scholarly journals Non-local symmetries for Yang-Mills theories and their massive counterparts in two and three dimensions

2012 ◽  
Vol 2012 (5) ◽  
Author(s):  
Abhishek Agarwal ◽  
Ansar Fayyazuddin
Keyword(s):  
Three Dimensions ◽  
Yang Mills ◽  
Non Local ◽  
Local Symmetries

scholarly journals Perturbative linearization of super-Yang-Mills theories in general gauges

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Hannes Malcha ◽  
Hermann Nicolai
Keyword(s):  
Large Class ◽  
Fourth Order ◽  
Landau Gauge ◽  
Third Order ◽  
Yang Mills ◽  
Free Theory ◽  
Non Linear ◽  
Functional Measure ◽  
Non Local ◽  
Jacobi Determinant

Abstract Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.

scholarly journals Hidden local, quasi-local and non-local symmetries in integrable systems

2000 ◽  
Vol 577 (3) ◽  
pp. 500-528 ◽  
Author(s):  
D. Fioravanti ◽  
M. Stanishkov
Keyword(s):  
Integrable Systems ◽  
Non Local ◽  
Local Symmetries

scholarly journals Exact extended supersymmetry on a lattice: Twisted N=4 super-Yang–Mills in three dimensions

2008 ◽  
Vol 798 (1-2) ◽  
pp. 168-183 ◽  
Author(s):  
Alessandro D'Adda ◽  
Issaku Kanamori ◽  
Noboru Kawamoto ◽  
Kazuhiro Nagata
Keyword(s):  
Extended Supersymmetry ◽  
Three Dimensions ◽  
Yang Mills

scholarly journals On the Mini-Superambitwistor Space and𝒩=8Super-Yang-Mills Theory

2009 ◽  
Vol 2009 ◽  
pp. 1-27 ◽  
Author(s):  
Christian Sämann
Keyword(s):  
Dimensional Reduction ◽  
Three Dimensions ◽  
Third Order ◽  
Yang Mills

We construct a new supertwistor space suited for establishing a Penrose-Ward transform between certain bundles over this space and solutions to the𝒩=8super-Yang-Mills equations in three dimensions. This mini-superambitwistor space is obtained by dimensional reduction of the superambitwistor space, the standard superextension of the ambitwistor space. We discuss in detail the construction of this space and its geometry before presenting the Penrose-Ward transform. We also comment on a further such transform for purely bosonic Yang-Mills-Higgs theory in three dimensions by considering third-order formal “subneighborhoods” of a miniambitwistor space.

scholarly journals Diluted mass gap in strongly coupled non-local Yang-Mills

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Marco Frasca ◽  
Anish Ghoshal
Keyword(s):  
Field Theory ◽  
Particle Physics ◽  
Mass Scale ◽  
Local Theory ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Mass Gap ◽  
Non Local ◽  
Non Locality

Abstract We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.

scholarly journals The Yang-Mills heat equation with finite action in three dimensions

2022 ◽  
Vol 275 (1349) ◽  
Author(s):  
Leonard Gross
Keyword(s):  
Heat Equation ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Three Dimensions ◽  
Dimensional Manifold ◽  
Uniqueness Of Solutions ◽  
Reconstruction Procedure ◽  
Content Type ◽  
Yang Mills ◽  
Gauge Functions

The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over R 3 \mathbb {R}^3 and over a bounded open convex set in R 3 \mathbb {R}^3 . The initial data is taken to lie in the Sobolev space of order one half, which is the critical Sobolev index for this equation over a three dimensional manifold. The existence is proven by solving first an augmented, strictly parabolic equation and then gauge transforming the solution to a solution of the Yang-Mills heat equation itself. The gauge functions needed to carry out this procedure lie in the critical gauge group of Sobolev regularity three halves, which is a complete topological group in a natural metric but is not a Hilbert Lie group. The nature of this group must be understood in order to carry out the reconstruction procedure. Solutions to the Yang-Mills heat equation are shown to be strong solutions modulo these gauge functions. Energy inequalities and Neumann domination inequalities are used to establish needed initial behavior properties of solutions to the augmented equation.

Sign in / Sign up

Export Citation Format

Share Document