arXiv subjects

Xia Gu

Publications and source records attributed to Xia Gu.

5 recordsLinked to original sources

arXiv2026

On the monodromy of KZ-connections with irregular singularities

We study Knizhnik-Zamolodchikov (KZ) connection in the presence of irregular singularities, that is, poles of higher order. We consider both the case of a universal connection and the case when it is associated with a specific simple Lie algebra, such as $\mathfrak{su}(2)$. We give some general results about the monodromies of such flat connections in the configuration spaces of points, and provide explicit examples of topological invariants of links (more generally, tangles) realized by the monodromy.

hep-th↗

arXiv2023

Irregular Fibonacci Conformal Blocks

This work studies Liouville conformal blocks of irregular type with the insertion of at least one level-$3$ degenerate field admitting a Fibonacci fusion rule. We algebraically derive the corresponding third-order BPZ equations for regular blocks and their modifications when a rank one irregular operator is inserted. Employing Lefschetz thimbles as integration cycles, we then successively proceed to construct integral representations and prove that they satisfy the corresponding BPZ equations. Finally, we show that taking a semiclassical limit, these integral representations can be expressed in terms of Heun functions and have correct leading behaviors consistent with conformal weights and fusion rules.

hep-th↗

arXiv2023

Generalized Cardy conditions of topological defect lines

We propose a systematic procedure to work out systems of topological defect lines (TDLs) in minimal models. The only input of this method is the modular invariant partition function. For diagonal and permutation diagonal models, we prove there is a bijection between simple TDLs and primary fields preserving fusion rules. For block-diagonal models, we work out simple TDLs in the $3$-state Potts model as an example. The results agree with those in $3D$ topological field theory methods.

hep-th↗

arXiv2023

Liouville conformal blocks and Stokes phenomena

In this work we derive braid group representations and Stokes matrices for Liouville conformal blocks with one irregular operator. By employing the Coulomb gas formalism, the corresponding conformal blocks can be interpreted as wavefunctions of a Landau-Ginzburg model specified by a superpotential $\mathcal{W}$. Alternatively, these can also be viewed as wavefunctions of a 3d TQFT on a 3-ball with boundary a 2-sphere on which the operator insertions represent Anyons whose fusion rules describe novel topological phases of matter.

hep-th↗

arXiv2021

Ising-like and Fibonacci-Anyons from KZ-equations

In this work we present solutions to Knizhnik-Zamolodchikov (KZ) equations corresponding to conformal block wavefunctions of non-Abelian Ising- and Fibonacci-Anyons. We solve these equations around regular singular points in configuration space in terms of hypergeometric functions and derive explicit monodromy representations of the braid group action. This confirms the correct non-Abelian statistics of the solutions. One novelty of our approach is that we explicitly keep track of spin basis states and identify conformal blocks uniquely with such states at relevant points in moduli space.

hep-th↗