Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality

• URL: http://arxiv.org/abs/2309.05702v1
• Date: Mon, 11 Sep 2023 18:00:01 GMT
• Title: Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality
• Authors: Rak-Kyeong Seong
• Abstract summary: We introduce unsupervised machine learning techniques in order to identify toric phases of 4d N=1 supersymmetric gauge theories. These 4d N=1 supersymmetric gauge theories are world theories of a D3-brane probing a toric Calabi-Yau 3-fold.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce unsupervised machine learning techniques in order to identify toric phases of 4d N=1 supersymmetric gauge theories corresponding to the same toric Calabi-Yau 3-fold. These 4d N=1 supersymmetric gauge theories are worldvolume theories of a D3-brane probing a toric Calabi-Yau 3-fold and are realized in terms of a Type IIB brane configuration known as a brane tiling. It corresponds to the skeleton graph of the coamoeba projection of the mirror curve associated to the toric Calabi-Yau 3-fold. When we vary the complex structure moduli of the mirror Calabi-Yau 3-fold, the coamoeba and the corresponding brane tilings change their shape, giving rise to different toric phases related by Seiberg duality. We illustrate that by employing techniques such as principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE), we can project the space of coamoeba labelled by complex structure moduli down to a lower dimensional phase space with phase boundaries corresponding to Seiberg duality. In this work, we illustrate this technique by obtaining a 2-dimensional phase diagram for brane tilings corresponding to the cone over the zeroth Hirzebruch surface F0.

Related papers

• Two-dopant origin of competing stripe and pair formation in Hubbard and $t$-$J$ models [0.0]
  We study single pairs of dopants in a cylindrical system using the density-matrix renormalization group algorithm. We establish that the interplay between order and uniform pairing, central to the models' phases at finite doping, has its origin at the single-pair level.
  arXiv  Detail & Related papers  (2024-09-26T17:59:57Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Hadrons in (1+1)D Hamiltonian hardcore lattice QCD [0.0]
  We study 2-flavor Hamiltonian lattice QCD in (1+1)D with hardcore gluons, at zero and finite density, by means of matrix product states. We introduce a formulation of the theory where gauge redundancy is absent and construct a gauge invariant tensor network ansatz.
  arXiv  Detail & Related papers  (2023-08-08T18:00:05Z)
• Quantum phase transition between symmetry enriched topological phases in tensor-network states [6.014569675344553]
  Quantum phase transitions between different topologically ordered phases exhibit rich structures and are generically challenging to study in microscopic lattice models. We propose a tensor-network solvable model that allows us to tune between different symmetry enriched topological (SET) phases.
  arXiv  Detail & Related papers  (2023-05-03T21:21:36Z)
• Bulk-to-boundary anyon fusion from microscopic models [2.025761610861237]
  We study the fusion events between anyons in the bulk and at the boundary in fixed-point models of 2+1-dimensional non-chiral topological order. A recurring theme in our construction is an isomorphism relating twisted cohomology groups to untwisted ones. The results of this work can directly be applied to study logical operators in two-dimensional topological error correcting codes with boundaries described by a twisted gauge theory of a finite group.
  arXiv  Detail & Related papers  (2023-02-03T16:20:36Z)
• Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
  We introduce a class of quantum optical Hamiltonian characterized by three-body couplings. We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
  arXiv  Detail & Related papers  (2022-04-07T15:39:21Z)
• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice [52.77024349608834]
  We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and non-local terms gives rise to a phase diagram with liquid phases with dominant cluster, spin, and density-wave quasi-long-range ordering.
  arXiv  Detail & Related papers  (2021-12-20T09:46:08Z)
• Topological aspects of the critical three-state Potts model [0.0]
  A complete characterization is obtained by breaking down the Fuchs-Runkel-Schweigert construction of 2d rational CFT to the lattice setting. The symmetries are represented by matrix product operators (MPO), as well as intertwiners between the diagonal tetracritical Ising model and the non-diagonal three-state Potts model.
  arXiv  Detail & Related papers  (2021-07-22T16:43:40Z)
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics [58.720142291102135]
  We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions. We show that our system exhibits topologicalband structures under appropriate conditions.
  arXiv  Detail & Related papers  (2020-08-06T19:58:05Z)
• Engineering multipartite entangled states in doubly pumped parametric down-conversion processes [68.8204255655161]
  We investigate the quantum state generated by optical parametric down-conversion in a $chi(2) $ medium driven by two modes. The analysis shows the emergence of multipartite, namely 3- or 4-partite, entangled states in a subset of the modes generated by the process.
  arXiv  Detail & Related papers  (2020-07-23T13:53:12Z)
• Radiative topological biphoton states in modulated qubit arrays [105.54048699217668]
  We study topological properties of bound pairs of photons in spatially-modulated qubit arrays coupled to a waveguide. For open boundary condition, we find exotic topological bound-pair edge states with radiative losses. By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.
  arXiv  Detail & Related papers  (2020-02-24T04:44:12Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.