The Quiver Matrix Model and 2d-4d Conformal Connection

We review the quiver matrix model (the ITEP model) in the light of the recent progress on 2d-4d connection of conformal field theories, in particular, on the relation between Toda field theories and a class of quiver superconformal gauge theories. On the basis of the CFT representation of the beta deformation of the model, a quantum spectral curve is introduced as << det (x- i g_s \partial \phi(z)) >>=0 at finite N and for beta \neq 1. The planar loop equation in the large N limit follows with the aid of W_n constraints. Residue analysis is provided both for the curve of the matrix model with the "multi-log" potential and for the Seiberg-Witten curve in the case of SU(n) with 2n flavors, leading to the matching of the mass parameters. The isomorphism of the two curves is made manifest.Comment: 37 pages; v2: version to appear in Prog. Theor. Phys. Title changed. Isomorphism of the SU(n) spectral curve and the SW curve of Witten-Gaiotto form as well as the matching of the mass parameters more fully give

Motions of the String Solutions in the XXZ Spin Chain under a Varying Twist

We determine the motions of the roots of the Bethe ansatz equation for the ground state in the XXZ spin chain under a varying twist angle. This is done by analytic as well as numerical study at a finite size system. In the attractive critical regime $0< \Delta <1$, we reveal intriguing motions of strings due to the finite size corrections to the length of the strings: in the case of two-strings, the roots collide into the branch points perpendicularly to the imaginary axis, while in the case of three-strings, they fluctuate around the center of the string. These are successfully generalized to the case of $n$-string. These results are used to determine the final configuration of the momenta as well as that of the phase shift functions. We obtain these as well as the period and the Berry phase also in the regime $\Delta \leq -1$, establishing the continuity of the previous results at $-1 < \Delta < 0$ to this regime. We argue that the Berry phase can be used as a measure of the statistics of the quasiparticle ( or the bound state) involved in the process.Comment: An important reference is added and mentioned at the end of the tex

Comments on T-dualities of Ramond-Ramond Potentials

The type IIA/IIB effective actions compactified on T^d are known to be invariant under the T-duality group SO(d, d; Z) although the invariance of the R-R sector is not so direct to see. Inspired by a work of Brace, Morariu and Zumino,we introduce new potentials which are mixture of R-R potentials and the NS-NS 2-form in order to make the invariant structure of R-R sector more transparent. We give a simple proof that if these new potentials transform as a Majorana-Weyl spinor of SO(d, d; Z), the effective actions are indeed invariant under the T-duality group. The argument is made in such a way that it can apply to Kaluza-Klein forms of arbitrary degree. We also demonstrate that these new fields simplify all the expressions including the Chern-Simons term.Comment: 26 pages; LaTeX; major version up; discussion on the Chern-Simons term added; references adde

qq-Virasoro/W Algebra at Root of Unity and Parafermions

We demonstrate that the parafermions appear in the $r$-th root of unity limit of $q$-Virasoro/$W_n$ algebra. The proper value of the central charge of the coset model $\frac{\widehat{\mathfrak{sl}}(n)_r \oplus \widehat{\mathfrak{sl}}(n)_{m-n}}{\widehat{\mathfrak{sl}}(n)_{m-n+r}}$ is given from the parafermion construction of the block in the limit.Comment: 13 pages, 1 figure; v2: references added, minor corrections mad

Weyl Groups in AdS(3)/CFT(2)

The system of D1 and D5 branes with a Kaluza-Klein momentum is re-investigated using the five-dimensional U-duality group E_{6(+6)}(Z). We show that the residual U-duality symmetry that keeps this D1-D5-KK system intact is generically given by a lift of the Weyl group of F_{4(+4)}, embedded as a finite subgroup in E_{6(+6)}(Z). We also show that the residual U-duality group is enhanced to F_{4(+4)}(Z) when all the three charges coincide. We then apply the analysis to the AdS(3)/CFT(2) correspondence, and discuss that among 28 marginal operators of CFT(2) which couple to massless scalars of AdS(3) gravity at boundary, 16 would behave as exactly marginal operators for generic D1-D5-KK systems. This is shown by analyzing possible three-point couplings among 42 Kaluza-Klein scalars with the use of their transformation properties under the residual U-duality group.Comment: 20 pages, 3 figue