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Related Concept Videos

Spin–Spin Coupling Constant: Overview01:08

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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
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Valence Bond Theory02:42

Valence Bond Theory

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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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The Pauli Exclusion Principle03:06

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The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence.

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We explore the duality between Anti-de Sitter (AdS) space and Super Yang-Mills theory using string energies. This reveals insights into quantum spectra and provides all-loop predictions for gauge theory scaling dimensions.

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Area of Science:

  • Theoretical Physics
  • String Theory
  • Quantum Field Theory
  • AdS/CFT Correspondence

Background:

  • The Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence posits a duality between string theory in Anti-de Sitter (AdS) space and a quantum field theory on its boundary.
  • Understanding this duality is crucial for probing strongly coupled regimes of quantum field theories using the more tractable framework of string theory.
  • Dynamical tests provide a powerful method to verify and explore the predictions of this correspondence.

Purpose of the Study:

  • To perform dynamical tests of the AdS5 × S5 string/SU(N) Super Yang-Mills duality.
  • To derive all-loop predictions for gauge theory scaling dimensions from semiclassical string energies.
  • To investigate the relationship between string energies and gauge theory spectra in specific limits.

Main Methods:

  • Calculating semiclassical string energies for folded and circular spinning string solutions in AdS5 × S5.
  • Reformulating the dilatation operator of SU(N) Super Yang-Mills in a minimal SU(2) subsector as a Heisenberg s=1/2 spin chain.
  • Employing the coordinate Bethe ansatz for the diagonalization of the spin chain and analyzing the thermodynamic limit of gauge theory Bethe equations.

Main Results:

  • Semiclassical string energies yield all-loop predictions for dual gauge theory scaling dimensions.
  • Matching between one-loop gauge theory Bethe equations and folded/closed string energies was demonstrated.
  • Discrepancies at the three-loop order between gauge theory scaling dimensions and string theory energies were uncovered.

Conclusions:

  • The study confirms the utility of dynamical tests in exploring the AdS/CFT duality.
  • The derived all-loop conjecture for gauge theory Bethe equations provides a framework for further investigation.
  • The identified discrepancies highlight areas for future theoretical development and refinement of the duality.