Integrable Deformations of Sine-Liouville Conformal Field Theory and Duality

We study integrable deformations of sine-Liouville conformal field theory. Every integrable perturbation of this model is related to the series of quantum integrals of motion (hierarchy). We construct the factorized scattering matrices for different integrable perturbed conformal field theories. The perturbation theory, Bethe ansatz technique, renormalization group and methods of perturbed conformal field theory are applied to show that all integrable deformations of sine-Liouville model possess non-trivial duality properties

Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks

Liouville field theory on a sphere is considered. We explicitly derive a differential equation for four-point correlation functions with one degenerate field $V_{-\frac{mb}{2}}$. We introduce and study also a class of four-point conformal blocks which can be calculated exactly and represented by finite dimensional integrals of elliptic theta-functions for arbitrary intermediate dimension. We study also the bootstrap equations for these conformal blocks and derive integral representations for corresponding four-point correlation functions. A relation between the one-point correlation function of a primary field on a torus and a special four-point correlation function on a sphere is proposed

Conformal Toda theory with a boundary

We investigate sl(n) conformal Toda theory with maximally symmetric boundaries. There are two types of maximally symmetric boundary conditions, due to the existence of an order two automorphism of the W(n>2) algebra. In one of the two cases, we find that there exist D-branes of all possible dimensions 0 =< d =< n-1, which correspond to partly degenerate representations of the W(n) algebra. We perform classical and conformal bootstrap analyses of such D-branes, and relate these two approaches by using the semi-classical light asymptotic limit. In particular we determine the bulk one-point functions. We observe remarkably severe divergences in the annulus partition functions, and attribute their origin to the existence of infinite multiplicities in the fusion of representations of the W(n>2) algebra. We also comment on the issue of the existence of a boundary action, using the calculus of constrained functional forms, and derive the generating function of the B"acklund transformation for sl(3) Toda classical mechanics, using the minisuperspace limit of the bulk one-point function.Comment: 42 pages; version 4: added clarifications in section 2.2 and footnotes 1 and

Thermodynamics of 2D string theory

We calculate the free energy, energy and entropy in the matrix quantum mechanical formulation of 2D string theory in a background strongly perturbed by tachyons with the imaginary Minkowskian momentum $\pm i/R$ (``Sine-Liouville'' theory). The system shows a thermodynamical behaviour corresponding to the temperature $T=1/(2\pi R)$. We show that the microscopically calculated energy of the system satisfies the usual thermodynamical relations and leads to a non-zero entropy.Comment: 13 pages, lanlmac; typos correcte

Structure-related bandgap of hybrid lead halide perovskites and close-packed APbX3 family of phases

Metal halide perovskites APbX3 (A+ = FA+ (formamidinium), MA+ (methylammonium) or Cs+, X- = I-, Br-) are considered as prominent innovative components in nowadays perovskite solar cells. Crystallization of these materials is often complicated by the formation of various phases with the same stoichiometry but structural types deviating from perovskites such as well-known the hexagonal delta FAPbI3 polytype. Such phases are rarely placed in the focus of device engineering due to their unattractive optoelectronic properties while they are, indeed, highly important because they influence on the optoelectronic properties and efficiency of final devices. However, the total number of such phases has not been yet discovered and the complete configurational space of the polytypes and their band structures have not been studied systematically. In this work, we predicted and described all possible hexagonal polytypes of hybrid lead halides with the APbI3 composition using the group theory approach, also we analyzed theoretically the relationship between the configuration of close-packed layers in polytypes and their band gap using DFT calculations. Two main factors affecting the bandgap were found including the ratio of cubic (c) and hexagonal (h) close-packed layers and the thickness of blocks of cubic layers in the structures. We also show that the dependence of the band gap on the ratio of cubic (c) and hexagonal (h) layers in these structures are non-linear. We believe that the presence of such polytypes in the perovskite matrix might be a reason for a decrease in the charge carrier mobility and therefore it would be an obstacle for efficient charge transport causing negative consequences for the efficiency of solar cell devices

Boundary RG Flow Associated with the AKNS Soliton Hierarchy

We introduce and study an integrable boundary flow possessing an infinite number of conserving charges which can be thought of as quantum counterparts of the Ablowitz, Kaup, Newell and Segur Hamiltonians. We propose an exact expression for overlap amplitudes of the boundary state with all primary states in terms of solutions of certain ordinary linear differential equation. The boundary flow is terminated at a nontrivial infrared fixed point. We identify a form of whole boundary state corresponding to this fixed point.Comment: 54 page

AlGaAs/GaAs Quantum Well Infrared Photodetectors

In this article, we present an overview of a focal plane array (FPA) with 640 × 512 pixels based on the AlGaAs quantum well infrared photodetector (QWIP). The physical principles of the QWIP operation and their parameters for the spectral range of 8–10 μm have been discussed. The technology of the manufacturing FPA based on the QWIP structures with the pixels 384 × 288 and 640 × 512 has been demonstrated. The parameters of the manufactured 640 × 512 FPA with a step of 20 μm have been given. At the operating temperature of 72 K, the temperature resolution of QWIP focal plane arrays is less than 35 mK. The number of defective elements in the matrix does not exceed 0.5%. The stability and uniformity of the FPA have been demonstrated

Non-Perturbative Effects in Matrix Models and D-branes

The large order growth of string perturbation theory in $c\le 1$ conformal field theory coupled to world sheet gravity implies the presence of $O(e^{-{1\over g_s}})$ non-perturbative effects, whose leading behavior can be calculated in the matrix model approach. Recently it was proposed that the same effects should be reproduced by studying certain localized D-branes in Liouville Field Theory, which were constructed by A. and Al. Zamolodchikov. We discuss this correspondence in a number of different cases: unitary minimal models coupled to Liouville, where we compare the continuum analysis to the matrix model results of Eynard and Zinn-Justin, and compact c=1 CFT coupled to Liouville in the presence of a condensate of winding modes, where we derive the matrix model prediction and compare it to Liouville theory. In both cases we find agreement between the two approaches. The c=1 analysis also leads to predictions about properties of D-branes localized in the vicinity of the tip of the cigar in SL(2)/U(1) CFT with c=26.Comment: 27 pages, lanlmac; minor change

Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as ``${\bf T}$-operators'', act in highest weight Virasoro modules. The ${\bf T}$-operators depend on the spectral parameter $\lambda$ and their expansion around $\lambda = \infty$ generates an infinite set of commuting Hamiltonians of the quantum KdV system. The ${\bf T}$-operators can be viewed as the continuous field theory versions of the commuting transfer-matrices of integrable lattice theory. In particular, we show that for the values $c=1-3{{(2n+1)^2}\over {2n+3}} , n=1,2,3,...$of the Virasoro central charge the eigenvalues of the ${\bf T}$-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of massless Thermodynamic Bethe Ansatz for the minimal conformal field theory ${\cal M}_{2,2n+3}$; in general they provide a way to generalize the technique of Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator $\Phi_{1,3}$. The relation of these ${\bf T}$-operators to the boundary states is also briefly described.Comment: 24 page