scholarly journals On a path integral representation of the Nekrasov instanton partition function and its Nekrasov–Shatashvili limit

2014 ◽  
Vol 92 (3) ◽  
pp. 267-270 ◽  
Author(s):  
Franco Ferrari ◽  
Marcin Piątek
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Path Integral ◽  
Equation Of Motion ◽  
Field Theories ◽  
Integral Expression ◽  
Path Integral Representation ◽  
Yang Mills ◽  
Fundamental Matter ◽  
Mills Field

In this work we study the Nekrasov–Shatashvili limit of the Nekrasov instanton partition function of Yang–Mills field theories with 𝒩 = 2 supersymmetry and gauge group SU(N). The theories are coupled with fundamental matter. A path integral expression of the full instanton partition function is derived. It is checked that in the Nekrasov–Shatashvili (thermodynamic) limit the action of the field theory obtained in this way reproduces exactly the equation of motion used in the saddle-point calculations.

Yang–Mills theory and fermionic path integrals

2016 ◽  
Vol 31 (04) ◽  
pp. 1630004 ◽  
Author(s):  
Kazuo Fujikawa
Keyword(s):  
Field Theory ◽  
Path Integral ◽  
Integral Formula ◽  
Path Integrals ◽  
Recent Analysis ◽  
Yang Mills ◽  
Fundamental Particles ◽  
Important Field ◽  
Quantum Anomalies ◽  
Mills Field

The Yang–Mills gauge field theory, which was proposed 60 years ago, is extremely successful in describing the basic interactions of fundamental particles. The Yang–Mills theory in the course of its developments also stimulated many important field theoretical machinery. In this brief review I discuss the path integral techniques, in particular, the fermionic path integrals which were developed together with the successful applications of quantized Yang–Mills field theory. I start with the Faddeev–Popov path integral formula with emphasis on the treatment of fermionic ghosts as an application of Grassmann numbers. I then discuss the ordinary fermionic path integrals and the general treatment of quantum anomalies. The contents of this review are mostly pedagogical except for a recent analysis of path integral bosonization.

scholarly journals Chiral correlators in $$ \mathcal{N} $$ = 2 superconformal quivers

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Francesco Galvagno ◽  
Michelangelo Preti
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Flat Space ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Yang Mills ◽  
The Matrix ◽  
Superspace Formalism ◽  
Model Approach

Abstract We consider a family of $$ \mathcal{N} $$ N = 2 superconformal field theories in four dimensions, defined as ℤq orbifolds of $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a perturbative level, using both the matrix model approach arising from supersymmetric localisation on the four-sphere and explicit field theory calculations on the flat space using the $$ \mathcal{N} $$ N = 1 superspace formalism. We implement a highly efficient algorithm to produce a large number of results for finite values of N , exploiting the symmetries of the quiver to reduce the complexity of the mixing between the operators. Finally the interplay with the field theory calculations allows to isolate special observables which deviate from $$ \mathcal{N} $$ N = 4 only at high orders in perturbation theory.

scholarly journals Black Holes in 4D N=4 Super-Yang-Mills Field Theory

2020 ◽  
Vol 10 (2) ◽  
Author(s):  
Francesco Benini ◽  
Paolo Milan
Keyword(s):  
Field Theory ◽  
Black Holes ◽  
Yang Mills ◽  
Mills Field

THE SUPERSYMMETRIC GAUGE FIELD COPIES

1987 ◽  
Vol 02 (11) ◽  
pp. 861-868
Author(s):  
ZIEMOWIT POPOWICZ
Keyword(s):  
Field Theory ◽  
Field Strength ◽  
Gauge Field ◽  
Yang Mills ◽  
Supersymmetric Gauge ◽  
Mills Field

The examples of Wu-Yang ambiguity in the supersymmetric Yang-Mills theory are given. We describe two different manners of copying the superconnection for the N = 1, N = 3 supersymmetric SU(2) Yang-Mills field theory, providing the same field strength superfield tensor.

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