CONFORMAL FIELD THEORIES ON SURFACES WITH BOUNDARIES AND CROSSCAPS

1989 ◽  
Vol 04 (02) ◽  
pp. 161-168 ◽  
Author(s):  
TETSUYA ONOGI ◽  
NOBUYUKI ISHIBASHI
Keyword(s):  
Crucial Role ◽  
Model Building ◽  
Open String ◽  
Theory Model ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Conformal Field ◽  
Loop Channel

We classify the possible operator contents of the minimal conformal field theories when boundaries and crosscaps are present by imposing loop channel-tree channel duality conditions. These are the open string analogues of modular invariant partition functions, which play a crucial role in string theory model building.

scholarly journals TOWERS OF ALGEBRAS IN RATIONAL CONFORMAL FIELD THEORIES

1991 ◽  
Vol 06 (12) ◽  
pp. 2045-2074 ◽  
Author(s):  
CÉSAR GOMEZ ◽  
GERMAN SIERRA
Keyword(s):  
Sufficient Conditions ◽  
Field Theories ◽  
Partition Functions ◽  
Polynomial Equations ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Conformal Field ◽  
Ade Classification

Jones fundamental construction is applied to rational conformal field theories. The Jones algebra which emerges in this application is realized in terms of duality operations. The generators of the algebra are an open version of Verlinde’s operators. The polynomial equations appear in this context as sufficient conditions for the existence of Jones algebra. The ADE classification of modular invariant partition functions is put in correspondence with Jones classification of subfactors.

scholarly journals CLONING SO(N) LEVEL 2

1999 ◽  
Vol 14 (08) ◽  
pp. 1283-1291 ◽  
Author(s):  
A. N. SCHELLEKENS
Keyword(s):  
Infinite Number ◽  
Essential Role ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Chiral Algebra ◽  
Conformal Field ◽  
N Level ◽  
Level 2

For each N an infinite number of conformal field theories is presented that has the same fusion rules as SO (N) level 2. These new theories are obtained as extensions of the chiral algebra of SO (NM2) level 2, and correspond to new modular invariant partition functions of these theories. A one-to-one map between the c=1 orbifolds of radius R2=2r and Dr level 2 plays an essential role.

scholarly journals THE CAPPELLI–ITZYKSON–ZUBER A-D-E CLASSIFICATION

2000 ◽  
Vol 12 (05) ◽  
pp. 739-748 ◽  
Author(s):  
TERRY GANNON
Keyword(s):  
Mathematical Structure ◽  
The Other ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Conformal Field ◽  
Affine Algebras ◽  
Order Of Magnitude ◽  
The Rich

In 1986 Cappelli, Itzykson and Zuber classified all modular invariant partition functions for the conformal field theories associated to the affine A1 algebra; they found they fall into an A-D-E pattern. Their proof was difficult and attempts to generalise it to the other affine algebras failed — in hindsight the reason is that their argument ignored most of the rich mathematical structure present. We give here the "modern" proof of their result; it is an order of magnitude simpler and shorter, and much of it has already been extended to all other affine algebras. We conclude with some remarks on the A-D-E pattern appearing in this and other RCFT classifications.

LOCALIZED MODES IN SINGULAR CALABI-YAU CONFORMAL FIELD THEORIES

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2184-2186
Author(s):  
SHUN'YA MIZOGUCHI
Keyword(s):  
Discrete Series ◽  
Field Theories ◽  
Partition Functions ◽  
Type Ii ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Heterotic Strings ◽  
Conformal Field ◽  
Series Representations ◽  
Discrete Series Representations

We construct spacetime supersymmetric, modular invariant partition functions for type II and heterotic strings on the conifold-type singularities such that they include contributions coming from the discrete-series representations of SL(2, R). In particular for the E8 × E8 heterotic case, they are in the 27 representation of E6 and localized on a four-dimensional "brane" at the tip of the cigar geometry.

GN ⊗ GL/GN+L CONFORMAL FIELD THEORIES AND THEIR MODULAR INVARIANT PARTITION FUNCTIONS

1989 ◽  
Vol 04 (04) ◽  
pp. 897-920 ◽  
Author(s):  
P. CHRISTE ◽  
F. RAVANINI
Keyword(s):  
Outer Automorphism ◽  
Principal Series ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Complementary Series ◽  
Moody Algebra ◽  
Modular Invariant ◽  
Conformal Field ◽  
Modular Invariants

We study a Feigin-Fuchs construction of conformal field theories based on a G ⊗ G/G coset space, in terms of screened bosons and parafermions. This allows us to get the formula for the conformal dimensions of primary operators. Lists of modular invariant partition functions for the SU(3), SO(5) and G2 Wess-Zumino-Witten models are given. Besides the principal series of diagonal invariants, a complementary series exists for SU(3) and SO(5), which is due to the outer automorphism of the Kac-Moody algebra. Moreover, exceptional solutions appear at levels 5, 9, 21 for SU(3), at levels 3, 7, 12 for SO(5) and at levels 3, 4 for G2. From these modular invariants, those for the corresponding GN ⊗ GL/GN+L models are constructed.

scholarly journals SIMPLE CURRENTS, MODULAR INVARIANTS AND FIXED POINTS

1990 ◽  
Vol 05 (15) ◽  
pp. 2903-2952 ◽  
Author(s):  
A.N. SCHELLEKENS ◽  
S. YANKIELOWICZ
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Fixed Points ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Conformal Field ◽  
Modular Invariants ◽  
Simple Currents

We review the use of simple currents in constructing modular invariant partition functions and the problem of resolving their fixed points. We present some new results, in particular regarding fixed point resolution. Additional empirical evidence is provided in support of our conjecture that fixed points are always related to some conformal field theory. We complete the identification of the fixed point conformal field theories for all simply laced and most non-simply laced Kac-Moody algebras, for which the fixed point CFT’s turn out to be Kac-Moody algebras themselves. For the remaining non-simply laced ones we obtain spectra that appear to correspond to new non-unitary conformal field theories. The fusion rules of the simplest unidentified example are computed.

AN INFINITE CLASS OF NEW CONFORMAL FIELD THEORIES WITH EXTENDED ALGEBRAS

1988 ◽  
Vol 03 (04) ◽  
pp. 397-412 ◽  
Author(s):  
F. RAVANINI
Keyword(s):  
Large Class ◽  
Lie Algebras ◽  
Field Theories ◽  
Irreducible Representations ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Infinite Class ◽  
Modular Invariant ◽  
Conformal Field ◽  
Highest Weight

A large class of 2D conformal field theories with extended Virasoro algebras related to the GKO construction on the coset SU(2)⊗SU(2)/SU(2) is introduced. Through a Feigin-Fuchs construction the Kac formula is deduced. Characters of the highest-weight irreducible representations are given in terms of the GKO decomposition branching functions. Modular invariant partition functions are constructed and an A-D-E classification based on a triple of simply-laced Lie algebras is analyzed in detail.

scholarly journals Rational conformal field theory with matrix level and strings on a torus

2014 ◽  
Vol 92 (1) ◽  
pp. 65-70 ◽  
Author(s):  
Ali Nassar ◽  
Mark A. Walton
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Complex Multiplication ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
The Matrix

Study of the matrix-level affine algebra Um,K is motivated by conformal field theory and the fractional quantum Hall effect. Gannon completed the classification of Um,K modular-invariant partition functions. Here we connect the algebra U2,K to strings on 2-tori describable by rational conformal field theories. As Gukov and Vafa proved, rationality selects the complex-multiplication tori. We point out that the rational conformal field theories describing strings on complex-multiplication tori have characters and partition functions identical to those of the matrix-level algebra Um,K. This connection makes it obvious that the rational theories are dense in the moduli space of strings on Tm, and may prove useful in other ways.

Sign in / Sign up

Export Citation Format

Share Document