arXiv subjects

Jian-Feng Wu

Publications and source records attributed to Jian-Feng Wu.

9 recordsLinked to original sources

arXiv2026

Singular band Induced by Long-Range Interaction Enables Unsplit Spreading of Localized Excitations

In conventional lattice models, the dispersion relation $ω(k)$ is assumed to be a smooth function which is periodic over the first Brillouin Zone. However, in subwavelength atom arrays the dispersion of the light-mediated long-range interaction is singular at the light cone. This observation prompts us to ask what effect arises from such band singularity. Here we demonstrate that, due to the topology of smooth functions defined over the periodic Brillouin zone, smoothness implies the splitting of an initially localized excitation into counter-propagating wave packets. Consequently, unsplit spreading can occur only when $ω(k)$ develops singular features, precisely what long-range interactions enable. We identify unsplit spreading in 1D toy tight-bounding models and the realistic models of 1D and 2D subwavelength atomic arrays. Our work establishes unsplit spreading as an experimentally accessible, smoking-gun signature of singular band structure.

quant-ph↗

arXiv2017

A Macdonald refined topological vertex

We consider the refined topological vertex of Iqbal et al, as a function of two parameters (x, y), and deform it by introducing Macdonald parameters (q, t), as in the work of Vuletic on plane partitions, to obtain 'a Macdonald refined topological vertex'. In the limit q -> t, we recover the refined topological vertex of Iqbal et al. In the limit x -> y, we obtain a qt-deformation of the topological vertex of Aganagic et al. Copies of the vertex can be glued to obtain qt-deformed 5D instanton partition functions that have well-defined 4D limits and, for generic values of (q, t), contain infinite-towers of poles for every pole in the limit q -> t.

hep-th↗

arXiv2015

From topological strings to minimal models

We glue four refined topological vertices to obtain the building block of 5D $U(2)$ quiver instanton partition functions. We take the 4D limit of the result to obtain the building block of 4D instanton partition functions which, using the AGT correspondence, are identified with Virasoro conformal blocks. We show that there is a choice of the parameters of the topological vertices that we start with, as well as the parameters and the intermediate states involved in the gluing procedure, such that we obtain Virasoro minimal model conformal blocks.

hep-th↗

arXiv2014

A new regularization of loop integral, no divergence, no hierarchy problem

We find a new regularization scheme which is motivated by the Bose-Einstein condensation. The energy of the virtual particle is considered as discrete. Summing them and regulating the summation by the Riemann $ζ$ function can give the result of loop integral. All the divergences vanish, we can get almost the same results as Dimensional Regularization. The prediction beyond Dimensional Regularization is also shown in the QED. The hierarchy problem of the radiative correction of scalar mass completely vanish.

hep-th↗

arXiv2014

Fermionization, Triangularization and Integrability

In this article, we derive the fermionic formalism of Hamiltonians as well as corresponding excitation spectrums and states of Calogero-Sutherland(CS), Laughlin and Halperin systems, respectively. In addition, we study the triangular property of these Hamiltonians and prove the integrability in these three cases.

math-ph↗

arXiv2014

Vertex Operators, $\mathbb{C}^3$ Curve and Topological Vertex

In this article, we prove the conjecture that Kodaira-Spencer theory for the topological vertex is a free fermion theory. By dividing the $\mathbb{C}^3$ curve into core and asymptotic regions and using Boson-Fermion correspondence, we construct a generic three-leg correlation function which reformulates the topological vertex in a vertex operator approach. We propose a conjecture of the correlation function identity which in a degenerate case becomes Zhou\rq{}s identity for a Hopf link.

hep-th↗

arXiv2011

AGT conjecture and AFLT states: a complete construction

A complete construction of the AFLT states is proposed. With this construction and for all the cases we have checked, the AGT conjecture on the equivalence of Nekrasov Instanton Counting (NIC) to the $Vir\oplus u(1)$ conformal block has been verified to be true.

hep-th↗

arXiv2011

Recursions in Calogero-Sutherland Model Based on Virasoro Singular Vectors

The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function, which is the spectrum generating function for the Calogero-Sutherland(CS) model. To accomplish this work, the hidden Virasoro structure in the CS model is much explored. In particular, we found that the Virasoro singular vectors form a skew hierarchy in the CS model. Literally, skew is analogous to coset, but here specifically refer to the operation on the Young tableaux. In fact, based on the construction of the Virasoro singular vectors, this hierarchical structure can be used to give a complete construction of the CS states, i.e. the Jack symmetric functions, recursively. The construction is given both in operator formalism as well as in integral representation. This new integral representation for the Jack symmetric functions may shed some insights on the spectrum constructions for the other integrable systems.

hep-th↗

arXiv2009

From Liouville to Chern-Simons, Alternative Realization of Wilson Loop Operators in AGT Duality

We propose an SL(2,R) Chern-Simons description of Liouville field theory (LFT), whose correlation function duals to partition function of N=2 SU(2) gauge theories. We give the dual expressions for conformal blocks, fusion rules, and Wilson loop operators in Chern-Simons theory. By realizing Wilson loop operator in Liouville as a Hopf link in S^3 on which lives an SL(2,R) Chern-Simons theory, we obtain an alternative description of monodromy of this loop operator in Liouville field theory as the ratio of link invariants. We show how to calculate t'Hooft loops in the simplest example -- the N=4 super Yang-Mills theory. The results we obtained are consistant with those in 0909.0945 and 0909.1105.

hep-th↗