Head of Department/ Relations between 2D and 4D Conformal Quantum Field Theory Diploma thesis by Daniel Meise from Soest Institute for Theoretical Physics Georg-August-Universität Göttingen January 2010. The conformal field theories (CFTs), in particular, admit a symmetry under rescaling (and more). Jeorg Teschner, A guide to two-dimensional conformal field theory, arXiv:1708.00680. In terms of representation theory, the quantum state space is built from representations of the algebra of infinitesimal symmetries that are indecomposable rather than irreducible. They also appear in string theories when spacetime is enlarged to admit fermionic directions, the famous AdS/CFT correspondence, and the study of black holes in three spacetime dimensions. B271 (1986). You appear to be using Internet Explorer 7, or have compatibility view turned on. Quantum field theories describe and unify the fundamental forces of nature, with the possible exception of gravity. For a discussion of mathematical formalization (vertex operator algebras, conformal nets, functorial QFT) see. Inspired by the recent work of Knizhnik, Polyakov and Zamolodchikov on the 2D quantum gravity in the “light cone” gauge, we present a proposal for solving the theory in the usual conformal gauge. There is a large class of 4d N=2 superconformal field theories called the theory of class S, and the corresponding VOAs are called chiral algebras of class S. This symmetry group is called the conformal group. These theories are relativistic, hence their symmetries include translations and Lorentz boosts. A conformal field theory is unitary if its space of states has a positive definite scalar product such that the dilation operator is self-adjoint. Not logged in This service is more advanced with JavaScript available, Quantum Non-linear Sigma-Models Phys. Updated: 15 January 2019/ The canonical reference for learning conformal ﬁeld theory is the excellent review by Ginsparg. © 2020 Springer Nature Switzerland AG. 45.56.221.112. Nuclear Physics B321 (1989) 509-527 North-Holland, Amsterdam CONFORMAL FIELD THEORY AND 2D QUANTUM GRAVITY Jacques DISTLER and Hikaru KAWAI* Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, NY 14853, USA Received 29 August 1988 (Revised 3 February 1989) Inspired by the recent work of Knizhnik, Polyakov and Zamolodchikov on the solution of 2D … Quantum field theories describe and unify the fundamental forces of nature, with the possible exception of gravity. Phys. Not affiliated B241 (1984). 2D conformal field theory. Applied Conformal Field Theory ... plications of conformal ﬁeld theory were covered in D. Friedan’s lectures, which followed. Research being undertaken at the ANU aims to better understand the mathematical structures underlying CFT. Exactly Solved Models in Statistical Mechanics, ANU Centre for Mathematical & Theoretical Physics. The properties of so-called logarithmic CFTs are of particular interest. Aside from applications to physics, the development of 2D CFT has also led to an enormous amount of mathematical progress in a wide variety of seemingly disparate fields. Unable to display preview. In two dimensions, the algebra of infinitesimal conformal transformations is infinite-dimensional. The standard reference for the material of the ﬁrst three sections is [1]. In mathematics, a recent exciting development is that logarithmic CFT should be closely related to the theory of Schramm-Loewner Evolutions. Some of the review articles that have inﬂuenced the presentation of the This is a preview of subscription content, https://doi.org/10.1007/978-3-662-04192-5_5. Logarithmic theories arise naturally when considering non-local observables, such as crossing probabilities and fractal dimensions, in many statistical lattice models (percolation, Ising). The Australian National University, Canberra A 2D CFT is therefore very strongly constrained by its symmetries and, in favourable cases, these symmetries can be used to exactly solve the theory. James E. Tener, Representation theory in chiral conformal field theory: from fields to observables (arXiv:1810.08168) In this chapter the 2d Wess-Zumino-Novikov-Witten (WZNW) models (as the NLSM in field theory) are discussed from the viewpoint of 2d Conformai Field Theory (CFT) [45]. Part of Springer Nature. Page Contact: Physics Webmaster, +61 2 6125 5111 We also consider supersymmetric generalizations of the WZNW models and gauging of their symmetries. A quantum field theory … Your browser is not supported by ANU web styles. Cite as. ABN : 52 234 063 906. Field Theory”, Nucl. These keywords were added by machine and not by the authors. Over 10 million scientific documents at your fingertips. Such theories accurately describe the thermodynamic limit of local observables in statistical lattice models such as percolation and the Ising model. Download preview PDF. Contents ... and a conformal ﬁeld theory without gravity living on the boundary of that space. Quantum field theories describe and unify the fundamental forces of nature, with the possible exception of gravity. This process is experimental and the keywords may be updated as the learning algorithm improves. Recently, Beem, Lemos, Liendo, Peelaers, Rastelli and van Rees have discovered a 4d/2d duality which associates a VOA to any 4d N=2 superconformal field theory. A quantum field theory may have more symmetries, however. The application to string theory was explained by Friedan, Martinec and Shenker in “Conformal Invariance, Supersymmetry and String Theory”, Nucl. We also consider supersymmetric generalizations of the WZNW models and gauging of their symmetries. Our results for the critical exponents of the theory agree with the genus-zero results of KPZ.

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