Related papers: Embedding Fractional Quantum Hall Solitons in M-th…
Recently, generalizations of fractional quantum Hall (FQH) states known as fractional quantum anomalous Hall or, equivalently, fractional Chern insulators states have been realized in lattice models. Ideal wavefunctions such as the Laughlin…
Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide quantizations of the algebra of functions on the…
In this paper we elaborate on the correspondence between the quantum Hall system with filling factor equal to one and the N=4 SYM theory in the 1/2 BPS sector, previously mentioned in the [hep-th/0409174, hep-th/0409115]. We show the…
A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in Fractional Quantum Hall states, and in predicting…
We study M-theory fivebranes wrapped on Special Lagrangian submanifolds ($\S_n$) in Calabi-Yau three- and fourfolds. When the M5 wraps a four-cycle, the resulting theory is a two-dimensional domain wall embedded in three-dimensional bulk…
We present M-theory compactifications on $K_3 \times K_3$ with membranes near the $A_n$ or $D_n$ singularities of the $K_3$ spaces. By realizing each of these compactifications in two different ways as type I' models with 2- and 6-branes,…
We study various three-dimensional supersymmetric Maxwell Chern-Simons solitons by using type IIB brane configurations. We give a systematic classification of soliton spectra such as topological BPS vortices and nontopological vortices in…
We give a direct calculation of the curvature of the Hitchin connection, in geometric quantization on a symplectic manifold, using only differential geometric techniques. In particular, we establish that the curvature acts as a first-order…
We study three-dimensional superconformal field theories on wrapped M5-branes. Applying the gauge/gravity duality and the recently proposed 3d-3d relation, we deduce quantitative predictions for the perturbative free energy of a…
We analyze a recently proposed method to create fractional quantum Hall (FQH) states of atoms confined in optical lattices [A. S{\o}rensen {\it et al.}, Phys. Rev. Lett. {\bf 94} 086803 (2005)]. Extending the previous work, we investigate…
In the Berkooz-Douglas matrix model of M theory in the presence of longitudinal $M5$-brane, we investigate the effective dynamics of the system by considering the longitudinal $M5$-brane as the background and the spherical $M5$-brane…
The interplay between topology and strong interactions gives rise to a variety of exotic quantum phases, including fractional quantum Hall (FQH) states and their lattice analogs - fractional Chern insulators (FCIs). Such topologically…
We describe a class of supersymmetric gauged linear sigma-model, whose target space is the infinite dimensional space of bundles on a Calabi-Yau 3- or 2-fold. This target space can be considered the configuration space of D-branes wrapped…
Density oscillations in quantum fluids can reveal their fundamental characteristic features. In this work, we study the density oscillation of incompressible fractional quantum Hall (FQH) fluids created by flux insertion. For the model…
Using brane quantization, we study the representation theory of the spherical double affine Hecke algebra of type $A_1$ in terms of the topological A-model on the moduli space of flat SL(2,C)-connections on a once-punctured torus. In…
We present a Landau-Ginzburg theory for a fractional quantized Hall nematic state and the transition to it from an isotropic fractional quantum Hall state. This justifies Lifshitz-Chern-Simons theory -- which is shown to be its dual -- on a…
These notes of a course given at IRMA in April 2009 cover some aspects of the representation theory of fundamental groups of manifolds of dimension at most 3 in compact Lie groups, mainly $\su$. We give detailed examples, develop the…
A pair $(K,K')$ consisting of a smooth triangulation $K$ of a compact smooth oriented Riemannian manifold $M$ and a sufficiently fine subdivision $K'$ determines a finite-dimensional Cheeger--Simons model $\mathscr{CS}(K,K')$ built from…
Recent experimental success in the realization of two-dimensional (2D) magnetism has stimulated the search for new magnetic 2D materials with strong magnetic anisotropy and high Curie temperature. One promising subgroup of 2D magnetic…
We study the correspondence between the moduli space of vacua of three-dimensional supersymmetric Yang-Mills (Maxwell) Chern-Simons theories and brane configurations with (p,q)5-brane. For Coulomb branches, the number of the massless…