The Spectrum of the Baryon Masses in a Self-consistent SU(3) Quantum Skyrme Model

The semiclassical SU(3) Skyrme model is traditionally considered as describing a rigid quantum rotator with the profile function being fixed by the classical solution of the corresponding SU(2) Skyrme model. In contrast, we go beyond the classical profile function by quantizing the SU(3) Skyrme model canonically. The quantization of the model is performed in terms of the collective coordinate formalism and leads to the establishment of purely quantum corrections of the model. These new corrections are of fundamental importance. They are crucial in obtaining stable quantum solitons of the quantum SU(3) Skyrme model, thus making the model self-consistent and not dependent on the classical solution of the SU(2) case. We show that such a treatment of the model leads to a family of stable quantum solitons that describe the baryon octet and decuplet and reproduce their masses in a qualitative agreement with the empirical values.Comment: 14 pages, 1 figure, 1 table; v2: published versio

Pseudo-symmetric pairs for Kac-Moody algebras

Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces and real forms of complex Lie algebras, and are well-studied in the context of symmetrizable Kac-Moody algebras. In this paper we study a generalization. Namely, we introduce the concept of a pseudo-involution, an automorphism which is only required to act involutively on a stable Cartan subalgebra, and the concept of a pseudo-fixed-point subalgebra, a natural substitute for the fixed-point subalgebra. In the symmetrizable Kac-Moody setting, we give a comprehensive discussion of pseudo-involutions of the second kind, the associated pseudo-fixed-point subalgebras, restricted root systems and Weyl groups, in terms of generalizations of Satake diagrams

Canonically quantized soliton in the bound state approach to heavy baryons in the Skyrme model

The bound state extension of Skyrme's topological soliton model for the heavy baryons is quantized canonically in arbitrary reducible representations of the SU(3) flavor group. The canonical quantization leads to an additional negative mass term, which stabilizes the quantized soliton solution. The heavy flavor meson in the field of the soliton is treated with semiclassical quantization. The representation dependence of the calculated spectra for the strange, charm and bottom baryons is explored and compared to the extant empirical spectra.Comment: 13 pages, 8 table

Coideal Quantum Affine Algebra and Boundary Scattering of the Deformed Hubbard Chain

We consider boundary scattering for a semi-infinite one-dimensional deformed Hubbard chain with boundary conditions of the same type as for the Y=0 giant graviton in the AdS/CFT correspondence. We show that the recently constructed quantum affine algebra of the deformed Hubbard chain has a coideal subalgebra which is consistent with the reflection (boundary Yang-Baxter) equation. We derive the corresponding reflection matrix and furthermore show that the aforementioned algebra in the rational limit specializes to the (generalized) twisted Yangian of the Y=0 giant graviton.Comment: 21 page. v2: minor correction

Twisted Yangians of small rank

We study quantized enveloping algebras called twisted Yangians associated with the symmetric pairs of types CI, BDI, and DIII (in Cartan’s classification) when the rank is small. We establish isomorphisms between these twisted Yangians and the well known Olshanskii’s twisted Yangians of types AI and AII, and also with the Molev-Ragoucy reflection algebras associated with symmetric pairs of type AIII. We also construct isomorphisms with twisted Yangians in Drinfeld’s original presentation

The Quantum Affine Origin of the AdS/CFT Secret Symmetry

We find a new quantum affine symmetry of the S-matrix of the one-dimensional Hubbard chain. We show that this symmetry originates from the quantum affine superalgebra U_q(gl(2|2)), and in the rational limit exactly reproduces the secret symmetry of the AdS/CFT worldsheet S-matrix.Comment: 22 page

Secret Symmetries in AdS/CFT

We discuss special quantum group (secret) symmetries of the integrable system associated to the AdS/CFT correspondence. These symmetries have by now been observed in a variety of forms, including the spectral problem, the boundary scattering problem, n-point amplitudes, the pure-spinor formulation and quantum affine deformations.Comment: 20 pages, pdfLaTeX; Submitted to the Proceedings of the Nordita program `Exact Results in Gauge-String Dualities'; Based on the talk presented by A.T., Nordita, 15 February 201

Quasitriangular coideal subalgebras of Uq(g) in terms of generalized Satake diagrams

© 2020 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits use, distribution and reproduction in any medium, provided the original work is properly cited.Let (Formula presented.) be a finite-dimensional semisimple complex Lie algebra and (Formula presented.) an involutive automorphism of (Formula presented.). According to Letzter, Kolb and Balagović the fixed-point subalgebra (Formula presented.) has a quantum counterpart (Formula presented.), a coideal subalgebra of the Drinfeld–Jimbo quantum group (Formula presented.) possessing a universal (Formula presented.) -matrix (Formula presented.). The objects (Formula presented.), (Formula presented.), (Formula presented.) and (Formula presented.) can all be described in terms of Satake diagrams. In the present work, we extend this construction to generalized Satake diagrams, combinatorial data first considered by Heck. A generalized Satake diagram naturally defines a semisimple automorphism (Formula presented.) of (Formula presented.) restricting to the standard Cartan subalgebra (Formula presented.) as an involution. It also defines a subalgebra (Formula presented.) satisfying (Formula presented.), but not necessarily a fixed-point subalgebra. The subalgebra (Formula presented.) can be quantized to a coideal subalgebra of (Formula presented.) endowed with a universal (Formula presented.) -matrix in the sense of Kolb and Balagović. We conjecture that all such coideal subalgebras of (Formula presented.) arise from generalized Satake diagrams in this way.Peer reviewe

Reflection algebra, Yangian symmetry and bound-states in AdS/CFT

We present the `Heisenberg picture' of the reflection algebra by explicitly constructing the boundary Yangian symmetry of an AdS/CFT superstring which ends on a boundary with non-trivial degrees of freedom and which preserves the full bulk Lie symmetry algebra. We also consider the spectrum of bulk and boundary states and some automorphisms of the underlying algebras.Comment: 31 page, 8 figures. Updated versio

The Bound State S-matrix of the Deformed Hubbard Chain

In this work we use the q-oscillator formalism to construct the atypical (short) supersymmetric representations of the centrally extended Uq (su(2|2)) algebra. We then determine the S-matrix describing the scattering of arbitrary bound states. The crucial ingredient in this derivation is the affine extension of the aforementioned algebra.Comment: 44 pages, 3 figures. v2: minor correction