scholarly journals GELFAND–DICKEY ALGEBRA AND HIGHER SPIN SYMMETRIES ON T2 = S1 × S1

2008 ◽  
Vol 23 (31) ◽  
pp. 5059-5080
Author(s):  
M. B. SEDRA
Keyword(s):  
Integrable Models ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Dimensional Torus ◽  
Conformal Field ◽  
Generalized Symmetries ◽  
Higher Spin

In this work we aim to renew the interest in higher conformal spins symmetries and their relations to quantum field theories and integrable models. We consider the extension of the conformal Frappat et al. symmetries containing the Virasoro and the Antoniadis et al. algebras as particular cases describing geometrically special diffeomorphisms of the two-dimensional torus T2. We show explicitly, in a consistent way, how one can extract these generalized symmetries from the Gelfand–Dickey algebra. The link with Liouville and Toda conformal field theories is established and various important properties are discussed.

NORMALIZATION FACTORS IN CONFORMAL FIELD THEORY AND THEIR APPLICATIONS

2000 ◽  
Vol 15 (04) ◽  
pp. 259-270 ◽  
Author(s):  
V. A. FATEEV
Keyword(s):  
Vacuum Expectation ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Conformal Field Theories ◽  
Expectation Values ◽  
Conformal Field ◽  
Cylindrically Symmetric ◽  
Toda Equations ◽  
Normalization Factors

We calculate the normalization factors and reflection amplitudes in the W-invariant conformal quantum field theories. Using these CFT data we derive vacuum expectation values of exponential fields in affine Toda theories and related perturbed conformal field theories. We also calculate the asymptotics of cylindrically symmetric solutions of the classical Toda equations.

FACTORIZABLE S MATRICES FOR PERTURBED W-INVARIANT THEORIES

1991 ◽  
Vol 06 (18) ◽  
pp. 3221-3234 ◽  
Author(s):  
H.J. de VEGA ◽  
V.A. FATEEV
Keyword(s):  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Conformal Field Theories ◽  
Conformal Field

[Formula: see text]-invariant conformal field theories admit perturbations preserving integrability and leading to massive quantum field theories. The unitary and crossing-invariant S matrices of such QFTs are explicitly constructed by restricting the SL (n, q)-symmetric solutions of the Yang-Baxter equations when qn+k=1. These scattering theories possess level-rank duality (n↔k).

scholarly journals A general construction of conformal field theories from scalar anti-de Sitter quantum field theories

2000 ◽  
Vol 587 (1-3) ◽  
pp. 619-644 ◽  
Author(s):  
Marco Bertola ◽  
Jacques Bros ◽  
Ugo Moschella ◽  
Richard Schaeffer
Keyword(s):  
Field Theories ◽  
General Construction ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Conformal Field

RECENT DEVELOPMENTS OF ALGEBRAIC METHODS IN QUANTUM FIELD THEORIES

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2041-2059 ◽  
Author(s):  
B. SCHROER
Keyword(s):  
Algebraic Methods ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Conformal Field Theories ◽  
One Dimensional ◽  
Conformal Field ◽  
Recent Developments

Recent results obtained by modular methods concerning the algebraic origin of spacetime covariance from modular and dual properties of causal nets are presented. Particular emphasis is given to one-dimensional nets which are important in the classification of chiral conformal field theories.

scholarly journals Orbifold groupoids

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Davide Gaiotto ◽  
Justin Kulp
Keyword(s):  
Three Dimensional ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Generalized Symmetries

Abstract We review the properties of orbifold operations on two-dimensional quantum field theories, either bosonic or fermionic, and describe the “Orbifold groupoids” which control the composition of orbifold operations. Three-dimensional TQFT’s of Dijkgraaf-Witten type will play an important role in the analysis. We briefly discuss the extension to generalized symmetries and applications to constrain RG flows.

scholarly journals Instantons beyond topological theory. I

2011 ◽  
Vol 10 (3) ◽  
pp. 463-565 ◽  
Author(s):  
E. Frenkel ◽  
A. Losev ◽  
N. Nekrasov
Keyword(s):  
Correlation Functions ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Conformal Field Theories ◽  
Four Dimensions ◽  
Yang Mills ◽  
Conformal Field ◽  
Mechanical Models ◽  
Perturbative Corrections

AbstractMany quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyse the corresponding models as full quantum field theories, beyond their topological sector. We show that the correlation functions of all, not only topological (or BPS), observables may be studied explicitly in these models, and the spectrum may be computed exactly. An interesting feature is that the Hamiltonian is not always diagonalizable, but may have Jordan blocks, which leads to the appearance of logarithms in the correlation functions. We also find that in the models defined on Kähler manifolds the space of states exhibits holomorphic factorization. We conclude that in dimensions two and four our theories are logarithmic conformal field theories.In Part I we describe the class of models under study and present our results in the case of one-dimensional (quantum mechanical) models, which is quite representative and at the same time simple enough to analyse explicitly. Part II will be devoted to supersymmetric two-dimensional sigma models and four-dimensional Yang–Mills theory. In Part III we will discuss non-supersymmetric models.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

scholarly journals Instability of complex CFTs with operators in the principal series

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Dario Benedetti
Keyword(s):  
Principal Series ◽  
Conformal Group ◽  
Point Of View ◽  
Field Theories ◽  
Operator Product ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Primary Operator ◽  
Tensor Models

Abstract We prove the instability of d-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension h = $$ \frac{d}{2} $$ d 2 + i r, with non-vanishing r ∈ ℝ. From an AdS/CFT point of view, this corresponds to a well-known tachyonic instability, associated to a violation of the Breitenlohner-Freedman bound in AdSd+1; we derive it here directly for generic d-dimensional CFTs that can be obtained as limits of multiscalar quantum field theories, by applying the harmonic analysis for the Euclidean conformal group to perturbations of the conformal solution in the two-particle irreducible (2PI) effective action. Some explicit examples are discussed, such as melonic tensor models and the biscalar fishnet model.

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