Boundary conditions, fusion rules and the Verlinde formula

Cardy, John

doi:10.1016/0550-3213(89)90521-x

Cited by 1,135 publications

(2,223 citation statements)

References 13 publications

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“…In the following we briefly review the algebraic formulation of boundary states for RCFTs [23,28]. A RCFT is characterized by a certain chiral algebra and the corresponding Hilbert space contains a finite number of the chiral algebra irrep.…”

Section: Rational Cfts: Classification Of Conformal Boundary Conditionsmentioning

confidence: 99%

Critical interfaces of the Ashkin–Teller model at the parafermionic point

Picco¹,

Santachiara²

2010

J. Stat. Mech.

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We present an extensive study of interfaces defined in the Z 4 spin lattice representation of the Ashkin-Teller (AT) model. In particular, we numerically compute the fractal dimensions of boundary and bulk interfaces at the Fateev-Zamolodchikov point. This point is a special point on the self-dual critical line of the AT model and it is described in the continuum limit by the Z 4 parafermionic theory. Extending on previous analytical and numerical studies [10,12], we point out the existence of three different values of fractal dimensions which characterize different kind of interfaces. We argue that this result may be related to the classification of primary operators of the parafermionic algebra. The scenario emerging from the studies presented here is expected to unveil general aspects of geometrical objects of critical AT model, and thus of c = 1 critical theories in general.

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Section: Rational Cfts: Classification Of Conformal Boundary Conditionsmentioning

confidence: 99%

Critical interfaces of the Ashkin–Teller model at the parafermionic point

Picco¹,

Santachiara²

2010

J. Stat. Mech.

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“…The utility of this point of view is that it will then become apparent why a D-brane state in IIB string theory is necessary for defining a phase factor associated with a Ramond-Ramond field in IIA theory. Looking a little further, it is to be hoped that computing in an appropriately defined K-homology theory for conformal field theories might lead to some insight into possible D-brane states in an abstract closed string background, perhaps explaining the Cardy conditions [8] as characterizing a cycle in K-homology.…”

mentioning

confidence: 99%

D-brane charges and K-homology

Periwal

2000

J. High Energy Phys.

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It is argued that D-brane charge takes values in K-homology. For smooth manifolds with spin structure, this could explain why the phase factor Ω(x) calculated with a D-brane state x in IIB theory appears in Diaconescu, Moore and Witten's computation of the partition function of IIA string theory.Diaconescu, Moore and Witten [1] recently compared the partition functions of IIA string theory and M-theory. They found agreement, amusingly interpreted as a derivation of K-theory from M-theory. Many subtle mathematical effects have to conspire for this agreement, so it seems important to explore further the building blocks of their results.K-theory will enter into the discussion in a variety of ways so here is a summary of K-theory in string theory. Witten [2] argued that D-brane charge should take values in K-theory, following earlier work by Cheung and Yin [5] and Moore and Minasian [4], and providing a mathematical setting for the results of Sen [6]. To be precise, the groups K 0(1) (X) are associated with D-branes in IIB(A) string theory on the spacetime X, respectively. In later work, Moore and Witten [3] argued that Ramond-Ramond fields should take values in K-theory as well, with K 1(0) (X) classifying these fields in IIB(A) string theory.An important point in [1] is the computation of a phase factor Ω(x) associated with an element x which is a Ramond-Ramond field in IIA string theory on a manifold X. Somewhat surprisingly, this phase factor is computed from a D-brane state in IIB string theory, also associated with x by means of the above arguments. The perplexing appearance of IIB string theory in a computation that a priori involves only IIA theory is pointed out in footnote 14 in [1].Regressing a little bit to Polchinski's basic operational definition of D-branes [7], recall that string theory in the presence of a D-brane is naïvely defined by specifying a submanifold M of X and including open strings which have both ends on M. Suppose we act with a diffeomorphismthen the submanifold1

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“…the modular invariant theory which pairs left-movers with right-moving Charge Conjugates). A complete set of boundary states that preserve a diagonal subalgebra of the left-right symmetry algebra A × A is given by the Cardy states [14] …”

Section: Boundary and Crosscap States For Simple Current Extensionsmentioning

confidence: 99%

BPS orientifold planes from crosscap states in Calabi-Yau compactifications

Huiszoon¹,

Schalm²

2003

J. High Energy Phys.

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We use the results of hep-th/0007174 on the simple current classification of open unoriented CFTs to construct half supersymmetry preserving crosscap states for rational Calabi-Yau compactifications. We show that the corresponding orientifold fixed planes obey the BPS-like relation M = e iφ Q. To prove this relation, it is essential that the worldsheet CFT properly includes the degrees of freedom from the uncompactified space-time component. The BPS-phase φ can be identified with the automorphism type of the crosscap states. To illustrate the method we compute crosscap states in Gepner models with each k i odd.

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Boundary conditions, fusion rules and the Verlinde formula

Cited by 1,135 publications

References 13 publications

Critical interfaces of the Ashkin–Teller model at the parafermionic point

Critical interfaces of the Ashkin–Teller model at the parafermionic point

D-brane charges and K-homology

BPS orientifold planes from crosscap states in Calabi-Yau compactifications

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