Large N $N$ Limits of Supersymmetric Quantum Field Theories: A Pedagogical Overview

IF 7.8 3区物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY

Fortschritte Der Physik-Progress of Physics Pub Date : 2025-05-14 DOI:10.1002/prop.70006

Leonardo Santilli

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Abstract

The different large $N$ limits of supersymmetric quantum field theories in three, four, and five dimensions are reviewed. The author distinguishes between the planar limit of SQCD theories, the M-theory limit suited in three and five dimensions, and the long quiver limit. The method to solve exactly the sphere partition functions in each type of limit is spelled out in a pedagogical way. After a comprehensive general treatment of the saddle point approximation in the large $N$ limit, the author also presents an extensive list of examples and detail the calculations. The scope of this overview is to provide an entry-level, computation-oriented understanding of the techniques featured in the field theory side of the AdS/CFT correspondence.

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超对称量子场论的大N$ N$极限：教学综述

讨论了三维、四维和五维超对称量子场论的不同大N$ N$极限。本文区分了SQCD理论的平面极限、适合于三维和五维的m理论极限和长颤振极限。从教学的角度阐述了在各种极限下球配分函数的精确求解方法。在对大N$ N$极限下的鞍点近似作了全面的一般处理之后，作者还提供了大量的例子和详细的计算。这个概述的范围是提供一个入门级的，以计算为导向的对AdS/CFT对应的现场理论方面的技术的理解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fortschritte Der Physik-Progress of Physics 物理-物理：综合

CiteScore

6.70

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal Fortschritte der Physik - Progress of Physics is a pure online Journal (since 2013). Fortschritte der Physik - Progress of Physics is devoted to the theoretical and experimental studies of fundamental constituents of matter and their interactions e. g. elementary particle physics, classical and quantum field theory, the theory of gravitation and cosmology, quantum information, thermodynamics and statistics, laser physics and nonlinear dynamics, including chaos and quantum chaos. Generally the papers are review articles with a detailed survey on relevant publications, but original papers of general interest are also published.