Some comments on Anti-de Sitter D-branes

We present some preliminary investigations about the AdS2*S2 D3-branes in AdS3*S3. We analyse the quadratic fluctuations of Dirac-Born-Infeld action around a given semi-classical D-brane configuration and compare them with results obtained by using conformal field theory techniques. We finally study classical motions of open strings attached to those D-branes and analyse the role of the spectral flow in this context.Comment: 12 pages, no figure

H(3)+ correlators from Liouville theory

We prove that arbitrary correlation functions of the H(3)+ model on a sphere have a simple expression in terms of Liouville theory correlation functions. This is based on the correspondence between the KZ and BPZ equations, and on relations between the structure constants of Liouville theory and the H(3)+ model. In the critical level limit, these results imply a direct link between eigenvectors of the Gaudin Hamiltonians and the problem of uniformization of Riemann surfaces. We also present an expression for correlation functions of the SL(2)/U(1) coset model in terms of correlation functions in Liouville theory.Comment: 24 pages, v3: minor changes, references adde

On AGT description of N=2 SCFT with N_f=4

We consider Alday-Gaiotto-Tachikawa (AGT) realization of the Nekrasov partition function of N=2 SCFT. We focus our attention on the SU(2) theory with N_f=4 flavor symmetry, whose partition function, according to AGT, is given by the Liouville four-point function on the sphere. The gauge theory with N_f=4 is known to exhibit SO(8) symmetry. We explain how the Weyl symmetry transformations of SO(8) flavor symmetry are realized in the Liouville theory picture. This is associated to functional properties of the Liouville four-point function that are a priori unexpected. In turn, this can be thought of as a non-trivial consistency check of AGT conjecture. We also make some comments on elementary surface operators and WZW theory.Comment: 18 pages. v2, a misinterpretation in the gauge theory side has been corrected; title and introduction were changed accordingl

Quantum Hall effect anomaly and collective modes in the magnetic-field-induced spin-density-wave phases of quasi-one-dimensional conductors

We study the collective modes in the magnetic-field-induced spin-density-wave (FISDW) phases experimentally observed in organic conductors of the Bechgaard salts family. In phases that exhibit a sign reversal of the quantum Hall effect (Ribault anomaly), the coexistence of two spin-density waves gives rise to additional collective modes besides the Goldstone modes due to spontaneous translation and rotation symmetry breaking. These modes strongly affect the charge and spin response functions. We discuss some experimental consequences for the Bechgaard salts.Comment: Final version (LaTex, 8 pages, no figure), to be published in Europhys. Let

Quantum Hall Transitions in (TMTSF)2_2PF6_6

We have studied the temperature dependence of the integer quantum Hall transitions in the molecular crystal (TMTSF)$_2$PF$_6$. We find that the transition width between the quantum Hall plateaus does not exhibit the universal power-law scaling behavior of the integer quantum Hall effect observed in semiconducting devices. Instead, the slope of the $\rho_{xy}$ risers, $d\rho_{xy}/dB$, and the (inverse) width of the $\rho_{xx}$ peaks, $(\Delta B)^{-1}$, show a BCS-like energy gap temperature dependence. We discuss these results in terms of the field-induced spin-density wave gap and order parameter of the system.Comment: 10 pages, RevTeX, 4 PostScript figure

Notes On The S-Matrix Of Bosonic And Topological Non-Critical Strings

We show that the equivalence between the c=1 non-critical bosonic string and the N=2 topologically twisted coset SL(2)/U(1) at level one can be checked very naturally on the level of tree-level scattering amplitudes with the use of the Stoyanovsky-Ribault-Teschner map, which recasts $H_3^+$ correlation functions in terms of Liouville field theory amplitudes. This observation can be applied equally well to the topologically twisted SL(2)/U(1) coset at level n>1, which has been argued recently to be equivalent with a c<1 non-critical bosonic string whose matter part is defined by a time-like linear dilaton CFT.Comment: harvmac, 22 pages; v2 typos corrected, version appearing in JHE

Affine sl(N) conformal blocks from N=2 SU(N) gauge theories

Recently Alday and Tachikawa proposed a relation between conformal blocks in a two-dimensional theory with affine sl(2) symmetry and instanton partition functions in four-dimensional conformal N=2 SU(2) quiver gauge theories in the presence of a certain surface operator. In this paper we extend this proposal to a relation between conformal blocks in theories with affine sl(N) symmetry and instanton partition functions in conformal N=2 SU(N) quiver gauge theories in the presence of a surface operator. We also discuss the extension to non-conformal N=2 SU(N) theories.Comment: 40 pages. v2: minor changes and clarification

The abelian cosets of the Heisenberg group

In this paper we study the abelian cosets of the H(4) WZW model. They coincide or are related to several interesting three-dimensional backgrounds such as the Melvin model, the conical point-particle space-times and the null orbifold. We perform a detailed CFT analysis of all the models and compute the coset characters as well as some typical three-point couplings of coset primaries.Comment: 26 pages; v2: minor typos corrected, also added section 3.3 and 4.3 with a few comments on a third class of geometries that have not been discussed in v

Generalized susceptibility of quasi-one dimensional system with periodic potential: model for the organic superconductor (TMTSF)2_2ClO4_4

The nesting vector and the magnetic susceptibility of the quasi-one-dimensional system having imperfectly nested Fermi surface are studied analytically and numerically. The magnetic susceptibility has the plateau-like maximum in ``\textit{sweptback}'' region in the momentum space, which is surrounded by $\mathbf{Q}=(2 k_F, \pi) + \mathbf{q}_i$ ($k_F$ is the Fermi wave number, $i=1,3,4$, and $\mathbf{q}_1$, $\mathbf{q}_3$ and $\mathbf{q}_{4}$ are given in this paper). The best nesting vector, at which the susceptibility $\chi_0(\mathbf{Q})$ has the absolute maximum at T=0, is obtained near but not at the inflection point, $\mathbf{Q}=(2 k_F, \pi)+\mathbf{q}_4$. The effect of the periodic potential $V$ on the susceptibility is studied, which is important for the successive transitions of the field-induced spin density wave in (TMTSF)$_2$ClO$_4$. We obtain that the sweptback region (surrounded by $\mathbf{q}_2$, $\mathbf{q}_3$ and $\mathbf{q}_4$ when $V>0$) becomes small as $V$ increases and it shrinks to $\mathbf{q}_3$ for $V \geq 4 t_b'$, where $t_b'$ gives the degree of imperfect nesting of the Fermi surface, i.e. the second harmonics of the warping in the Fermi surface. The occurrence of the sign reversal of the Hall coefficient in the field-induced spin density wave states is discussed to be possible only when $V<2 t_b'-2 t_4$, where $t_4$ is the amplitude of the fourth harmonics of the warping in the Fermi surface. This gives the novel limitation for the magnitude of $V$