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Register a new userQ-systems with boundary parameters
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Added by
Rafael I. Nepomechie
Publication date
2019
fields
Physics
and research's language is
English
Authors
Rafael I. Nepomechie
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No Arabic abstract
Q-systems provide an efficient way of solving Bethe equations. We formulate here Q-systems for both the isotropic and anisotropic open Heisenberg quantum spin-1/2 chains with diagonal boundary magnetic fields. We check these Q-systems using novel Wronskian-type formulas (relating the fundamental Q-function and its dual) that involve the boundary parameters.
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We explore boundary scattering in the sine-Gordon model with a non-integrable family of Robin boundary conditions. The soliton content of the field after collision is analysed using a numerical implementation of the direct scattering problem associated with the inverse scattering method. We find that an antikink may be reflected into various combinations of an antikink, a kink, and one or more breathers, depending on the values of the initial antikink velocity and a parameter associated with the boundary condition. In addition we observe regions with an intricate resonance structure arising from the creation of an intermediate breather whose recollision with the boundary is highly dependent on the breather phase.
We show how q-Virasoro constraints can be derived for a large class of (q,t)-deformed eigenvalue matrix models by an elementary trick of inserting certain q-difference operators under the integral, in complete analogy with full-derivative insertions for beta-ensembles. From free-field point of view the models considered have zero momentum of the highest weight, which leads to an extra constraint T_{-1} Z = 0. We then show how to solve these q-Virasoro constraints recursively and comment on the possible applications for gauge theories, for instance calculation of (supersymmetric) Wilson loop averages in gauge theories on D^2 cross S^1 and S^3.
We propose a Q-system for the $A_m^{(1)}$ quantum integrable spin chain. We also find compact determinant expressions for all the Q-functions, both for the rational and trigonometric cases.
The Virasoro constraints play the important role in the study of matrix models and in understanding of the relation between matrix models and CFTs. Recently the localization calculations in supersymmetric gauge theories produced new families of matrix models and we have very limited knowledge about these matrix models. We concentrate on elliptic generalization of hermitian matrix model which corresponds to calculation of partition function on $S^3 times S^1$ for vector multiplet. We derive the $q$-Virasoro constraints for this matrix model. We also observe some interesting algebraic properties of the $q$-Virasoro algebra.
We consider the problem of the real analytic dependence of the accessory parameters of Liouville theory on the moduli of the problem, for general elliptic singularities. We give a simplified proof of the almost everywhere real analyticity in the case of a single accessory parameter as it occurs e.g. in the sphere topology with four sources or for the torus topology with a single source by using only the general analyticity properties of the solution of the auxiliary equation. We deal then the case of two accessory parameters. We use the obtained result for a single accessory parameter to derive rigorous properties of the projection of the problem on lower dimensional planes. We derive the real analyticity result for two accessory parameters under an assumption of irreducibility.
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