Quiver Matrix Mechanics for IIB String Theory (I): Wrapping Membranes and Emergent Dimension

In this paper we present a discrete, non-perturbative formulation for type IIB string theory. Being a supersymmetric quiver matrix mechanics model in the framework of M(atrix) theory, it is a generalization of our previous proposal of compactification via orbifolding for deconstructed IIA strings. In the continuum limit, our matrix mechanics becomes a $(2+1)$-dimensional Yang-Mills theory with 16 supercharges. At the discrete level, we are able to construct explicitly the solitonic states that correspond to membranes wrapping on the compactified torus in target space. These states have a manifestly SL(2,\integer)-invariant spectrum with correct membrane tension, and give rise to an emergent flat dimension when the compactified torus shrinks to vanishing size.Comment: LaTeX 2e; 39 pages, 3 eps figures. v2: typos corrected; references added; identification of certain membrane states added. v3: minor corrections on membrane state

Quiver matrix mechanics for IIB string theory (II): generic dual tori, fractional matrix membrane and SL(2, Z) duality

ManuscriptWith the deconstruction technique, the geometric information of a torus can be encoded in a sequence of orbifolds. By studying the Matrix Theory on these orbifolds as quiver mechanics, we present a formulation that (de)constructs the torus of generic shape on which Matrix Theory is "compactified". The continuum limit of the quiver mechanics gives rise to a (1+2)-dimensional SYM. A hidden (fourth) dimension, that was introduced before in the Matrix Theory literature to argue for the electric-magnetic duality, can be easily identified in our formalism. We construct membrane wrapping states rigorously in terms of Dunford calculus in the context of matrix regularization. Unwanted degeneracy in the spectrum of the wrapping states is eliminated by using SL(2,Z) symmetry and the relations to the FD-string bound states. The dual IIB circle emerges in the continuum limit, constituting a critical evidence for IIB/M duality

Dynamics of giant-gravitons in the LLM geometry and the fractional quantum Hall effect

ManuscriptThe LLM's 1/2 BPS solutions of IIB supergravity are known to be closely related to the integer quantum Hall droplets with filling factor v = 1, and the giant gravitons in the LLM geometry behave like the quasi-holes in those droplets. In this paper we consider how the fractional quantum Hall effect may arise in this context, by studying the dynamics of giant graviton probes in a special LLM geometry, the AdS5 × S5 background, that corresponds to a circular droplet. The giant gravitons we study are D3-branes wrapping on a 3-sphere in S5. Their low energy world-volume theory, truncated to the 1/2 BPS sector, is shown to be described by a Chern-Simons finite-matrix model. We demonstrate that these giant gravitons may condense at right density further into fractional quantum Hall fluid due to the repulsive interaction in the model, giving rise to the new states in IIB string theory. Some features of the novel physics of these new states are discussed

Converting normal insulators into topological insulators via tuning orbital levels

Tuning the spin-orbit coupling strength via foreign element doping and/or modifying bonding strength via strain engineering are the major routes to convert normal insulators to topological insulators. We here propose an alternative strategy to realize topological phase transition by tuning the orbital level. Following this strategy, our first-principles calculations demonstrate that a topological phase transition in some cubic perovskite-type compounds CsGeBr$_3$ and CsSnBr$_3$ could be facilitated by carbon substitutional doping. Such unique topological phase transition predominantly results from the lower orbital energy of the carbon dopant, which can pull down the conduction bands and even induce band inversion. Beyond conventional approaches, our finding of tuning the orbital level may greatly expand the range of topologically nontrivial materials