Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

The Precise Definition of a Limit01:27

The Precise Definition of a Limit

472
Understanding the formal definition of a limit is essential for precise mathematical analysis. This concept allows us to rigorously determine how a function behaves near a particular point without relying on ambiguous notions such as "getting close." The ε-δ definition plays a foundational role in calculus, ensuring analytical clarity and logical consistency in limit evaluation.The formal definition states that the limit of a function f(x) as x approaches a is L, written asif for...
472
Introduction to Limits01:30

Introduction to Limits

428
A limit describes the value a function approaches as its input moves closer to a particular point. Even when a function is undefined at a specific value, limits allow us to analyze its behavior near that point. This concept is fundamental in calculus and essential for understanding continuity, derivatives, and integrals.Mathematically, a function f(x) has a limit L at x = a if its values L approach x as x gets arbitrarily close to a. This is written as:This notation expresses that the function...
428
Planar Rigid-Body Motion01:22

Planar Rigid-Body Motion

1.4K
Understanding the movement of a rigid body in planar motion involves recognizing that every particle within this body is traversing a path that maintains a consistent distance from a specific plane. This concept is fundamental in the study of physics and mechanical engineering, and it allows us to comprehend better how objects move in space.
Planar motion is typically divided into three distinct categories. The first is rectilinear translation, demonstrated by a subway train that moves along...
1.4K
Types of Limits II01:24

Types of Limits II

268
When observing how a curve behaves near a specific point along the horizontal axis, there are cases where the curve’s height increases or decreases without limit as the position draws closer to that point. The curve does not settle at any particular value; instead, the values grow more extreme—upward or downward—the nearer they get. No defined value exists exactly at that location, yet the surrounding behavior becomes more dramatic, indicating a sharp change in direction.The...
268
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

7.5K
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...
7.5K
Limits at Infinity01:24

Limits at Infinity

421
The function that decreases as the input becomes very large provides a clear example of how mathematical functions can behave at extreme values. When the input increases continuously, the output becomes smaller and smaller, getting closer to a particular fixed value. Although the output never actually reaches this value, it moves nearer to it without limit. This behavior is a fundamental concept in understanding how functions behave as the input grows indefinitely. The graphical representation...
421

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A universal framework for the quantum simulation of Yang-Mills theory.

Communications physics·2026
Same author

Two-local modifications of Sachdev-Ye-Kitaev model with quantum chaos.

Physical review. E·2026
Same author

Characterization of quantum chaos by two-point correlation functions.

Physical review. E·2020
Same author

Universality in chaos: Lyapunov spectrum and random matrix theory.

Physical review. E·2018
Same author

Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models.

Physical review letters·2018
Same author

Holographic description of a quantum black hole on a computer.

Science (New York, N.Y.)·2014

Related Experiment Video

Updated: Apr 25, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.2K

From the planar limit to M theory.

Tatsuo Azeyanagi1, Mitsutoshi Fujita2, Masanori Hanada3

  • 1Center for the Fundamental Laws of Nature, Harvard University, Cambridge, Massachusetts 02138, USA.

Physical Review Letters
|August 29, 2014
PubMed
Summary

We propose that a general large-N limit of gauge theories, where

More Related Videos

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices
11:24

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Published on: July 11, 2025

13.8K
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

10.2K

Related Experiment Videos

Last Updated: Apr 25, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.2K
Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices
11:24

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Published on: July 11, 2025

13.8K
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

10.2K

Area of Science:

  • Theoretical Physics
  • High Energy Physics
  • String Theory

Background:

  • The large-N limit of gauge theories is crucial in theoretical physics.
  • Understanding beyond the planar limit (fixed 't Hooft coupling) is limited.
  • General large-N limits are important for non-perturbative M-theory formulations.

Purpose of the Study:

  • To explore general large-N limits of gauge theories where 't Hooft coupling grows with N.
  • To investigate the relationship between these general large-N limits and the planar limit.
  • To support conjectures about the identity of certain quantum field theories.

Main Methods:

  • Consideration of gauge theories where 't Hooft coupling grows with N.
  • Analysis of the commutation of large-N and strong coupling limits.
  • Analytic continuation from the planar limit.
  • Reproducing properties of the six-dimensional N=(2,0) theory from five-dimensional maximal super Yang-Mills theory.

Main Results:

  • Proposed that general large-N limits are essentially identical to the planar limit.
  • Demonstrated that the order of large-N and strong coupling limits commute.
  • Showed smooth connection and justified analytic continuation from the planar limit for a wide class of theories.
  • Successfully reproduced properties of the six-dimensional N=(2,0) theory.

Conclusions:

  • The study provides strong evidence that general large-N limits are equivalent to the planar limit.
  • This equivalence justifies analytic continuation and supports conjectures regarding M-theory and specific quantum field theories.
  • The findings advance the understanding of non-perturbative aspects of gauge theories and M-theory.