WESS-ZUMINO-WITTEN MODEL AS A THEORY OF FREE FIELDS

1990 ◽  
Vol 05 (13) ◽  
pp. 2495-2589 ◽  
Author(s):  
A. GERASIMOV ◽  
A. MOROZOV ◽  
M. OLSHANETSKY ◽  
A. MARSHAKOV ◽  
S. SHATASHVILI
Keyword(s):  
Riemann Surfaces ◽  
Central Charge ◽  
Free Field ◽  
Heisenberg Algebra ◽  
Momentum Tensor ◽  
Point Of View ◽  
Special Role ◽  
Field Representation ◽  
Conformal Blocks ◽  
Free Fields

The free field representation or "bosonization" rule1 for Wess-Zumino-Witten model (WZWM) with arbitrary Kac-Moody algebra and arbitrary central charge is discussed. Energy-momentum tensor, arising from Sugawara construction, is quadratic in the fields. In this way, all known formulae for conformal blocks and correlators may be easily reproduced as certain linear combinations of correlators of these free fields. Generalization to conformal blocks on arbitrary Riemann surfaces is straightforward. However, projection rules in the spirit of Ref. 2 are not specified. The special role of βγ systems is emphasized. From the mathematical point of view, the construction involved represents generators of Kac-Moody (KM) algebra in terms of generators of a Heisenberg one. If WZW Lagrangian is considered as d−1 of Kirillov form on an orbit of KM algebra,3 then the free fields of interest (i.e. generators of the Heisenberg algebra) diagonalize Kirillov form and the action. Reduction of KM algebra within the same construction should naturally lead to arbitrary coset models.

scholarly journals Free field representation for WZNW models on Riemann surfaces

1990 ◽  
Vol 245 (3-4) ◽  
pp. 453-464 ◽  
Author(s):  
M. Frau ◽  
A. Lerda ◽  
J.G. McCarthy ◽  
S. Sciuto ◽  
J. Sidenius
Keyword(s):  
Riemann Surfaces ◽  
Free Field ◽  
Field Representation

scholarly journals FREE-FIELD REPRESENTATION OF GROUP ELEMENT FOR SIMPLE QUANTUM GROUPS

1998 ◽  
Vol 13 (10) ◽  
pp. 1651-1707 ◽  
Author(s):  
ALEXEI MOROZOV ◽  
LUC VINET
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Free Field ◽  
Group Element ◽  
Field Representation ◽  
Universal Formula ◽  
Simple Quantum ◽  
Free Fields ◽  
Usual Formula

A representation of the group element (also known as "universal [Formula: see text]-matrix") which satisfies Δ(g)=g⊗g, is given in the form [Formula: see text]where [Formula: see text], qi= q‖αi‖2/2 and Hi=2Hαi/ ‖αi‖2 and T±i are the generators of quantum group associated respectively with Cartan algebra and the simple roots. The "free fields" χ, ϕ, ψ form a Heisenberg-like algebra: [Formula: see text] We argue that the d G -parametric "manifold" which g spans in the operator-valued universal envelopping algebra, can also be invariant under the group multiplication g→ g′ · g′′. The universal ℛ-matrix with the property that ℛ(g⊗ I)(I⊗g)= (I⊗ g)(g⊗ I)ℛ is given by the usual formula [Formula: see text]

scholarly journals N = 2 SUPERCONFORMAL FIELD THEORY ON THE BASIS OF osp(2|2)

1998 ◽  
Vol 13 (01) ◽  
pp. 47-57 ◽  
Author(s):  
A. SHAFIEKHANI ◽  
W.-S. CHUNG
Keyword(s):  
Central Charge ◽  
Free Field ◽  
Irreducible Representations ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Field Representation ◽  
Superconformal Field Theory ◽  
Systematic Scheme ◽  
Free Field Realization ◽  
Stress Energy

Using a unified and systematic scheme, the free field realization of irreducible representations of osp(2|2) is constructed. By using these realizations, the correlation functions of N = 2 superconformal model based on osp(2|2) symmetry and free field representation of [Formula: see text] generators are calculated. Free field representation of currents are used to determine the stress-energy tensor and the central charge of the model.

MODULAR INVARIANT ONE-POINT CORRELATION FUNCTIONS FOR SU(2) WESS-ZUMINO MODEL

1992 ◽  
Vol 07 (25) ◽  
pp. 6257-6272 ◽  
Author(s):  
O.D. ANDREEV
Keyword(s):  
Correlation Functions ◽  
Riemann Surfaces ◽  
Free Field ◽  
Necessary Condition ◽  
Modular Invariant ◽  
Field Representation ◽  
Conformal Field ◽  
Higher Genus ◽  
Point Correlation ◽  
Zumino Model

We calculate one-point correlation functions of SU(2) Wess-Zumino model (WZM) on a torus using the Wakimoto free field representation. Their modular invariance is proved. It is a necessary condition of extending the WZ conformal field theory to higher genus Riemann surfaces.

scholarly journals Trinion conformal blocks from topological strings

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Ioana Coman ◽  
Elli Pomoni ◽  
Joerg Teschner
Keyword(s):  
Topological String ◽  
Free Field ◽  
Partition Functions ◽  
Integration Contour ◽  
Topological Vertex ◽  
Field Representation ◽  
Conformal Blocks ◽  
Starting Point ◽  
Topological Recursion ◽  
Rank One

Abstract In this paper we investigate the relation between conformal blocks of Liouville CFT and the topological string partition functions of the rank one trinion theory T2. The partition functions exhibit jumps when passing from one chamber in the parameter space to another. Such jumps can be attributed to a change of the integration contour in the free field representation of Liouville conformal blocks. We compare the partition functions of the T2 theories representing trifundamental half hypermultiplets in N = 2, d = 4 field theories to the partition functions associated to bifundamental hypermultiplets. We find that both are related to the same Liouville conformal blocks up to inessential factors. In order to establish this picture we combine and compare results obtained using topological vertex techniques, matrix models and topological recursion. We furthermore check that the partition functions obtained by gluing two T2 vertices can be represented in terms of a four point Liouville conformal block. Our results indicate that the T2 vertex offers a useful starting point for developing an analog of the instanton calculus for SUSY gauge theories with trifundamental hypermultiplets.

FREE FIELD REPRESENTATION OF THE N=3 SUPERCONFORMAL ALGEBRA FROM HAMILTONIAN REDUCTION OF osp(3|2) AFFINE LIE SUPERALGEBRA

1993 ◽  
Vol 08 (19) ◽  
pp. 1763-1777 ◽  
Author(s):  
AKIRA FUJITSU
Keyword(s):  
Central Charge ◽  
Free Field ◽  
Lie Superalgebra ◽  
Superconformal Algebra ◽  
Hamiltonian Reduction ◽  
Field Representation ◽  
Gauge Fixing

We have constructed the free field representation of the N=3 superconformal algebra with an arbitrary value of the central charge c by using Hamiltonian reduction of the osp (3|2) Lie superalgebra without BRST gauge-fixing procedure.

Operator formalism and free field representation for minimal models on Riemann surfaces

1990 ◽  
Vol 338 (2) ◽  
pp. 415-441 ◽  
Author(s):  
M. Frau ◽  
A. Lerda ◽  
J.G. McCarthy ◽  
S. Sciuto
Keyword(s):  
Riemann Surfaces ◽  
Free Field ◽  
Minimal Models ◽  
Operator Formalism ◽  
Field Representation

scholarly journals Toda Conformal Blocks, Quantum Groups, and Flat Connections

2019 ◽  
Vol 375 (2) ◽  
pp. 1117-1158
Author(s):  
Ioana Coman ◽  
Elli Pomoni ◽  
Jörg Teschner
Keyword(s):  
Moduli Spaces ◽  
Free Field ◽  
Field Theories ◽  
Laurent Polynomials ◽  
Field Representation ◽  
Conformal Blocks ◽  
Flat Connections ◽  
Conformal Field ◽  
The Matrix ◽  
Elementary Operators

Abstract This paper investigates the relations between the Toda conformal field theories, quantum group theory and the quantisation of moduli spaces of flat connections. We use the free field representation of the $${{\mathcal {W}}}$$W-algebras to define natural bases for spaces of conformal blocks of the Toda conformal field theory associated to the Lie algebra $${\mathfrak {s}}{\mathfrak {l}}_3$$sl3 on the three-punctured sphere with representations of generic type associated to the three punctures. The operator-valued monodromies of degenerate fields can be used to describe the quantisation of the moduli spaces of flat $$\mathrm {SL}(3)$$SL(3)-connections. It is shown that the matrix elements of the monodromies can be expressed as Laurent polynomials of more elementary operators which have a simple definition in the free field representation. These operators are identified as quantised counterparts of natural higher rank analogs of the Fenchel–Nielsen coordinates from Teichmüller theory. Possible applications to the study of the non-Lagrangian SUSY field theories are briefly outlined.

FREE FIELD AND PARAFERMIONIC REALIZATIONS OF TWISTED $su(3)^{(2)}_k$ CURRENT ALGEBRA

2002 ◽  
Vol 16 (14n15) ◽  
pp. 2153-2159
Author(s):  
XIANG-MAO DING ◽  
MARK D. GOULD ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Scalar Field ◽  
Current Algebra ◽  
Energy Momentum Tensor ◽  
Free Field ◽  
Scalar Fields ◽  
Momentum Tensor ◽  
Free Fields

Free field and twisted parafermionic representations of twisted [Formula: see text] current algebra are obtained. The corresponding twisted Sugawara energy-momentum tensor is given in terms of three (β,γ) pairs and two scalar fields and also in terms of twisted parafermionic currents and one scalar field. Two screening currents of the first kind are presented in terms of the free fields.

Gemeinsprachliche Ressourcen beim Wissens- und Wissenschaftstransfer - die Rolle der Deixis bei der propositionalen Komposition in universitären Vorlesungen in den Fächern Physik und Maschinenbau

Fachsprache ◽  
2019 ◽  
Vol 41 (3-4) ◽  
pp. 104-122
Author(s):  
Winfried Thielmann
Keyword(s):  
Knowledge Transfer ◽  
Key Words ◽  
Mechanical Engineering ◽  
Academic Language ◽  
Ordinary Language ◽  
Point Of View ◽  
Special Role ◽  
Academic Teaching

Abstract Languages for special purposes have mainly been considered from the point of view that they are specialized, i.e. that they satisfy the terminological needs of expression of specialized groups. The purpose of this contribution is to demonstrate that specialized discourses such as university lectures may make specific use of ordinary language devices. An analysis of sections from German lectures in physics and mechanical engineering reveals that deictics play a special role in propositional  composition. The findings are relevant for the general principles of linguistic science and knowledge transfer as well as for teaching German as a first or second academic language. Schlagwörter: Sprache wissenschaftlicher Lehre – Deixis – Physik – Maschinenbau – propositionale Komposition Key words: Language of academic teaching – deictics – physics – mechanical engineering – propositional composition

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