Related papers: Dualities in Quantum Hall System and Noncommutativ…
We consider $\mathrm{U}(N)$ gauge theories with a pair of two-index tensors interacting through a quartic superpotential, in addition to fundamentals and antifundamentals. The models have a brane engineering in terms of NS, D4, D6 branes…
In this paper we study the algebra of quantum observables of the Chern-Simons matrix model which was originally proposed by Susskind and Polychronakos to describe electrons in fractional quantum Hall effects. We establish the commutation…
We have conclusively established the duality between noncommutative Maxwell-Chern-Simons theory and Self-Dual model, the latter in ordinary spacetime, to the first non-trivial order in the noncommutativity parameter $\theta^{\mu\nu}$, with…
Noncollinear and noncoplanar magnetic orders lead to unusual electronic structures and transport properties. We here investigate two types of multiple-Q magnetically ordered states and a topological phase transition between them in two…
While the internal structure of Abelian topological order is well understood, how to characterize the non-Abelian topological order is an outstanding issue. We propose a distinctive scheme based on the many-body Chern number matrix to…
Instantons, monopoles and vortices have become paradigms of topological structures in field theory and quantum mechanics, with important applications in particle physics, astrophysics, condensed matter physics and mathematics. We have…
It is shown how the electromagnetic response of the 2DEG under Quantumm Hall Effect regime, chracterized by the Chern-Simons topological action, transforms the sample impurities and defects in charge reservoirs that stabilize the the Hall…
A general study of non-abelian duality is presented. We first identify a possible obstruction to the conformal invariance of the dual theory for non-semisimple groups. We construct the exact non-abelian dual for any Wess-Zumino-Witten (WZW)…
We reconsider the Mott transition in the context of a two-dimensional fermion model with density-density coupling. We exhibit a Hilbert space mapping between the original model and the Double Lattice Chern-Simons theory at the critical…
We formulate a continuum quantum mechanics for non-relativistic, dipole-conserving fractons. Imposing symmetries and locality results in novel phenomena absent in ordinary quantum mechanical systems. A single fracton has a vanishing…
Recent experiments have shown that a quantized Hall plateau can occur in double layer systems at total filling factor v=1/2, though there is no plateau at v=1/2 in a normal single layer system. For the single layer system, considerable…
Kontsevich and Soibelman defined the Donaldson-Thomas invariants of a 3d Calabi-Yau category with a stability condition. Any cluster variety can produce an example of such a category, whose corresponding Donaldson-Thomas invariants are…
Mirror symmetry is a type of infrared duality in 3D quantum field theory that relates the low-energy dynamics of two distinct ultraviolet descriptions. Though first discovered in the supersymmetric context, it has far-reaching implications…
We explore some of the global aspects of duality transformations in String Theory and Field Theory. We analyze in some detail the equivalence of dual models corresponding to different topologies at the level of the partition function and in…
The supersymmetric structure of a generalized non-Hermitian driven two-level system is demonstrated. A unitary rotation turns the Hamiltonian into a more convenient form. After decoupling a set of differential equations, the supersymmetric…
The Morita equivalence for field theories on noncommutative two-tori is analysed in detail for rational values of the noncommutativity parameter theta (in appropriate units): an isomorphism is established between an abelian noncommutative…
It has recently pointed out that a four-dimensional analog of Chern-Simons theory provides an elegant framework for understanding integrable models with spectral parameters. The goal of this short note is to better understand the relation…
We investigate the spectrum of the gauge theory with Chern-Simons term on the noncommutative plane, a modification of the description of the Quantum Hall fluid recently proposed by Susskind. We find a series of the noncommutative massive…
Expanding the classic works of Kazhdan-Lusztig and Deodhar, we establish bar involutions and canonical (i.e., quasi-parabolic KL) bases on quasi-permutation modules over the type B Hecke algebra, where the bases are parameterized by cosets…
The interplay between non-Hermiticity and topology opens an exciting avenue for engineering novel topological matter with unprecedented properties. While previous studies have mainly focused on one-dimensional systems or Chern insulators,…