Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory

• URL: http://arxiv.org/abs/2203.11838v1
• Date: Tue, 22 Mar 2022 16:05:58 GMT
• Title: Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Authors: Hisham Sati, Urs Schreiber
• Abstract summary: We show that twisted equivariant differential K-theory accommodates exotic charges of the form expected of codimension=2 defect branes. This provides a concrete first-principles realization of anyon statistics of -- and hence of topological quantum computation on -- defect branes in string/M-theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We demonstrate that twisted equivariant differential K-theory of transverse complex curves accommodates exotic charges of the form expected of codimension=2 defect branes, such as of D7-branes in IIB/F-theory on A-type orbifold singularities, but also of their dual 3-brane defects of class-S theories on M5-branes. These branes have been argued, within F-theory and the AGT correspondence, to carry special SL(2)-monodromy charges not seen for other branes, but none of these had previously been identified in the expected brane charge quantization law given by K-theory. Here we observe that it is the subtle (and previously somewhat neglected) twisting of equivariant K-theory by flat complex line bundles appearing inside orbi-singularities ("inner local systems") that makes the secondary Chern character on a punctured plane inside an A-type singularity evaluate to the twisted holomorphic de Rham cohomology which Feigin, Schechtman & Varchenko showed realizes sl(2,C)-conformal blocks, here in degree 1 -- in fact it gives the direct sum of these over all admissible fractional levels. The remaining higher-degree conformal blocks appear similarly if we assume our previously discussed "Hypothesis H" about brane charge quantization in M-theory. Since conformal blocks -- and hence these twisted equivariant secondary Chern characters -- solve the Knizhnik-Zamolodchikov equation and thus constitute representations of the braid group of motions of defect branes inside their transverse space, this provides a concrete first-principles realization of anyon statistics of -- and hence of topological quantum computation on -- defect branes in string/M-theory.

Related papers

• Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems [0.0]
  Recently observed fractional quantum anomalous Hall materials (FQAH) are candidates for topological quantum hardware.<n>We point out dependence on monodromy in the fragile band topology in 2-cohomotopy.<n>An algebro-topological theorem of Larmore & Thomas (1980) then identifies FQAH anyons over momentum space.
  arXiv  Detail & Related papers  (2025-06-30T18:00:07Z)
• Emergence of cosmic structure from Planckian discreteness [47.03992469282679]
  In the standard paradigm the inhomogeneities observed in the CMB arise from quantum fluctuations of an initially homogeneous and isotropic vacuum state.<n>We propose an alternative paradigm in which such inhomogeneities are present from the very beginning.<n>Specifically, inhomogeneities in the quantum state at the Planck scale propagate into semiclassical inhomogeneities on CMB scales.
  arXiv  Detail & Related papers  (2025-06-18T12:33:31Z)
• On Infinite Tensor Networks, Complementary Recovery and Type II Factors [39.58317527488534]
  We study local operator algebras at the boundary of infinite tensor networks. We decompose the limiting Hilbert space and the algebras of observables in a way that keeps track of the entanglement in the network.
  arXiv  Detail & Related papers  (2025-03-31T18:00:09Z)
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes. We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram. We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• Engineering of Anyons on M5-Probes via Flux Quantization [0.0]
  We develop a novel derivation of anyonic topological order on single magnetized M5-branes. The rigorous construction is non-Lagrangian and non-perturbative. Results imply from this the quantum observables and modular functor of abelian Chern-Simons theory.
  arXiv  Detail & Related papers  (2025-01-29T19:00:04Z)
• Linearization (in)stabilities and crossed products [0.0]
  Linearization (in)stabilities occur in any gauge-covariant field theory with non-linear equations. We study when linearized solutions can be integrated to exact ones. We translate the subject from the usual canonical formulation into a systematic covariant phase space language.
  arXiv  Detail & Related papers  (2024-11-29T18:47:17Z)
• Non-chiral non-Bloch invariants and topological phase diagram in non-unitary quantum dynamics without chiral symmetry [26.179241616332387]
  We identify the non-Bloch topological phase diagram of a one-dimensional (1D) non-Hermitian system without chiral symmetry. We find that such topological invariants can distinguish topologically distinct gapped phases. Our work provides a useful platform to study the interplay among topology, symmetries and the non-Hermiticity.
  arXiv  Detail & Related papers  (2024-07-26T03:29:30Z)
• Structural Stability Hypothesis of Dual Unitary Quantum Chaos [0.0]
  spectral correlations over small enough energy scales are described by random matrix theory. We consider fate of this property when moving from dual-unitary to generic quantum circuits.
  arXiv  Detail & Related papers  (2024-02-29T12:25:29Z)
• Quantum quenches in fractonic field theories [0.0]
  We study out-of-equilibrium dynamics caused by global quantum quenches in fractonic scalar field theories. We discuss a generalization to $mathbbZ_n$-symmetric field theories, and introduce a proper regularization.
  arXiv  Detail & Related papers  (2023-06-26T18:00:02Z)
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory [0.0]
  We argue that 2d semi-metal phases modulo global mass terms are classified by the twisted equivariant K-theory of the complement of the nodal points. The induced su(2)-anyonic topological order is reflected in the twisted Chern classes of the interacting valence bundle over configuration space.
  arXiv  Detail & Related papers  (2022-06-27T18:05:31Z)
• 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)
• Electric-magnetic duality and $\mathbb{Z}_2$ symmetry enriched Abelian lattice gauge theory [2.206623168926072]
  Kitaev's quantum double model is a lattice gauge theoretic realization of Dijkgraaf-Witten topological quantum field theory (TQFT) Topologically protected ground state space has broad applications for topological quantum computation and topological quantum memory.
  arXiv  Detail & Related papers  (2022-01-28T14:13:38Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• A Wigner-Eckart Theorem for Group Equivariant Convolution Kernels [16.143012623830792]
  Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors. Recent advances in the theoretical description of GCNNs revealed that such models can generally be understood as performing convolutions with G-steerable kernels.
  arXiv  Detail & Related papers  (2020-10-21T12:42:23Z)
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories [55.53519491066413]
  We find pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace. We analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories.
  arXiv  Detail & Related papers  (2020-09-24T18:00:13Z)
• The quasi-particle picture and its breakdown after local quenches: mutual information, negativity, and reflected entropy [0.0]
  We study the dynamics of (R'enyi) mutual information, logarithmic negativity, and (R'enyi) reflected entropy after exciting the ground state by a local operator. We are able to conjecture a close-knit structure between the three quantities that emerges in states excited above the vacuum.
  arXiv  Detail & Related papers  (2020-08-25T20:47:05Z)

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.