Two more fermionic minimal models

Kulp, Justin

doi:10.1007/jhep03(2021)124

Cited by 34 publications

(51 citation statements)

References 18 publications

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“…Therefore, the critical theories of fermions (e.g., the critical theory of Majorana chains) are called "fermionic conformal field theories" to be distinguished from the critical bosonic theories, i.e., the so-called conformal field theories (CFTs). The classification [29] and the minimal and rational models of fermionic CFTs [27,[30][31][32] are of intense interest recently.…”

Section: Jhep04(2021)285mentioning

confidence: 99%

“…The bosonic minimal models have been exactly solved and classified into an ADE classification [35,36]. The fermionic (i.e., Z k=2parafermionic) minimal models are also exhausted by fermionizations of the bosonic minimal models with a global Z 2 symmetry [27,30,31].…”

Section: Minimal Parafermionic Models and Fractional Statisticsmentioning

confidence: 99%

“…Moreover, this bosonic theory has a global Z k>2 symmetry "inherited" from the parafermionic model. However, it has been shown that the only bosonic minimal models with a global Z k>2 symmetry are the critical and the tricritical three-state Potts models [30,31,42], where k = 3. The central charges are c = 4/5 for the critical Potts model and c = 6/7 for the tricritical Potts model.…”

Section: Minimal Z K>2 -Parafermionic Modelsmentioning

confidence: 99%

“…The partition functions under other paraspin structures (s 1 , s 2 ) can be found in appendix C, which complete the derivation of the last Z k -parafermionic minimal model. So far, we have exhausted all the Z k -parafermionic minimal models in addition to the completed fermionic minimal models [27,30]. In the following part, we will consider a large class of parafermionic models which are not necessarily Virasoro minimal.…”

Section: Jhep04(2021)285mentioning

confidence: 99%

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Parafermionization, bosonization, and critical parafermionic theories

Yao

Furusaki

2021

J. High Energ. Phys.

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We formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality at k = 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory when k > 2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.

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Section: Jhep04(2021)285mentioning

confidence: 99%

Section: Minimal Parafermionic Models and Fractional Statisticsmentioning

confidence: 99%

Section: Minimal Z K>2 -Parafermionic Modelsmentioning

confidence: 99%

Section: Jhep04(2021)285mentioning

confidence: 99%

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Parafermionization, bosonization, and critical parafermionic theories

Yao

Furusaki

2021

J. High Energ. Phys.

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“…For example, we now know that an abstract version of the Jordan-Wigner transformation can be formulated in the continuum, and any continuum fermionic theory in 1+1 dimensions is obtained from a bosonic (1+1)-dimensional system with a non-anomalous 2 symmetry by this transformation [3][4][5][6][7][8], generalizing the relation between the Ising conformal field theory (CFT) and the Majorana fermion CFT. It was also learned recently 1 that fermionic versions of unitary minimal models can be constructed in this manner [11][12][13]. 23 The aim of this paper is to study how this map between fermionic models and bosonic models with 2 symmetry affects the boundary states.…”

Section: Introductionmentioning

confidence: 99%

Fermionization and boundary states in 1+1 dimensions

2021

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Bootstrapping fermionic rational CFTs with three characters

Bae

Duan

Lee

et al. 2022

J. High Energ. Phys.

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Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups Γθ, Γ0(2) and Γ0(2) of SL2(ℤ) was developed and used to classify the fermionic rational conformal field theories (RCFT). Two character solutions of the second-order fermionic MLDE without poles were found and their corresponding CFTs are identified. Here we extend this analysis to explore the landscape of three character fermionic RCFTs obtained from the third-order fermionic MLDE without poles. Especially, we focus on a class of the fermionic RCFTs whose Neveu-Schwarz sector vacuum character has no free-fermion currents and Ramond sector saturates the bound hR ≥ $$ \frac{C}{24} $$ C 24 , which is the unitarity bound for the supersymmetric case. Most of the solutions can be mapped to characters of the fermionized WZW models. We find the pairs of fermionic CFTs whose characters can be combined to produce K(τ), the character of the c = 12 fermionic CFT for Co0 sporadic group.

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Two more fermionic minimal models

Cited by 34 publications

References 18 publications

Parafermionization, bosonization, and critical parafermionic theories

Parafermionization, bosonization, and critical parafermionic theories

Fermionization and boundary states in 1+1 dimensions

Bootstrapping fermionic rational CFTs with three characters

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