TY - JOUR

T1 - Extended current algebras and the coset construction of conformal field theories

AU - Blok, B.

AU - Yankielowicz, S.

N1 - Funding Information:
Conformal field theories (CFT) in 2 dimensions are of interest to the study of critical phenomena as well as to the study of string theories. From the statistical mechanics point of view, a CFT describes the critical behavior of the underlying two-dimensional statistical system. From the string theory point of view, each modular invariant conformal field theory describes a possible vacuum. A systematic study of conformal theories was initiated in \[1\]a nd is under a very active investigation. The basic idea is that states and fields of any given system fall into a finite sum of representations of an extended algebra, which includes the Virasoro algebra as a subalgebra. The only unitary theories which are finitely reducible with respect to the Virasoro algebra alone, are the theories of the minimal discrete series with c < 1 \[2\]. Other series of theories with c > 1 have been constructed such as superconformal minimal series \[3\], the parafermionic models \[4\], the WZW models \[5\] with Kac-Moody symmetry algebra and the S 3 model \[6\].T he last one has been shown to be a member of a new series \[7\]. In all of these cases the extended algebra has been constructed and the primary fields and their operator algebra are known. The common feature to all of these theories is that the currents have simple monodromy properties \[8\], and can be constructed as composite operators in terms of G* * Work supported in part by the US-Israel Binational Science Foundation, and the Israel Academy of Science. * G refers to the symmetry group appearing in the coset G/H construction of this model.

PY - 1989/3/13

Y1 - 1989/3/13

N2 - We investigate extended algebras associated with coset construction. We associate a Verlinde type algebra A with the branching functions. Each allowed choice of a subalgebra B corresponds to an extended algebra whose classes of currents are in one to one correspondence with the elements of B. The subalgebra B encodes the fusion rules of the currents. The elements of A/B are in one to one correspondence with the primary fields. Each coset element corresponds to one primary field and its descendants. The fusion rules of the operator algebra are encoded in A.

AB - We investigate extended algebras associated with coset construction. We associate a Verlinde type algebra A with the branching functions. Each allowed choice of a subalgebra B corresponds to an extended algebra whose classes of currents are in one to one correspondence with the elements of B. The subalgebra B encodes the fusion rules of the currents. The elements of A/B are in one to one correspondence with the primary fields. Each coset element corresponds to one primary field and its descendants. The fusion rules of the operator algebra are encoded in A.

UR - http://www.scopus.com/inward/record.url?scp=45149145352&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(89)90447-1

DO - 10.1016/0550-3213(89)90447-1

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AN - SCOPUS:45149145352

SN - 0550-3213

VL - 315

SP - 25

EP - 42

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 1

ER -