D-string fluid in conifold: II. Matrix model for D-droplets on and

Abstract

Motivated by similarities between Fractional Quantum Hall (FQH) systems and aspects of topological string theory on conifold, we continue in the present paper our previous study (hep-th/0604001, hep-th/0601020) concerning FQH droplets on conifold. Here we focus our attention on the conifold sub-varieties S 3 and S 2 and study the non commutative quantum dynamics of D1 branes wrapped on a circle.We give a matrix model proposal for FQH droplets of N point like particles on S 3 and S 2 with filling fraction ν = 1 k . We show that the ground state of droplets on S 3 carries an isospin j = kand gives remarkably rise to 2j + 1 droplets on S 2 with Cartan-Weyl charge |j z | ≤ j.

D-string fluid in conifold, I: Topological gauge model

“…This may be done by extending the results of [13,14] obtained in the framework of fractional quantum Hall droplets. An attempt using matrix field variables valued in GL (N, C) representations is under study in [15], progress in this direction will be reported elsewhere.…”

“…We will give a brief comment on this method in the end of this section. More involved details may be found in [15].…”

“…A way 1 to study the quantum effects on the holomorphy feature of the D-string fluid model is to proceed as follows. First think about the D string fluid model as a 1 An other tentative to approach the fluid of D-strings in conifold, by using a generalization of matrix model method based on canonical quantization, has been developed in [15]. There and as a first step in classical field theory based on the conifold geometry xy − zw = µ.…”

On Exceptional 't Hooft Lines in 4D-Chern-Simons Theory

“…While standard Chern-Simons (CS) gauge theories are topological theories involving hermitian gauge fields in odd spacetime [6], the Costello-Witten Yamazaki (CWY) theory lives in 4D space and goes beyond the hermiticity property. This non unitary feature allowed to extend the application of methods of standard QFT to complexified gauge fields living on complex manifolds [1,2,8,9,10]. The 4D-CS theory gives a new approach to describe major elements and phenomena of 2D integrable systems in terms of a complex CS gauge potential living on Σ × C and valued in a complex Lie algebra.…”

Graphene, Lattice Field Theory and Symmetries

“…In this paper, we use TBM to engineer a board class of lattice QFTs that are based on ADE Lie algebras [21,22] and their basic representations [23,24]. These engineered lattice systems classify the electronic properties of acetylene chain as a su (2) model, graphene as a su (3) lattice model and may have application in other fields; in particular in QFT on non commutative geometry [25,26,27], where space time is viewed as a crystal, and in the special subset of conformal field models based on affine Kac-Moody invariance and vertex operators [28,29,30]. To fix the ideas; let us describe briefly the main lines of the construction in the case of the series A N −1 ≃ su (N) [31] which is generated by (N − 1) commuting Cartan generators h i and N (N − 1) step operators E ±β where the vectors β = β 1 , ..., β N −1 stand for the positive roots of su (N).…”