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Gauss's Law: Cylindrical Symmetry01:20

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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...
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Gauss's Law: Planar Symmetry01:27

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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String Universality and Non-Simply-Connected Gauge Groups in 8D.

Mirjam Cvetič1,2, Markus Dierigl1, Ling Lin3

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We found a new consistency condition for 8D supergravity theories. Most theories with non-Abelian gauge groups lack string theory realization and are inconsistent quantum theories when coupled to gravity.

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Area of Science:

  • Theoretical Physics
  • String Theory
  • Quantum Gravity

Background:

  • Supergravity theories in 8 dimensions (8D N=1 supergravity) are crucial for understanding quantum gravity.
  • The global structure G/Z for non-Abelian gauge groups introduces complexities.
  • Swampland criteria are used to distinguish consistent quantum gravity theories from inconsistent ones.

Purpose of the Study:

  • To present a novel consistency condition for 8D N=1 supergravity theories with nontrivial global structure G/Z.
  • To investigate the implications of this condition in conjunction with other swampland criteria.
  • To identify theories lacking string theory realization as inconsistent quantum theories when coupled to gravity.

Main Methods:

  • The study is based on an anomaly involving the Z 1-form center symmetry.
  • The consistency condition is analyzed in the context of F-theory compactifications.
  • Comparison with existing swampland criteria is performed.

Main Results:

  • A new consistency condition for 8D N=1 supergravity theories with non-Abelian gauge groups G/Z is derived.
  • The majority of 8D theories with gauge group G/Z, which lack string theory realization, are identified as inconsistent quantum theories when coupled to gravity.
  • The derived condition is shown to be equivalent to geometric properties of elliptic K3 surfaces in F-theory.

Conclusions:

  • The presented consistency condition provides a powerful tool for analyzing 8D supergravity theories.
  • This work significantly constrains the landscape of possible gauge groups in 8D string models.
  • The findings have implications for understanding the relationship between string theory, F-theory, and quantum gravity.