Justin Kulp
In this short note, we comment on the existence of two more fermionic unitary minimal models not included in recent work by Hsieh, Nakayama, and Tachikawa. These theories are obtained by fermionizing the $\mathbb{Z}_2$ symmetry of the m=11 and m=12 exceptional unitary minimal models. Furthermore, these should be the only missing cases.
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We show that there is a fermionic minimal model, i.e. a 1+1d conformal field theory which contains operators of half-integral spins in its spectrum, for each $c=1-6/m(m+1)$, $m\ge 3$. This generalizes the Majorana fermion for $c=1/2$, $m=3$ and the smallest $\mathcal{N}{=}1$ supersymmetric minimal model for $c=7/10$, $m=4$. We provide explicit Hamiltonians on Majorana chains realizing these fermionic minimal models.
The conjecture that the states of the fermionic quasi-particles in minimal conformal field theories are eigenstates of the integrals of motion to certain eigenvalues is checked and shown to be correct only for the Ising model.
We present fermionic sum representation for the general Virasoro character of the unitary minimal superconformal series ($N=1$). Example of the corresponding ``finitizated" identities relating corner transfer matrix polynomials with fermionic companions is considered. These identities in the thermodynamic limit lead to the generalized Rogers-Ramanujan identities.
We investigate some cosmological models arising from a non-minimal coupling of a fermionic field to gravity in the geometrical setting of Einstein-Cartan-Sciama-Kibble gravity. The role played by the non-minimal coupling together with torsion in facing problems such as cosmological singularity, inflation and dark energy is discussed.
Characters and linear combinations of characters that admit a fermionic sum representation as well as a factorized form are considered for some minimal Virasoro models. As a consequence, various Rogers-Ramanujan type identities are obtained. Dilogarithm identities producing corresponding effective central charges and secondary effective central charges are derived. Several ways of constructing more general fermionic representations are discussed.
The fermionic minimal models are a recently-introduced family of two-dimensional spin conformal field theories. We determine all of their conformal boundary states and potentially anomalous $\mathbb{Z}_2$ global symmetries. The latter task hinges upon on a conjecture about $\mathfrak{su}(2)$ affine parities generalising an earlier result known to have an interpretation in terms of Fermat curves. Our results indicate a close connection between several properties of the models, including the matching of the sizes of the SPT classes of boundary states, the existence of anomalous $\mathbb{Z}_2$ sy…
We investigate the effective Dirac equation, corrected by merging two scenarios that are expected to emerge towards the quantum gravity scale. Namely, the existence of a minimal length, implemented by the generalized uncertainty principle, and exotic spinors, associated with any non-trivial topology equipping the spacetime manifold. We show that the free fermionic dynamical equations, within the context of a minimal length, just allow for trivial solutions, a feature that is not shared by dynamical equations for exotic spinors. In fact, in this coalescing setup, the exoticity is shown to preve…
We consider sl(2) minimal conformal field theories on a cylinder from a lattice perspective. To each allowed one-dimensional configuration path of the A_L Restricted Solid-on-Solid (RSOS) models we associate a physical state |h> and a monomial in a finite fermionic algebra. The orthonormal states produced by the action of these monomials on the primary states generate finite Virasoro modules with dimensions given by the finitized Virasoro characters $χ^{(N)}_h(q)$. These finitized characters are the generating functions for the double row transfer matrix spectra of the critical RSOS models. We…
We present fermionic sum representations of the characters $χ^{(p,p')}_{r,s}$ of the minimal $M(p,p')$ models for all relatively prime integers $p'>p$ for some allowed values of $r$ and $s$. Our starting point is binomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin ${1\over 2}$ chain of anisotropy $-Δ=-\cos(π{p\over p'})$. We use the Takahashi-Suzuki method to express the allowed values of $r$ (and $s$) in terms of the continued fraction decomposition of $\{{p'\over p}\}$ (and ${p\over p'}$) where $\{x\}$ stands for the fractional part of $…
Fermionic Spectral Functions in a Two-Current Gubser-Rocha Model with Axion Momentum Relaxation
该研究在具有轴子动量弛豫的双电流Gubser-Rocha模型中，分析不同非最小费米子耦合通道对费米子谱函数的影响，阐明了电流混合等因素对全息费米子激发的重塑作用。
The Hilbert space of an RSOS-model, introduced by Andrews, Baxter, and Forrester, can be viewed as a space of sequences (paths) {a_0,a_1,...,a_L}, with a_j-integers restricted by 1<=a_j<=ν, |a_j-a_{j+1}|=1, a_0=s, a_L=r. In this paper we introduce different basis which, as shown here, has the same dimension as that of an RSOS-model. Following McCoy et al, we call this basis -- fermionic (FB). Our first theorem Dim(FB)=Dim(RSOS-basis) can be succinctly expressed in terms of some identities for binomial coefficients. Remarkably, these binomial identities can be q-deformed. Here, we give a simple…
We interpret aspects of the Schur indices, that were identified with characters of highest weight modules in Virasoro $(p,p')=(2,2k+3)$ minimal models for $k=1,2,\dots$, in terms of paths that first appeared in exact solutions in statistical mechanics. From that, we propose closed-form fermionic sum expressions, that is, $q, t$-series with manifestly non-negative coefficients, for two infinite-series of Macdonald indices of $(A_1,A_{2k})$ Argyres-Douglas theories that correspond to $t$-refinements of Virasoro $(p,p')=(2,2k+3)$ minimal model characters, and two rank-2 Macdonald indices that cor…
We present sum representations for all characters of the unitary Virasoro minimal models. They can be viewed as fermionic companions of the Rocha-Caridi sum representations, the latter related to the (bosonic) Feigin-Fuchs-Felder construction. We also give fermionic representations for certain characters of the general $(G^{(1)})_k \times (G^{(1)})_l \over (G^{(1)})_{k+l}}$ coset conformal field theories, the non-unitary minimal models ${\cal M}(p,p+2)$ and ${\cal M}(p,kp+1)$, the $N$=2 superconformal series, and the $\ZZ_N$-parafermion theories, and relate the $q\to 1$ behaviour of all these …
In these lecture notes, we review some recent works on Hamiltonian lattice gauge theories, that involve, in particular, tensor network methods. The results reviewed here are tailored together in a slightly different way from the one used in the contexts where they were first introduced, by looking at the Gauss law from two different points of view: for the gauge field it is a differential equation, while from the matter point of view, on the other hand, it is a simple, explicit algebraic equation. We will review and discuss what these two points of view allow and do not allow us to do, in term…
We consider two different conformal field theories with central charge c=7/10. One is the diagonal invariant minimal model in which all fields have integer spins; the other is the local fermionic theory with superconformal symmetry in which fields can have half-integer spin. We construct new conformal (but not topological or factorised) defects in the minimal model. We do this by first constructing defects in the fermionic model as boundary conditions in a fermionic theory of central charge c=7/5, using the folding trick as first proposed by Gang and Yamaguchi. We then acting on these with int…
By using a bosonization we uncover the topological gravity structure of Labastida, Pernici and Witten in ordinary $2d$ gravity coupled to $(p,q)$ minimal models. We study the cohomology class associated with the fermionic charge of the topological gravity which is shown to be isomorphic to that of the total $BRST$ charge. One of the ground ring generators of $c_M <1$ string theory is found to be in the equivariant cohomology of this fermionic charge.
We investigate the quantum effects of the non-minimal matter-gravity couplings derived by Cangemi and Jackiw in the realm of a specific fermionic theory, namely the abelian Thirring model on a Riemann surface of genus zero and one. The structure and the strength of the new interactions are seen to be highly constrained, when the topology of the underlying manifold is taken into account. As a matter of fact, by requiring to have a well-defined action, we are led both to quantization rules for the coupling constants and to selection rules for the correlation functions. Explicit quantum computati…
The fate of non-supersymmetric Gross-Neveu-Yukawa fixed point in two dimensions
本文通过费米子最小模型分类、拓扑缺陷线自旋匹配及双重辫子关系约束，确定二维非超对称Gross-Neveu-Yukawa不动点最可能对应于非幺正的费米子$(11,4)$最小模型。
It has been recently pointed out by Arkani-Hamed and Dimopoulos that if the universe is a landscape of vacua, and if therefore fine-tuning is not a valid guidance principle for searching for physics beyond the standard model, supersymmetric unification only requires the fermionic superpartners. We argue that in that landscape scenario, the fermionic superpartners are not needed for unification, which can be achieved in SO(10) either via a direct breaking to the standard model at the grand unification scale or through an intermediate gauge symmetry. In most minimal SO(10) models, the proton lif…
We prove a generalization of the Verlinde formula to fermionic rational conformal field theories. The fusion coefficients of the fermionic theory are equal to sums of fusion coefficients of its bosonic projection. In particular, fusion coefficients of the fermionic theory connecting two conjugate Ramond fields with the identity are either one or two. Therefore, one is forced to weaken the axioms of fusion algebras for fermionic theories. We show that in the special case of fermionic W(2,d)-algebras these coefficients are given by the dimensions of the irreducible representations of the horizon…
Path integral quantization of generic two-dimensional dilaton gravity non-minimally coupled to a Dirac fermion is performed. After integrating out geometry exactly, perturbation theory is employed in the matter sector to derive the lowest order gravitational vertices. Consistency with the case of scalar matter is found and issues of relevance for bosonisation are pointed out.
An overview of old and new results in studies of the quasi-realistic free fermionic models is presented, which include the recent discovery of exophobic string vacua and reproduction of the Higgs-matter splitting mechanism in a corresponding orbifold construction.
We present and prove Rogers-Schur-Ramanujan (Bose/Fermi) type identities for the Virasoro characters of the minimal model $M(p,p').$ The proof uses the continued fraction decomposition of $p'/p$ introduced by Takahashi and Suzuki for the study of the Bethe's Ansatz equations of the XXZ model and gives a general method to construct polynomial generalizations of the fermionic form of the characters which satisfy the same recursion relations as the bosonic polynomials of Forrester and Baxter. We use this method to get fermionic representations of the characters $χ_{r,s}^{(p,p')}$ for many classes…
A derivation of the basis of states for the $SM(2,4k)$ superconformal minimal models is presented. It relies on a general hypothesis concerning the role of the null field of dimension $2k-1/2$. The basis is expressed solely in terms of $G_r$ modes and it takes the form of simple exclusion conditions (being thus a quasi-particle-type basis). Its elements are in correspondence with $(2k-1)$-restricted jagged partitions. The generating functions of the latter provide novel fermionic forms for the characters of the irreducible representations in both Ramond and Neveu-Schwarz sectors.
We perform a BRST analysis of the N=2 superconformal minimal unitary models. A bosonic as well as fermionic BRST operators are used to construct irreducible representations of the N=2 superconformal algebra on the Fock space as BRST cohomology classes of the BRST operators. Also a character formula is rederived by using the BRST analysis.
The metric-affine bumblebee model in the presence of fermionic matter minimally coupled to the connection is studied. We show that the model admits an Einstein frame representation in which the matter sector is described by a non-minimal Dirac action without any analogy in the literature. Such non-minimal terms involve unconventional couplings between the bumblebee and the fermion field. We then rewrite the quadratic fermion action in the Einstein frame in the basis of 16 Dirac matrices in order to identify the coefficients for Lorentz/CPT violation in all orders of the non-minimal coupling $ξ…
Topological Defect Lines in Two Dimensional Fermionic CFTs
本文研究了二维费米子共形场论中的拓扑缺陷线，利用超融合范畴数学语言对其进行分类，求解F-移动并推导自旋选择规则，同时在极小模型中给出了具体实现。
Gravitational Wave-Induced Freeze-In of Fermionic Dark Matter
研究通过引力波背景实现费米暗物质冻结，利用in-out方法计算Weyl费米子能量密度，探讨其作为暗物质的可行性。
The Gordon-Andrews identities, which generalize the Rogers-Ramanujan-Schur identities, provide product and fermionic forms for the characters of the minimal conformal field theories (CFTs) M(2,2k+1). We discuss/conjecture identities of a similar type, providing two different fermionic forms for the characters of the models SM(2,4k) in the minimal series of N=1 super-CFTs. These two forms are related to two families of thermodynamic Bethe Ansatz (TBA) systems, which are argued to be associated with the $\hatϕ_{1,3}^{\rm top}$- and $\hatϕ_{1,5}^{\rm bot}$-perturbations of the models SM(2,4k). Ce…
This is the second of two articles (independent of each other) devoted to the analysis of the path description of the states in su(2)_k WZW models. Here we present a constructive derivation of the fermionic character at level k based on these paths. The starting point is the expression of a path in terms of a sequence of nonlocal (formal) operators acting on the vacuum ground-state path. Within this framework, the key step is the construction of the level-k operator sequences out of those at level-1 by the action of a new type of operators. These actions of operators on operators turn out to h…
We derive the fermionic polynomial generalizations of the characters of the integrable perturbations $ϕ_{2,1}$ and $ϕ_{1,5}$ of the general minimal $M(p,p')$ conformal field theory by use of the recently discovered trinomial analogue of Bailey's lemma. For $ϕ_{2,1}$ perturbations results are given for all models with $2p>p'$ and for $ϕ_{1,5}$ perturbations results for all models with ${p'\over 3}<p< {p'\over 2}$ are obtained. For the $ϕ_{2,1}$ perturbation of the unitary case $M(p,p+1)$ we use the incidence matrix obtained from these character polynomials to conjecture a set of TBA equations. …
We derive new finitized fermionic characters for the superconformal unitary minimal models by interpreting the RSOS configuration sums as fermi-gas partition functions. This extends to the supersymmetric case the method introduced by Warnaar for the Virasoro unitary mimimal models. The key point in this construction is the proper identification of fermi-type charged particles in terms of the path's peaks. For this, an instrumental preliminary step is the adaptation to the superconformal case of the operator description of the usual RSOS paths introduced recently.
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