N=2 minimal models on Riemann surfaces

Frau, M.; McCarthy, John A.; Lerda, A.; Sciuto, S.; Sidenius, J.R.

doi:10.1016/0370-2693(91)91172-r

Cited by 8 publications

(9 citation statements)

References 22 publications

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“…Although we have not given explicit examples in this paper, the technique for finding exact correlation functions in the disk topology also applies to the Z k parafermion theory (with the primary fields of (41)). As the N = 2 supersymmetric minimal models [63][64][65][66][67][68][69] differ from the SU (2) k WZNW model only by the U (1) k compactification radius, we expect that the same technique should also apply to these models without much difficulty.…”

Section: Discussionmentioning

confidence: 99%

Coulomb-gas formulation ofSU(2) branes and chiral blocks

Hemming¹,

Kawai²,

Keski-Vakkuri³

2005

J. Phys. A: Math. Gen.

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We construct boundary states in SU (2) k WZNW models using the bosonized Wakimoto free-field representation and study their properties. We introduce a Fock space representation of Ishibashi states which are coherent states of bosons with zero-mode momenta (boundary Coulomb-gas charges) summed over certain lattices according to Fock space resolution of SU (2) k . The Virasoro invariance of the coherent states leads to families of boundary states including the B-type D-branes found by Maldacena, Moore and Seiberg, as well as the A-type corresponding to trivial current gluing conditions. We then use the Coulomb-gas technique to compute exact correlation functions of WZNW primary fields on the disk topology with A-and B-type Cardy states on the boundary. We check that the obtained chiral blocks for A-branes are solutions of the Knizhnik-Zamolodchikov equations.

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Section: Discussionmentioning

confidence: 99%

Coulomb-gas formulation ofSU(2) branes and chiral blocks

Hemming¹,

Kawai²,

Keski-Vakkuri³

2005

J. Phys. A: Math. Gen.

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“…Such representations can be obtained from the Fock space through a suitable projection like in the case of the standard free-field realization of the minimal models as given for instance in [38]. In this section our aim is to make contact with this Coulomb gas formalism, which, as we will see in the sequel, enables us to calculate explicitly (perturbed) topological correlation functions in the presence of a LG interaction.…”

Section: Bosonization Of the (B C β γ)-Systemmentioning

confidence: 99%

“…The operators ϕ due to the existence of a map between the two that commutes with all generators of the algebra [38]. In order to relate this realization of the N=2 minimal models to the one provided by our (b, c, β, γ)-system, we bosonize the latter according to the standard rules and write…”

Section: Bosonization Of the (B C β γ)-Systemmentioning

confidence: 99%

“…Adopting the conventions of [38], an N=2 minimal model with central charge as in (4.1), can be described in terms of three scalar fields φ 0 , φ 1 and φ 2 with mode expansions…”

Section: Bosonization Of the (B C β γ)-Systemmentioning

confidence: 99%

“…In Section 3 we discuss the quantum properties of our theories and show that the classical (2,2)-superconformal invariance extends trivially to the quantum level due to the absence of loop corrections. In Section 4 we bosonize the first-order systems and make contact with the usual Coulomb gas representation of N=2 minimal models [38,39]. Section 5 contains explicit calculations of topological correlation functions and a direct verification that our coordinates are indeed the flat ones.…”

Section: Introductionmentioning

confidence: 99%

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Topological first-order systems with Landau-Ginzburg interactions

et al. 1992

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Lagrangian formulation of N=2 theories with (b, c, β, γ)-systems and comparison with the Landau-Ginzburg approachIn this section we consider the realization of (2,2)-supersymmetric models in terms of free (b, c, β, γ)-systems recently introduced in [37], and generalize it to include interactions of the Landau-Ginzburg (LG) type. As stressed in the introduction, N=2 superconformal theories with c = 9 are of primary interest in connection with superstring compactifications on six-dimensional Calabi-Yau spaces. More generally, a (2,2)-superconformal theory with c = 3d corresponds to the critical point of an N=2 σ-model on a target space with complex dimension d and vanishing first Chern class. We will call these spaces Calabi-Yau d-folds.In the LG formulation of (2,2)-supersymmetric models, the superconformal theory is viewed as the infrared fixed point of a two-dimensional N=2 Wess-Zumino model with a polynomial superpotential W . In particular, when W is an analytic quasi-homogeneous function of the chiral superfields X i , one can recover the complete ADE classification of the N=2 minimal models from the ADE classification of quasi-homogeneous potentials with zero modality [5,[33][34][35][36]. Furthermore, the polynomials W 's can be identified with those used in the construction of Calabi-Yau d-folds. Indeed, it can be shown [5,35] that a superconformal model with c = 3d, corresponding to a LG potential W , is the same as that associated to a σ-model on the Calabi-Yau d-fold defined by the polynomial constraint W (X i ) = 0 in a suitable projective or weighted projective space 1 . In this section we show that it is possible to add a polynomial interaction V of the LG type to a collection of free first-order (b, c, β, γ)-systems in such a way that, if V is a quasi-homogeneous function, the theory possesses an N=2 superconformal symmetry already at the classical level. We also show that the interaction potential unambiguously fixes the weights of the pseudo-ghost fields. As in the standard LG case, also here we can recover the ADE classification of the N=2 minimal models from ADE classification of the interaction potential [35,36]; however in our case the theory is always manifestly superconformal invariant. Our formulation allows us to add all relevant perturbations (versal deformations of the potential) and to study the renormalization group flows in a very simple way. Whenever we use a quasi-homogeneous potential with modality different from zero, we can study marginal deformations and eventually Zamolodchikov's metric on the associated moduli space. Alternatively, we can consider topological models by "twisting" the generators of the superconfromal algebra and compute topological correlation functions. Our formulation provides valuable methods to evaluate these latter.We start this program by defining our model. We consider a collection of pseudoghost fields {b ℓ , c ℓ , β ℓ , γ ℓ ;b r ,c r ,β r ,γ r } where ℓ = 1, . . . , N L and r = 1, . . . , N R . β ℓ and γ ℓ form a bosonic first-order system with weights...

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BRST quantization ofN = 2, 3, and 4 superconformal theories on higher-genus Riemann surfaces

Le-Man

1994

Int J Theor Phys

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N=2 minimal models on Riemann surfaces

Cited by 8 publications

References 22 publications

Coulomb-gas formulation ofSU(2) branes and chiral blocks

Coulomb-gas formulation ofSU(2) branes and chiral blocks

Topological first-order systems with Landau-Ginzburg interactions

BRST quantization ofN = 2, 3, and 4 superconformal theories on higher-genus Riemann surfaces

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