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Gauss's Law: Planar Symmetry

Gauss's Law: Planar Symmetry

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...

Gauss's Law: Cylindrical Symmetry

Gauss's Law: Cylindrical Symmetry

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,...

Coplanar Forces

Coplanar Forces

Consider an object upon which multiple forces are acting. If the lines of action of each force lie within the same plane, the system can be considered coplanar. The Cartesian vector form can be used to resolve each force into its respective components. For a coplanar system, the system will be in equilibrium if each component of the resultant force equals zero and the resultant force on the system is zero. If the sum of the forces is not equal to zero, then the object will not be in equilibrium...

Transformation of Plane Strain

Transformation of Plane Strain

When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...

Gauss's Law: Spherical Symmetry

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...

Scaling

Scaling

In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...

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Related Experiment Video

Updated: May 24, 2026

Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization

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Published on: July 5, 2016

Holographic Constraint on Scale Separation.

Nikolay Bobev¹, Hynek Paul¹, Filippo Revello¹

¹KU Leuven, Instituut voor Theoretische Fysica and Leuven Gravity Institute, Celestijnenlaan 200D, B-3001 Leuven, Belgium.

Physical Review Letters

|May 22, 2026

Summary

We introduce a new condition to ensure gravitational effective field theories in Anti-de Sitter space (AdS) are compatible with holographic descriptions using large-N conformal field theories (CFTs). This condition requires specific bulk couplings to vanish, a finding confirmed in string theory models.

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Area of Science:

Theoretical Physics
String Theory
Quantum Field Theory

Background:

Investigating the compatibility between gravitational effective field theories in Anti-de Sitter (AdS) space and their holographic duals in large-N conformal field theories (CFTs) is crucial for understanding quantum gravity.
The relationship between AdS and CFT is a cornerstone of the holographic principle, offering insights into strongly coupled systems.

Purpose of the Study:

To propose and verify a novel consistency condition for the compatibility of gravitational effective field theories in AdS with their holographic duals.
To determine the vanishing conditions for cubic scalar bulk couplings in specific string theory vacua.

Main Methods:

Utilizing large-N factorization of correlation functions in CFTs.
Defining single- and multiparticle operators to analyze bulk couplings.
Applying the derived consistency condition to 4d N=1 effective supergravity theories in DGKT AdS4 vacua.

Main Results:

Demonstrated that cubic scalar bulk couplings for fields dual to operators with extremal conformal dimensions must vanish.
Showed that this condition is non-trivially satisfied for the simplest DGKT AdS4 vacua in type IIA string theory.
Explicitly calculated all non-vanishing three-point correlation functions for low-lying scalar operators in the dual 3D CFTs.

Conclusions:

The proposed consistency condition provides a robust criterion for holographic duality in gravitational effective field theories.
The results confirm the validity of the holographic principle in the studied string theory backgrounds.
The explicit calculation of correlation functions offers valuable data for further exploration of these dualities.