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 Cohomological localization of $$ \mathcal{N} $$ = 2 gauge theories with matter

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Guido Festuccia ◽  
Anastasios Gorantis ◽  
Antonio Pittelli ◽  
Konstantina Polydorou ◽  
Lorenzo Ruggeri
Keyword(s):  
Vector Field ◽  
Extended Supersymmetry ◽  
General Framework ◽  
Gauge Theories ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Explicit Result ◽  
Yang Mills ◽  
Self Duality ◽  
Witten Theory

Abstract We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $$ \mathcal{N} $$ N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

scholarly journals Exact extended supersymmetry on a lattice: Twisted N=2 super-Yang–Mills in two dimensions

2006 ◽  
Vol 633 (4-5) ◽  
pp. 645-652 ◽  
Author(s):  
Alessandro D'Adda ◽  
Issaku Kanamori ◽  
Noboru Kawamoto ◽  
Kazuhiro Nagata
Keyword(s):  
Extended Supersymmetry ◽  
Two 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 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.

scholarly journals Chern–Simons vs. Yang–Mills gaugings in three dimensions

2003 ◽  
Vol 668 (1-2) ◽  
pp. 167-178 ◽  
Author(s):  
Hermann Nicolai ◽  
Henning Samtleben
Keyword(s):  
Three Dimensions ◽  
Yang Mills ◽  
Chern Simons

scholarly journals Self-dual Yang-Mills multiplet in three dimensions coupled to supergravity

2007 ◽  
Vol 75 (12) ◽  
Author(s):  
Roy Montalvo ◽  
Hitoshi Nishino ◽  
Subhash Rajpoot
Keyword(s):  
Three Dimensions ◽  
Yang Mills

scholarly journals THE “DUAL” VARIABLES OF YANG-MILLS THEORY AND LOCAL GAUGE-INVARIANT VARIABLES

1996 ◽  
Vol 11 (32) ◽  
pp. 5701-5728 ◽  
Author(s):  
ORI GANOR ◽  
J. SONNENSCHEIN
Keyword(s):  
Degrees Of Freedom ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Six Degrees Of Freedom ◽  
Local Gauge ◽  
Dual Variables ◽  
Topological Part

After adding auxiliary fields and integrating out the original variables, the Yang-Mills action can be expressed in terms of local gauge-invariant variables. This method reproduces the known solution of the two-dimensional SU (N) theory. In more than two dimensions the action splits into a topological part and a part proportional to αs. We demonstrate the procedure for SU (2) in three dimensions where we reproduce a gravitylike theory. We discuss the four-dimensional case as well. We use a cubic expression in the fields as a space-time metric to obtain a covariant Lagrangian. We also show how the four-dimensional SU (2) theory can be expressed in terms of a local action with six degrees of freedom only.

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