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# Fermionic Expressions For Minimal Model Virasoro Characters (Memoirs of the American Mathematical Society) by Trevor A. Welsh

Written in English

## Subjects:

• Functional analysis,
• Discrete Mathematics,
• Mathematics,
• Combinatorial enumeration problems,
• Lie algebras,
• Science/Mathematics

## Book details

The Physical Object
FormatPaperback
Number of Pages160
ID Numbers
Open LibraryOL11420166M
ISBN 100821836560
ISBN 109780821836569

Download Fermionic Expressions For Minimal Model Virasoro Characters (Memoirs of the American Mathematical Society)

Fermionic expressions for all minimal model Virasoro characters $\chi^{p,p'}_{r,s}$ are stated and proved. Each such expression is a sum of terms of fundamental fermionic form type.

Read more. FERMIONIC EXPRESSIONS FOR MINIMAL MODEL VIRASORO CHARACTERS TREVOR A. WELSH Abstract. Fermionic expressions for all minimal model Virasoro characters χp,p ′ r,s are stated and proved. Each such expression is a sum of terms of fun-damental fermionic form type. In most cases, all these terms are written.

Fermionic expressions for all minimal model Virasoro characters $\chi^{p, p'}_{r, s}$ are stated and proved. Each such expression is a sum of terms of fundamental fermionic form type. Fermionic expressions for all minimal model Virasoro characters $\chi^{p, p'}_{r, s}$ are stated and proved.

Each such expression is a sum of terms of fundamental fermionic form type. In most cases, all these terms are written down using certain trees which are constructed for $s$ and $r$ from the Takahashi lengths and truncated Takahashi lengths associated with the continued fraction of $p'/p$.Cited by: Fermionic expressions for all minimal model Virasoro characters χ p,p′ r,s are stated and proved.

Each such expression is a sum of terms of fundamental fermionic form type. In most cases, all these terms are written down using certain trees which are constructed for s and r from the Takahashi lengths and truncated Takahashi lengths associated with the continued fraction of p ′/p.

Fermionic expressions for all minimal model Virasoro characters χ p,p′ r,s are stated and proved. Each such expression is a sum of terms of fundamental fermionic form type.

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, 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. integrable perturbations of Ising model; Integrable perturbation of Yang-Lee model; related items. Massive integrable perturbations of CFT and quasi-particles; sources of Bailey pairs; coset characters and Fermionic character formula; books.

Trevor Alan Welsh Fermionic expressions for minimal model Virasoro characters. Bosonic and Fermionic Character Expressions Motivation Bosonic-Fermionic q-Series Identities Bosonic and Fermionic Character Expressions Nahm’s conjecture cp;1 Logarithmic Conformal Field Theories Michael Flohr, Carsten Grabow and Michael Koehn Fermionic Expressions in LCFT Œ 4 / 21 Rogers-Ramanujan identities (a 2 f0;1g): X1 n=0 qn(n+a) (q.

including the superconformal index, the Schur operators, the fermionic forms of the characters of the Virasoro (p,p′) = (2,2k + 3) non-unitary minimal models (k = 1,2,), as well a speciﬁc W 3 non-unitary minimal model. Based on the fermionic form of the characters, we review the. This bosonic type expression is the well-known Rocha-Caridi expression for the (normalised) Virasoro character χ r, s p, p ′ from the minimal model M (p, p ′).

A fermionic expression encodes a construction of the Hilbert space by a filling process in which each species of quasiparticle is subject to a generalized exclusion principle.

This is in agreement with previous results on fermionic expressions, since it is known to also be the case for the characters of a given minimal model (see e.g.). Note that in [17], fermionic expressions for the characters of the free boson with central charge c = 1 and compactification radius r = p 2 [27] have been obtained.

fermionic sum representations for: All of the characters of the unitary Virasoro minimal models M(n +2;n+ 3), which correspond to the cosets (A (1) 1)n (A (1) 1)1 (A(1) 1)n+1; Certain characters of (G (1)) k (G (1)) l (G(1))k+l for G a simply-laced Lie algebra; Certain characters of non-unitary minimal models M(p;p+2)andM(p;kp+1).

We derive new fermionic expressions for the characters of the Virasoro minimal models M(k,2k±1) by analysing the recently introduced half-lattice paths. We present a "natural finitization" of the fermionic q-series (certain generalizations of the Rogers–Ramanujan sums) which were recently conjectured to be equal to Virasoro characters of the unitary minimal conformal field theory (CFT) ℳ (p, p + 1).

Fermionic counting of RSOS states and Virasoro character formulas for the unitary minimal series M(v, v+ 1): Exact results. A quartet of fermionic expressions for M (k,2 k ± 1) Virasoro characters via half-lattice paths Olivier Blondeau-Fournier et al-Path representation of states II: Operator construction of the fermionic character and spin- RSOS factorization Joël Lamy-Poirier and Pierre Mathieu-A Bijection Between Paths for the $${\mathcal{M}(p, 2p + 1)}$$ Minimal.

fermionic character expressions for other conformal ﬁeld theories such as the minimal Vira- soro models and SU(2) Wess-Zumino-Witten (WZW) models are given, some of the latter also being new. We prove q series identities between bosonic and fermionic representations of certain Virasoro characters.

These identities include some of the conjectures made by the Stony Brook group as special cases. Our method is a direct application of Andrews' extensions of Bailey's lemma to recently obtained polynomial identities.

Fermionic expressions for all minimal model Virasoro characters $\chi^{p,p'}_{r,s}$ are stated and proved.

Each such expression is a sum of terms of fundamental fermionic form type. The book is suitable for graduate students and researchers interested in algebra. Minimal elements in the poset of tilting modules; nsky,and v, Dynamical twists Minimal Model Virasoro Characters Trevor A.

Welsh, University of Melbourne, Parkville, Victoria, Australia University of. We first briefly review the role of lattice paths in the derivation of fermionic expressions for the M(p,p') minimal model characters of the Virasoro Lie algebra.

We then focus on the recently introduced half-lattice paths for the M(p,2p+/-1) characters, reformulating them in such a way that the two cases may be treated uniformly. That the generating functions of these half-lattice paths are.

To state the fermionic expressions of FGK we let Bbe the inverse Cartan matrix notation of Andrews’ book Partition Theory we have Q k;i(x) = J Fermionic expressions for minimal model Virasoro characters, Mem.

Amer. Math. Soc. (), no.viii+ pp. We first briefly review the role of lattice paths in the derivation of fermionic expressions for the M(p, p')minimalmodel characters of the Virasoro Lie algebra. We then focus on the recently introduced half-lattice paths for the M(p, 2pš1) characters, reformulating them in such a way that the two cases may be treated uniformly.

For p∈{3,4} and all p′>p, with p′ coprime to p, we obtain fermionic expressions for the combination χ 1,s p,p′ +q Δ χ p−1,s p,p′ of Virasoro (W 2) characters for various values of s, and particular choices of ng these expressions with known product expressions, we obtain q-series identities which are akin to the Andrews–Gordon identities.

We first briefly review the role of lattice paths in the derivation of fermionic expressions for the M(p, p′) minimal model characters of the Virasoro Lie algebra. We then focus on the recently introduced half-lattice paths for the M(p, 2p ± 1) characters, reformulating them in such a way that the two cases may be treated uniformly.

algebra. The signature of bosonic character expressions is the alternating sign, which reﬂects the subtraction of null vectors, whereas each summand of a fermionic character formula is manifestly positive. Furthermore, the factor (q)∞ keeps track of the free action of the Virasoro “creation” modes.

= bosonic sum’ expressions yield precisely the E8 Rogers-Ramanujan identity for the Virasoro character as given by Kedem et al [9]. Thermodynamic Bethe ansatz computations were also carried out [ 11 in the 3+ regime of the dilute A3 model.

In this case the model is known [3] to decouple, in the scaling limit, into an king model and a 6. algebra. The signature of bosonic character expressions is the alternating sign, which re ects the subtraction of null vectors, whereas each summand of a fermionic character formula is manifestly positive.

Furthermore, the factor (q) 1keeps track of the free action of the Virasoro \creation" modes. The Zk parafermionic conformal field theories, despite the relative complexity of their modes algebra, offer the simplest context for the study of the bases of states and their different combinator.

Abstract: We first briefly review the role of lattice paths in the derivation of fermionic expressions for the M(p, p′) minimal model characters of the Virasoro Lie algebra. We then focus on the recently introduced half-lattice paths for the M(p, 2p ± 1) characters, reformulating them in such a way that the two cases may be treated uniformly.

and is just a character of M(3,4),that is Ising model. To write down the generic formula for characters of minimal models let us remind some facts on CFT [3]. The symmetry of CFT is Virasoro algebra whose generating elements L n satisfy the following relations [L n;L m]=(n−m)L n+m+ c 12 (n3 −n) n;−m (3) For the minimal models M pthe.

Character expressions for conformal ﬁeld theories with W-symmetry 5 Virasoro characters 5 - and η-functions and their modular transformation properties 6 Torus amplitudes 7 The modular differential equation 8 3. Bosonic and fermionic expressions for characters.

Unitary Representations of the Virasoro and Supervirasoro Algebras. Goddard (COMMUN. MATH. PHYS. () ) AND CAMBRIDGE UNIV. - DAMTP (85,) 31 P. (SEE BOOK INDEX) • DOI: /BF; Integrals of Motion in Scaling Three State Potts Model Field Theory Fermionic expressions for minimal model Virasoro.

We first briefly review the role of lattice paths in the derivation of fermionic expressions for the M(p, p′) minimal model characters of the Virasoro Lie algebra. We then focus on the recently introduced half-lattice paths for the M(p, 2p ± 1) characters, reformulating them in such a way that the two cases may be treated uniformly.

That the generating functions of these half-lattice paths. The Virasoro algebra is an infinite dimensional Lie algebra that plays an increasingly important role in mathematics and theoretical physics. This book describes some fundamental facts about the representation theory of the Virasoro algebra in a self-contained manner.

Topics include the structure. Fermionic expressions for minimal model Virasoro characters / Trevor A. Welsh.

PUBLISHER: Providence, R.I.: American Mathematical Society, SERIES: Memoirs of the American Mathematical Society, no.

CALL NUMBER: QA 3.A57 no. CIMM:. The character is recognized as a Kac character of the logarithmic minimal model and is the character of a so-called Kac module [64, 65]. These characters are associated with an infinitely extended Kac table as the Kac labels r and s are unbounded from above.

Berkovich and B. McCoy, “Continued Fractions and Fermionic Representations for Characters of M(p,p′) Minimal Models,” preprint BONN-TH–28, ITPSB 94–, hep-th/ (to appear in Lett. Math. Phys.). Google Scholar; G. James and A. Kerber, The Representation Theory of the Symmetric Group (Addison-Wesley, Reading, MA, ).

We present fermionic formulas for the characters of superconformal models. and %$& ', and the * superconformal model with central charge$ '. The method used to derive these formulas is known as Bailey ﬂow.

We show Bailey ﬂows from the nonunitary minimal model with coprime positive integers to and, superconformal algebras. We derive a new. Skip to content. Previous; Archives; Next;» Posted: by cysy by cysy.Fermionic Construction of Free-Fermionic Models Non confidentiel Option Physics Directeur d’option Michel Gonin of which is the Minimal SuperSymmetric Model (often named as MSSM), but this new theory itself requires a larger context to account for the diﬀerent values.A minimal model is a CFT whose spectrum is built from finitely many irreducible representations of the Virasoro algebra.

Minimal models only exist for particular values of the central charge, = − (−), > ∈ {, }. There is an ADE classification of minimal models. In particular, the A-series minimal model with the central charge =, is a diagonal CFT whose spectrum is built from.

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