Fermi-gas interpretation of the RSOS path representation of the superconformal unitary minimal models

Jacob, P.; Mathieu, Pierre

doi:10.1016/j.nuclphysb.2008.07.004

Cited by 5 publications

(14 citation statements)

References 38 publications

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“…For these models, the constructive method following the lines of [28] is not so directly worked out. It turns out that in this context, the logic underlying the fermi-gas description of the paths is reversed: a path has a natural operator construction and it is this very operator interpretation which, once finitized, allows us to clearly identify the particles within the path [22]. We suspect that the same situation will hold for the fermi-gas analysis of the more general models [9] su(2) k ⊗ su(2) ℓ / su(2) k+ℓ , for ℓ > 2: working at the level of the operator basis induced by the path description is likely to be simpler than working directly at the level of the paths.…”

Section: Discussionmentioning

confidence: 99%

A nonlocal operator basis from the path representation of the {\cal M}(k+1\hbox{,}\,k+2) and the {\cal M}(k+1\hbox{,}\,2k+3) minimal models

Jacob¹,

Mathieu²

2008

J. Phys. A: Math. Theor.

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We reinterpret a path describing a state in an irreducible module of the unitary minimal model M(k + 1, k + 2) in terms of a string of charged operators acting on the module's ground-state path. Each such operator acts non-locally on a path. The path characteristics are then translated into a set of conditions on sequences of operators that provide an operator basis. As an application, we re-derive the vacuum finite fermionic character by constructing the generating function of these basis states. These results generalize directly to the M(k + 1, 2k + 3) models, the close relatives of the unitary models in terms of path description. * patrick.jacob@phy.ulaval.ca, pmathieu@phy.ulaval.ca. This work is supported by NSERC.

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Section: Discussionmentioning

confidence: 99%

A nonlocal operator basis from the path representation of the {\cal M}(k+1\hbox{,}\,k+2) and the {\cal M}(k+1\hbox{,}\,2k+3) minimal models

Jacob¹,

Mathieu²

2008

J. Phys. A: Math. Theor.

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“…Using this bijection, we can now verify the expressions (26) and (27) giving the values of s and j for P paths. For the expression of j l , we have…”

Section: Bijection S ↔ Pmentioning

confidence: 99%

“…where in the last step, we used h L+1 = h L +(−1) L+2j (cf. (26)) and a case-by-case comparison of the two sides of the equality. This is the announced expression (27).…”

Section: Bijection S ↔ Pmentioning

confidence: 99%

Path representation of states I: Operators and particles for

Lamy-Poirier¹,

Mathieu²

2011

Nuclear Physics B

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This is the first of two articles devoted to the analysis of the path description of the states in su(2) k WZW models, a representation well suited for constructive derivations of the fermionic characters. In this first article, the cases k = 1, 2 are treated in detail, emphasizing a different description in each case (operators vs particles). For k = 1, we first prove, as a side result, the equivalence of two known path representations for the finitized su(2) 1 states by displaying an explicit bijection. An immediate offshoot is the gain of a new and simple weighting for the (Kyoto) path representation that generalizes to level k. The bijection also suggests two operator constructions for the su(2) 1 paths, a local and a nonlocal one, both interrelated. These are formal operators that map a path to another path, so that any path can be obtained by successive applications of these operators on a simple reference (ground-state) path. The nonlocal operator description is the starting point for a direct and elementary derivation of the su(2) 1 spinon character. The second part presents an extensive study of the su(2) 2 paths from their particle point of view, where the particles are defined as the path building blocks. The resulting generating functions appear to provide new (at least superficially) fermionic forms of the characters. In particular, a nice relationship between the sum of the j = 0, 1 characters at k = 2 and the two ones at k = 1 is unravelled.

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“…The crucial point is the demonstration of the weight preserving character of the bijection, namely, the proof of (14). To present the key point without the complications induced by the boundary effects, let us restrict to the case s = r = 1, for which ŵgsc = 0.…”

Section: Rsos(p ′ P) Pathsmentioning

confidence: 99%

“…For instance, with the edges NE, SE and H represented respectively by 1, 1 and 0, the three configurations with m 3 = m 4 = 1, regarded e.g. as B(5,14) paths (cf. Fig.8), are :…”

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confidence: 99%

Particles in RSOS paths

Jacob¹,

Mathieu

2009

J. Phys. A: Math. Theor.

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We introduce a new representation of the paths of the Forrester-Baxter RSOS models which represents the states of the irreducible modules of the minimal models M(p ′ , p). This representation is obtained by transforming the RSOS paths, for the cases p ≥ 2p ′ − 1, to new paths for which horizontal edges are allowed at certain heights. These new paths are much simpler in that their weight is nothing but the sum of the position of the peaks. This description paves the way for the interpretation of the RSOS paths in terms of fermi-type charged particles out of which the fermionic characters could be obtained constructively. The derivation of the fermionic character for p ′ = 2 and p = kp ′ ± 1 is outlined. Finally, the particles of the RSOS paths are put in relation with the kinks and the breathers of the restricted sine-Gordon model.

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Fermi-gas interpretation of the RSOS path representation of the superconformal unitary minimal models

Cited by 5 publications

References 38 publications

A nonlocal operator basis from the path representation of the {\cal M}(k+1\hbox{,}\,k+2) and the {\cal M}(k+1\hbox{,}\,2k+3) minimal models

A nonlocal operator basis from the path representation of the {\cal M}(k+1\hbox{,}\,k+2) and the {\cal M}(k+1\hbox{,}\,2k+3) minimal models

Path representation of states I: Operators and particles for

Particles in RSOS paths

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