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Coupled Free Fermion Conformal Field Theory and Representations
Mathematical Physics · Submitted 11 Dec 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We reveal an unexpected connection that integrates the coset construction, lattice construction, and orbifold construction, which is supported by proving a range of character identities within the context of coupled free fermions.
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The abstract, sentence by sentence
Conformal field theory (CFT) has become an active area of research beyond its origins in statistical physics and attracted much attention due to its intrinsic mathematical interest, which reveals deep connections with other diverse branches of mathematics. We study a specific subclass of CFTs that involve either uncoupled or coupled free fermions. Coupled free fermion CFTs arise from parafermion CFTs and lattice constructions. We analyse their representation spaces and reveal the exclusion statistics of coupled free fermions with universal chiral partition functions under specific bases. We explicitly decompose their modules into Virasoro modules of minimal models. We reveal an unexpected connection that integrates the coset construction, lattice construction, and orbifold construction, which is supported by proving a range of character identities within the context of coupled free fermions. Simultaneously, we obtain explicit expressions of certain string functions in terms of Dedekind eta functions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Conformal field theory (CFT) has become an active area of research beyond its origins in statistical physics and attracted much attention due to its intrinsic mathematical interest, which reveals deep connections with other diverse branches of mathematics. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | We study a specific subclass of CFTs that involve either uncoupled or coupled free fermions. | contribution 0.98 | 0.90 | 0.05 | asserted 0.99 |
| s2 | Coupled free fermion CFTs arise from parafermion CFTs and lattice constructions. | background 0.99 | 0.10 | 0.05 | asserted 1.00 |
| s3 | We analyse their representation spaces and reveal the exclusion statistics of coupled free fermions with universal chiral partition functions under specific bases. | result 0.75 | 0.95 | 0.26 | asserted 1.00 |
| s4 | We explicitly decompose their modules into Virasoro modules of minimal models. | contribution 0.52 | 0.96 | 0.13 | asserted 1.00 |
| s5 | We reveal an unexpected connection that integrates the coset construction, lattice construction, and orbifold construction, which is supported by proving a range of character identities within the context of coupled free fermions. | result 0.92 | 0.93 | 0.55 | asserted 1.00 |
| s6 | Simultaneously, we obtain explicit expressions of certain string functions in terms of Dedekind eta functions. | result 0.98 | 0.96 | 0.08 | asserted 1.00 |
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The paper
Original abstract
Conformal field theory (CFT) has become an active area of research beyond its origins in statistical physics and attracted much attention due to its intrinsic mathematical interest, which reveals deep connections with other diverse branches of mathematics. We study a specific subclass of CFTs that involve either uncoupled or coupled free fermions. Coupled free fermion CFTs arise from parafermion CFTs and lattice constructions. We analyse their representation spaces and reveal the exclusion statistics of coupled free fermions with universal chiral partition functions under specific bases. We explicitly decompose their modules into Virasoro modules of minimal models. We reveal an unexpected connection that integrates the coset construction, lattice construction, and orbifold construction, which is supported by proving a range of character identities within the context of coupled free fermions. Simultaneously, we obtain explicit expressions of certain string functions in terms of Dedekind eta functions.
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How the literature uses it
1 arXiv paper cite this in 7 sentences
Papers citing it · 5 sentences without a confident label
Builds on it 1 paper
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In this case, extra work is needed to deal with the intertwiners related to the module $L^2000_0020$ with details given in [ref] .
q-Identities for parafermion theories · $_4$ · 0.80
Uses its method or tool 1 paper
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In the case of $PF_2(𝔰𝔩_n)$, generalised commutation relations [ref] allow us to analyse the exclusion statistics of intertwiners.
q-Identities for parafermion theories · Universal chiral partition functions · 0.89
What it cites · 5 sentences without a confident label
Cites as background 1 paper
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There are also other applications such as [ref] .
One-Dimensional Statistical Mechanics for Identical Particles : The Calogero and Anyon Cases · Universal chiral partition functions for exclusion statistics · 0.89
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