Breakdown of Current Algebra in Lagrangian Field Theories

1969 ◽  
Vol 178 (5) ◽  
pp. 2154-2159 ◽  
Author(s):  
C. R. HAGEN
Keyword(s):  
Current Algebra ◽  
Field Theories

The current algebra on the circle as a germ of local field theories

1988 ◽  
Vol 5 (2) ◽  
pp. 20-56 ◽  
Author(s):  
Detlev Buchholz ◽  
Gerhard Mack ◽  
Ivan Todorov
Keyword(s):  
Local Field ◽  
Current Algebra ◽  
Field Theories

SOME LANDAU-GINZBURG MODELS FROM CONFORMAL FIELD THEORY

1990 ◽  
Vol 05 (12) ◽  
pp. 2343-2358 ◽  
Author(s):  
KEKE LI
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Conformal Field Theory ◽  
Current Algebra ◽  
Operator Algebra ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Coset Models ◽  
Marginal Deformation

A method of constructing critical (fixed point) Landau-Ginzburg action from operator algebra is applied to several classes of conformal field theories, including lines of c = 1 models and the coset models based on SU(2) current algebra. For the c = 1 models, the Landau-Ginzberg potential is argued to be physically consistent, and it resembles a modality-one singularity with modal deformation representing exactly the marginal deformation. The potentials for the coset models manifestly possess correct discrete symmetries.

scholarly journals CURRENT ALGEBRA IN THE PATH INTEGRAL FRAMEWORK

1998 ◽  
Vol 13 (27) ◽  
pp. 2193-2198
Author(s):  
V. CÁRDENAS ◽  
S. LEPE ◽  
J. SAAVEDRA
Keyword(s):  
Path Integral ◽  
Current Algebra ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Integral Formalism ◽  
Path Integral Formalism ◽  
Current Algebras

In this letter we describe an approach to the current algebra based on the path integral formalism. We use this method for Abelian and non-Abelian quantum field theories in (1+1) and (2+1) dimensions and the correct expressions are obtained. Our results show the independence of the regularization of the current algebras.

THE BOUNDARY AND CROSSCAP STATES IN CONFORMAL FIELD THEORIES

1989 ◽  
Vol 04 (03) ◽  
pp. 251-264 ◽  
Author(s):  
NOBUYUKI ISHIBASHI
Keyword(s):  
Current Algebra ◽  
Open String ◽  
Closed String ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Boundary States ◽  
String Theories

A method to obtain the boundary states and the crosscap states explicitly in various conformal field theories, is presented. This makes it possible to construct and analyse open string theories in several closed string backgrounds. We discuss the construction of such theories in the case of the backgrounds corresponding to the conformal field theories with SU(2) current algebra symmetry.

scholarly journals MORE ABOUT ALL CURRENT-ALGEBRAIC ORBIFOLDS

2001 ◽  
Vol 16 (01) ◽  
pp. 97-162 ◽  
Author(s):  
M. B. HALPERN ◽  
J. E. WANG
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Current Algebra ◽  
Ground State ◽  
Field Theories ◽  
Conformal Weight ◽  
Conformal Field Theories ◽  
Twisted Sector ◽  
Conformal Field ◽  
Adjoint Operation

Recently a construction was given for the stress tensors of all sectors of the general current-algebraic orbifold A(H)/H, where A(H) is any current-algebraic conformal field theory with a finite symmetry group H. Here we extend and further analyze this construction to obtain the mode formulation of each sector of each orbifold A(H)/H, including the twisted current algebra, the Virasoro generators, the orbifold adjoint operation and the commutator of the Virasoro generators with the modes of the twisted currents. As applications, general expressions are obtained for the twisted current–current correlator and ground state conformal weight of each twisted sector of any permutation orbifold A(H)/H, H⊂SN. Systematics are also outlined for the orbifolds A(Lie h(H))/H of the (H and Lie h)-invariant conformal field theories, which include the general WZW orbifold and the general coset orbifold. Finally, two new large examples are worked out in further detail: the general SNpermutation orbifold A(SN)/SNand the general inner-automorphic orbifold A(H(d))/H(d).

scholarly journals CURRENT OSCILLATIONS, INTERACTING HALL DISCS AND BOUNDARY CFTs

1999 ◽  
Vol 14 (07) ◽  
pp. 1061-1085 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
S. VAIDYA ◽  
G. BIMONTE ◽  
T. R. GOVINDARAJAN ◽  
K. S. GUPTA ◽  
...  
Keyword(s):  
Current Algebra ◽  
Single Point ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Point Interactions ◽  
Interaction Point ◽  
Anomaly Cancellation ◽  
Conformal Field ◽  
Boundary Interaction ◽  
Current Oscillations

In this paper, we discuss the behavior of conformal field theories interacting at a single point. The edge states of the quantum Hall effect (QHE) system give rise to a particular representation of a chiral Kac–Moody current algebra. We show that in the case of QHE systems interacting at one point we obtain a "twisted" representation of the current algebra. The condition for stationarity of currents is the same as the classical Kirchoff's law applied to the currents at the interaction point. We find that in the case of two discs touching at one point, since the currents are chiral, they are not stationary and one obtains current oscillations between the two discs. We determine the frequency of these oscillations in terms of an effective parameter characterizing the interaction. The chiral conformal field theories can be represented in terms of bosonic Lagrangians with a boundary interaction. We discuss how these one-point interactions can be represented as boundary conditions on fields, and how the requirement of chirality leads to restrictions on the interactions described by these Lagrangians. By gauging these models we find that the theory is naturally coupled to a Chern–Simons gauge theory in 2+1 dimensions, and this coupling is completely determined by the requirement of anomaly cancellation.

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