Supersymmetric Yang--Mills theories with exact supersymmetry on the lattice

Details Supersymmetric Yang--Mills theories with exact supersymmetry on the lattice Supersymmetric Yang--Mills theories with exact supersymmetry on the lattice

2011-10-27

arxiv.org/abs/1110.5983v2

Int.J.Mod.Phys.A26:5057-5132,2011

Physics

High Energy Physics

High Energy Physics - Lattice

74 pages, 15 figures, minor revision, references added, published version

Scientific paper

10.1142/S0217751X11054863

Inspired by the ideas from topological field theory it is possible to rewrite the supersymmetric charges of certain classes of extended supersymmetric Yang--Mills (SYM) theories in such a way that they are compatible with the discretization on a Euclidean spacetime lattice. Such theories are known as maximally twisted SYM theories. In this review we discuss the construction and some applications of such classes of theories. The one-loop perturbative renormalization of the four-dimensional lattice ${\cal N}=4$ SYM is discussed in particular. The lattice theories constructed using twisted approach play an important role in investigating the thermal phases of strongly coupled SYM theories and also the thermodynamic properties of their dual gravitational theories.

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