arXiv subjects
Publications and source records attributed to Bo-Yu Hou.
With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representation of the partition function of the six-vertex model with a non-diagonal reflecting end under domain wall boundary condition.
With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representations of the scalar products of Bethe states of the model.
A Higgs-Yang Mills monopole scattering spherical symmetrically along light cones is given. The left incoming anti-self-dual αplane fields are holomorphic, but the right outgoing SD βplane fields are antiholomorphic, meanwhile the diffeomorphism symmetry is preserved with mutual inverse affine rapidity parameters μand μ^{-1}. The Dirac wave function scattering in this background also factorized respectively into the (anti)holomorphic amplitudes. The holomorphic anomaly is realized by the center term of a quasi Hopf algebra corresponding to an integrable conform affine massive field. We find explicit Nahm transformation matrix(Fourier-Mukai transformation) between the Higgs YM BPS (flat) bundles (D modules) and the affinized blow up ADHMN twistors (perverse sheafs). Thus establish the algebra for the Hecke-'t Hooft operators in the Hecke correspondence of the geometric Langlands Program.
By extending the dressing symmetric action of IIB string in $AdS_5\times S^5$ to the $D_3$ brane, we find a gauged WZW action of Higgs Yang-Mills field including the 2-cocycle of axially anomaly. The left and right twistor structure of left and right $α$-planes glue into an ambitwistor. The symmetry group of Nahm equations is central extended to an affine group, thus we explain why the spectral curve is given by affine Toda.
In this paper we interpret the hidden symmetry of the moduli space of IIB superstring on $AdS_{5}\times S^{5}$ in terms of the chiral embedding in $AdS_{5}$, which turns to be the $\mathbb{CP}^{3}$ conformal affine Toda model. We review how the position $μ$ of poles in the Riemann-Hilbert formulation of dressing transformation and how the value of loop parameters $μ$ in the vertex operator of affine algebra determines the moduli space of the soliton solutions, which describes the moduli space of the Green-Schwarz superstring. We show also how this affine SU(4) symmetry affinize the conformal symmetry in the twistor space, and how a soliton string corresponds to a Robinson congruence with twist and dilation spin coefficients $μ$ of twistor.
In this paper, we give the general forms of the minimal $L$ matrix (the elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal representation of the $A_{n-1}$ series elliptic quantum group given by Felder and Varchenko. The explicit dependence of elements of $L$-matrices on spectral parameter $z$ are given. They are of five different forms (A(1-4) and B). The algebra for the coefficients (which do not depend on $z$) are given. The algebra of form A is proved to be trivial, while that of form B obey Yang-Baxter equation (YBE). We also give the PBW base and the centers for the algebra of form B.
In this paper, we motivate how the Hodge dual related with S-duality gives the hidden symmetry in the moduli space of IIB string. Utilizing the static $% κ$-symmetric Killing gauge, if we take the Hodge dual of the vierbeins keeping the connection invariant, the duality of Maure-Cartan equations and the equations of motion becomes manifest. Thus by twistly transforming the vierbein, we can express the BPR currents as the Lax connections by a unique spectral parameter. Then we construct the generators of the infinitesimal dressing symmetry, the related symmetric algebra becomes the affine $% gl(2,2|4)^{(1)}$, which can be used to find the classical $r$ matrix.
In this paper, we construct the common eigenstates of "translation" operators $\{U_{s}\}$ and establish the generalized $Kq$ representation on integral noncommutative torus $T^{2N}$. We then study the finite rotation group $G$ in noncommutative space as a mapping in the $Kq$ representation and prove a Blocking Theorem. We finally obtain the complete set of projection operators on the integral noncommutative orbifold $T^{2N}/G$ in terms of the generalized $Kq$ representation. Since projectors are soliton solutions on noncommutative space in the limit $α^{\prime}B_{ij}\to \infty (Θ_{ij}/α^{\prime}\to 0)$, we thus obtain all soliton solutions on that orbifold $T^{2N}/G$.
In this paper, we construct a closed form of projectors on the integral noncommutative orbifold $T^2/Z_6$ in terms of elliptic functions by $GHS$ construction. After that, we give a general solution of projectors on $% T^{2}/Z_{6}$ and $T^{2}/Z_{3}$ with minimal trace and continuous reduced matrix $M(k,q_{0})$.The projectors constructed by us possess symmetry and manifest covariant forms under $Z_{6}$ rotation. Since projectors correspond to the soliton solutions of field theory on the noncommutative orbifold, we thus present a series of corresponding manifest covariant soliton solutions.
In this paper, we explicitly construct a series of projectors on integral noncommutative orbifold $T^2/Z_4$ by extended $GHS$ constrution. They include integration of two arbitary functions with $Z_4$ symmetry. Our expressions possess manifest $Z_{4}$ symmetry. It is proved that the expression include all projectors with minimal trace and in their standard expansions, the eigen value functions of coefficient operators are continuous with respect to the arguments $k$ and $q$. Based on the integral expression, we alternately show the derivative expression in terms of the similar kernal to the integral one.Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a series of corresponding solitons.
After review the quantum Hall effect on the fuzzy two-sphere $S^2$ and Zhang and Hu's 4-sphere $S^4$, the incompressible quantum Hall fluid on $S^2$, $S^4$ and torus are discussed respectively. Next, the corresponding Laughlin wavefunctions on $S^2$ are also given out. The ADHM construction on $S^4$ is discussed. We also point out that on torus, the incompressible quantum Hall fluid is related to the integrable Gaudin model and the solution can be given out by the Yang Bethe ansatz.
We develop the description of non-commutative geometry of the 4-dimensional quantum Hall fluid's theory proposed recently by Zhang and Hu. The non-commutative structure of fuzzy $S^{4}$ appears naturally in this theory. The fuzzy monopole harmonics, which are the essential elements in this non-commutative geometry, are explicitly constructed and their obeying the matrix algebra is obtained. This matrix algebra is associative. We also propose a fusion scheme of the fuzzy monopole harmonics of the coupling system from those of the subsystems, and determine the fusion rule in such fusion scheme. By products, we provide some essential ingredients of the theory of SO(5) angular momentum. In particular, the explicit expression of the coupling coefficients, in the theory of SO(5) angular momentum, are given. It is discussed that some possible applications of our results to the 4-dimensional quantum Hall system and the matrix brane construction in M-theory.
For the noncommutative torus ${\cal T}$, in case of the N.C. parameter $θ= \frac{Z}{n}$ and the area of ${\cal T}$ is an integer, we construct the basis of Hilbert space ${\cal H}_n$ in terms of $θ$ functions of the positions $z_i$ of $n$ solitons. The loop wrapping around the torus generates the algebra ${\cal A}_n$. We show that ${\cal A}_n$ is isomorphic to the $Z_n \times Z_n$ Heisenberg group on $θ$ functions. We find the explicit form for the local operators, which is the generators $g$ of an elliptic $su(n)$, and transforms covariantly by the global gauge transformation of the Wilson loop in ${\cal A}_n$. By acting on ${\cal H}_n$ we establish the isomorphism of ${\cal A}_n$ and $g$. Then it is easy to give the projection operators corresponding to the solitons and the ABS construction for generating solitons. We embed this $g$ into the $L$-matrix of the elliptic Gaudin and C.M. models to give the dynamics. For $θ$ generic case, we introduce the crossing parameter $η$ related with $θ$ and the modulus of ${\cal T}$. The dynamics of solitons is determined by the transfer matrix $T$ of the elliptic quantum group ${\cal A}_{τ, η}$, equivalently by the elliptic Ruijsenaars operators $M$. The eigenfunctions of $T$ found by Bethe ansatz appears to be twisted by $η$.
For the noncommutative torus ${\cal T}$, in case of the N.C. parameter $θ= \frac{Z}{n}$, we construct the basis of Hilbert space ${\ca$H}_n$ in terms of $θ$ functions of the positions $z_i$ of $n$ solitons. The wrapping around the torus generates the algebra ${\cal A}_n$, which is the $Z_n \times Z_n$ Heisenberg group on $θ$ functions. We find the generators $g$ of an local elliptic $su(n)$, w$transform covariantly by the global gauge transformation of ${\cal A}$By acting on ${\cal H}_n$ we establish the isomorphism of ${\cal A}_n$$g$. We embed this $g$ into the $L$-matrix of the elliptic Gaudin and$models to give the dynamics. The moment map of this twisted cotangent $su_n({\cal T})$ bundle is matched to the $D$-equation with Fayet-Illiopoulos source term, so the dynamics of the N.C. solitons becomes that of the brane. The geometric configuration $(k, u)$ of th$spectral curve ${\rm det}|L(u) - k| = 0$ describes the brane configuration, with the dynamical variables $z_i$ of N.C. solitons as$moduli $T^{\otimes n} / S_n$. Furthermore, in the N.C. Chern-Simons theory for the quantum Hall effect, the constrain equation with quasiparticle source is identified also with the moment map eqaution $the N.C. $su_n({\cal T})$ cotangent bundle with marked points. The eigenfunction of the Gaudin differential $L$-operators as the Laughli$wavefunction is solved by Bethe ansatz.
We study the algebra ${\cal A}_n$ and the basis of the Hilbert space ${\cal H}_n$ in terms of the $θ$ functions of the positions of $n$ solitons. Then we embed the Heisenberg group as the quantum operator factors in the representation of the transfer matrice of various integrable models. Finally we generalize our result to the generic $θ$ case.
The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$. We give the bosonization of the boundary states. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy.
We propose a rational quantum deformed nonlocal currents in the homogenous space $SU(2)_k/U(1)$, and in terms of it and a free boson field a representation for the Drinfeld currents of Yangian double at a general level $k=c$ is obtained. In the classical limit $\hbar \to 0$, the quantum nonlocal currents become $SU(2)_k$ parafermion, and the realization of Yangian double becomes the parafermion realization of $SU(2)_k$ current algebra.
Elliptic current algebras E_{q,p}(\hat{g}) for arbitrary simply laced finite dimensional Lie algebra g are defined and their co-algebraic structures are studied. It is shown that under the Drinfeld like comultiplications, the algebra E_{q,p}(\hat{g}) is not co-closed for any g. However putting the algebras E_{q,p}(\hat{g}) with different deformation parameters together, we can establish a structure of infinite Hopf family of algebras. The level 1 bosonic realization for the algebra E_{q,p}(\hat{g}) is also established.