Automorphic Symmetries, String integrable structures and Deformations
Citation:
Pribitoks, Antons, Automorphic Symmetries, String integrable structures and Deformations, Trinity College Dublin, School of Mathematics, Pure & Applied Mathematics, 2022Download Item:
Abstract:
We address the novel structures arising in quantum and string integrable
theories, as well as construct methods to obtain them and provide further
analysis. Specifically, we implement the automorphic symmetries on peri-
odic lattice systems for obtaining integrable hierarchies, whose commutativity
along with integrable transformations induces a generating structure of inte-
grable classes. This prescription is first applied to 2-dim and 4-dim setups,
where we find the new sl2 sector, su(2) ⊕ su(2) with superconductive modes,
Generalised Hubbard type classes and more. The corresponding 2- and 4-dim
R matrices are resolved through perturbation theory, that allows to recover
an exact result. We then construct a boost recursion that allows to address
the systems, whose R-/S-matrices exhibit arbitrary spectral dependence, that
also is an apparent property of the scattering operators in AdS integrability. It
is then possible to implement the last for Hamiltonian Ansätze in D = 2, 3, 4,
which leads to new models in all dimensions. We also provide a method based
on a coupled differential system that allows to resolve for R matrices ex-
actly. Importantly, one can isolate a special class of models of non-difference
form in 2-dim case (6vB/8vB), which provides a new structure consistently
arising in AdS3 and AdS2 string backgrounds. We prove that these classes
can be represented as deformations of the AdS{2,3} models. We also work
out that the latter satisfy free fermion constraint, braiding unitarity, crossing
and exhibit deformed algebraic structure that shares certain properties with
AdS3 × S3 × M4 and AdS2 × S2 × T 6 models. The embedding and mappings
of known AdS{2,3} models to 6vB/8vB deformations are demonstrated, along
with a discussion on the associated candidates of sigma models.
Author's Homepage:
https://tcdlocalportal.tcd.ie/pls/EnterApex/f?p=800:71:0::::P71_USERNAME:PRIBITOADescription:
APPROVED
Author: Pribitoks, Antons
Advisor:
De Leeuw, MariusPublisher:
Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied MathematicsType of material:
ThesisCollections
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Full text availableKeywords:
Quantum Integrable systems, AdS Integrability, Boost, Automorphism, String integrable backgrounds, AdS/CFT integrability, Quantum Symmetries, Yangians, Integrable Spin Chains, R-matrix, S-matrix, Integrable deformations, 8v-vertex, GHM, AdS_3 Integrability, YBE, mYBE, Hopf a;gebra, Supersymmetric spin chains, Free Fermion condition, Algebraic Bethe Ansatz, Coordinate Bethe Ansatz, Sigma models, Worldsheet integrability, Transfer matrix, Jacobi Elliptic functions, q-deformation, Quantum GroupsMetadata
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