Contributions à l'Etude du Vertex Topologique en Théorie ... - Toubkal
Contributions à l'Etude du Vertex Topologique en Théorie ... - Toubkal
Contributions à l'Etude du Vertex Topologique en Théorie ... - Toubkal
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Nuclear Physics B 801 [FS] (2008) 316–345www.elsevier.com/locate/nuclphysbG<strong>en</strong>eralized MacMahon G d (q) as q-deformed CFT 2correlation functionLalla Btissam Drissi a,b , Houda Jehjouh a,b , El Hassan Saidi a,b,c,∗a Lab/UFR-Physique des Hautes Energies, Faculté des Sci<strong>en</strong>ces, Rabat, Moroccob GNPHE, Groupem<strong>en</strong>t National de Physique des Hautes Energies, Siège Focal: FS, Rabat, Moroccoc Académie Hassan II des Sci<strong>en</strong>ces et Techniques, Collège des Sci<strong>en</strong>ces Physiques et Chimiques, Rabat, MoroccoReceived 18 January 2008; received in revised form 27 February 2008; accepted 4 March 2008Available online 16 March 2008AbstractUsing Γ ± (z) vertex operators of the c = 1 two-dim<strong>en</strong>sional conformal field theory, we give a 2d-quantumfield theoretical derivation of the conjectured d-dim<strong>en</strong>sional MacMahon function G d (q). We interpretthis function G d (q) as a (d + 1)-point correlation function G d+1 (z 0 ,...,z d ) of some local vertex operatorsO j (z j ). We determine these operators and show that they are particular composites of q-deformedhierarchical vertex operators Γ (p)± , with a positive integer p. In agreem<strong>en</strong>t with literature’s results, we findthat G d (q), d 4, cannot be the g<strong>en</strong>erating functional of all d-dim<strong>en</strong>sional g<strong>en</strong>eralized Young diagrams.© 2008 Elsevier B.V. All rights reserved.Keywords: Topological string; <strong>Vertex</strong> operators; Young diagrams and solid partitions; c = 1 2d conformal field model;G<strong>en</strong>eralized MacMahon function; q-deformed QFT 21. Intro<strong>du</strong>ctionThe study of two-dim<strong>en</strong>sional (2d) MacMahon function G 2 , and its 3d-g<strong>en</strong>eralization G 3 appearin many areas of statistical physics, such as crystals growth, crystals melting, Bose–Einsteinstatistics and dimer model [1–7]. Rec<strong>en</strong>tly, these functions have known a revival of interest inconnection with topological string theory [8–10]; in particular in the study of BPS black holes,giv<strong>en</strong> by branes wrapping collapsed cycles in Calabi–Yau orbifolds, and in the infinite n limit* Corresponding author at: Lab/UFR-Physique des Hautes Energies, Faculté des Sci<strong>en</strong>ces, Rabat, Morocco.E-mail addresses: drissilb@gmail.com (L.B. Drissi), jehjouh@gmail.com (H. Jehjouh), h-saidi@fsr.ac.ma(E.H. Saidi).0550-3213/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.nuclphysb.2008.03.006
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