scholarly journals FREE FIELD CONSTRUCTIONS FOR THE ELLIPTIC ALGEBRA $\rscr{A}_{q,p}(\widehat{sl}_2)$ AND BAXTER'S EIGHT-VERTEX MODEL

2004 ◽  
Vol 19 (supp02) ◽  
pp. 363-380 ◽  
Author(s):  
J. SHIRAISHI
Keyword(s):  
Integral Formula ◽  
Free Field ◽  
Virasoro Algebra ◽  
Vertex Operators ◽  
Vertex Model ◽  
Elliptic Algebra ◽  
Deformed Virasoro Algebra ◽  
The One ◽  
Level 2 ◽  
Elliptic Quantum

Three examples of free field constructions for the vertex operators of the elliptic quantum group [Formula: see text] are obtained. Two of these ( for p1/2=±q3/2, p1/2=-q2) are based on representation theories of the deformed Virasoro algebra, which correspond to the level 4 and level 2 Z-algebra of Lepowsky and Wilson. The third one (p1/2=q3) is constructed over a tensor product of a bosonic and a fermionic Fock spaces. The algebraic structure at (p1/2=q3), however, is not related to the deformed Virasoro algebra. Using these free field constructions, an integral formula for the correlation functions of Baxter's eight-vertex model is obtained. This formula shows different structure compared with the one obtained by Lashkevich and Pugai.

FUSION CONSTRUCTION OF THE VERTEX OPERATORS IN HIGHER LEVEL REPRESENTATION OF THE ELLIPTIC QUANTUM GROUP

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1995-2001
Author(s):  
HITOSHI KONNO
Keyword(s):  
Quantum Group ◽  
Free Field ◽  
Vertex Operators ◽  
Type I ◽  
Field Representation ◽  
Short Summary ◽  
Higher Spin ◽  
Elliptic Algebra ◽  
Elliptic Quantum ◽  
Weight Coefficients

After a short summary on the elliptic quantum group [Formula: see text] and the elliptic algebra [Formula: see text], we present a free field representation of the Drinfeld currents and the vertex operators (VO's) in the level k. We especially demonstrate a construction of the higher spin type I VO's by fusing the spin 1/2 type I VO's and fix a rule of attaching the screening current S(z) associated with the q-deformed ℤk-parafermion theory. As a result we get a free field representation of the higher spin type I VO's which commutation relation by the fused Boltzmann weight coefficients is manifest.

scholarly journals THE 19-VERTEX MODEL AT CRITICAL REGIME |q|=1

2001 ◽  
Vol 16 (09) ◽  
pp. 1559-1578 ◽  
Author(s):  
TAKEO KOJIMA
Keyword(s):  
Quantum Group ◽  
Correlation Functions ◽  
Free Field ◽  
Integral Representations ◽  
Critical Regime ◽  
Vertex Operators ◽  
Vertex Model ◽  
Free Fermions

We study the 19-vertex model associated with the quantum group [Formula: see text] at critical regime |q|=1. We give the realizations of the vertex operators in terms of free bosons and free fermions. Using these free field realizations, we present integral representations for the correlation functions.

scholarly journals LEVEL 2 IRREDUCIBLE REPRESENTATIONS OF $U_q (\widehat{{\rm sl}}_2)$, VERTEX OPERATORS, AND THEIR CORRELATIONS

1994 ◽  
Vol 09 (25) ◽  
pp. 4449-4484 ◽  
Author(s):  
MAKOTO IDZUMI
Keyword(s):  
Correlation Functions ◽  
Spin Chain ◽  
Integral Formula ◽  
Spin Correlation ◽  
Quantum Spin ◽  
Irreducible Representations ◽  
Vertex Operators ◽  
Quantum Spin Chain ◽  
Level 2

Vertex operators associated with level 2 [Formula: see text] modules are explicitly constructed using bosons and fermions. An integral formula is derived for the trace of products of vertex operators. These results are applied to give n-point spin correlation functions of an integrable S = 1 quantum spin chain, extending an earlier work of Jimbo et al. for the case S = 1/2.

scholarly journals Vertex operators for deformed Virasoro algebra

JETP Letters ◽  
1996 ◽  
Vol 63 (11) ◽  
pp. 917-923 ◽  
Author(s):  
A. A. Kadeishvili
Keyword(s):  
Virasoro Algebra ◽  
Vertex Operators ◽  
Deformed Virasoro Algebra

scholarly journals On local and integrated stress-tensor commutators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Mert Besken ◽  
Jan de Boer ◽  
Grégoire Mathys
Keyword(s):  
Stress Tensor ◽  
Free Field ◽  
Virasoro Algebra ◽  
Light Sheet ◽  
Operator Product ◽  
Local Form ◽  
Two Dimensional ◽  
Conformal Embedding ◽  
General Aspects ◽  
The Right

Abstract We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.

scholarly journals Monodromy defects in free field theories

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Lorenzo Bianchi ◽  
Adam Chalabi ◽  
Vladimír Procházka ◽  
Brandon Robinson ◽  
Jacopo Sisti
Keyword(s):  
Entanglement Entropy ◽  
Free Field ◽  
Operator Product ◽  
Dirac Fermions ◽  
Maxwell Theory ◽  
Conformal Field ◽  
Defect Operator ◽  
Crucial Information ◽  
The One ◽  
Group Flow

Abstract We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of d = 4, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum Rényi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a d = 4 theory of free $$ \mathcal{N} $$ N = 2 hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free d = 4 Maxwell theory and show that their central charges vanish.

A quantization of the electromagnetic field

1983 ◽  
Vol 61 (8) ◽  
pp. 1172-1183
Author(s):  
Anton Z. Capri ◽  
Gebhard Grübl ◽  
Randy Kobes
Keyword(s):  
Hilbert Space ◽  
Electromagnetic Field ◽  
Gauge Invariance ◽  
Free Field ◽  
External Source ◽  
Field Level ◽  
Manifest Covariance ◽  
The One ◽  
Physical Spaces

Quantization of the electromagnetic field in a class of covariant gauges is performed on a positive metric Hilbert space. Although losing manifest covariance, we find at the free field level the existence of two physical spaces where Poincaré transformations are implemented unitarily. This gives rise to two different physical interpretations of the theory. Unitarity of the S operator for an interaction with an external source then forces one to postulate that a restricted gauge invariance must hold. This singles out one interpretation, the one where two transverse photons are physical.

scholarly journals The Deformed Virasoro Algebra at Roots of Unity

1998 ◽  
Vol 196 (2) ◽  
pp. 249-288 ◽  
Author(s):  
Peter Bouwknegt ◽  
Krzysztof Pilch
Keyword(s):  
Virasoro Algebra ◽  
Roots Of Unity ◽  
Deformed Virasoro Algebra

scholarly journals Free field construction for correlation functions of the eight-vertex model

1998 ◽  
Vol 516 (3) ◽  
pp. 623-651 ◽  
Author(s):  
Michael Lashkevich ◽  
Yaroslav Pugai
Keyword(s):  
Correlation Functions ◽  
Free Field ◽  
Vertex Model
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