Abstract
We formulate ${\cal N} = 2^*$ supersymmetric Yang-Mills theory on a Euclidean spacetime lattice using the method of topological twisting. The lattice formulation preserves one scalar supersymmetry charge at finite lattice spacing. The lattice theory is also local, gauge invariant and free from doublers. We can use the lattice formulation of ${\cal N} = 2^*$ supersymmetric Yang-Mills to study finite temperature nonperturbative sectors of the theory and thus validate the gauge-gravity duality conjecture in a nonconformal theory.
Highlights
Supersymmetric quantum field theories are interesting classes of theories by themselves
We note that O3 contains the Konishi operator, which is an SOð6Þ singlet, 1In Appendix A, we briefly review the gravitational dual of N 1⁄4 2Ã supersymmetric YangMills (SYM)
We have provided a Euclidean lattice formulation of four-dimensional N 1⁄4 2Ã SYM
Summary
Supersymmetric quantum field theories are interesting classes of theories by themselves. We note that there are terms in Sm that contain uncontracted twisted Lorentz indices The presence of such terms is expected from the fact that the mass deformation of N 1⁄4 4 SYM breaks R-symmetry from SUð4Þ to SUð2Þ × Uð1Þ. We note that we are unable to express the twisted action of N 1⁄4 2Ã SYM as successive variations of QðmÞ and QðmÞ on an action functional, say, F ðmÞ This could be due to the fact that we are interested in giving mass to the N 1⁄4 2 multiplet associated with the supercharge QðmÞ, that is, for the multiplet with the twisted fields ðC; Bμν; ζ; χμ; ψμνÞ, where the fermions ζ, χμ and ψμν are originally associated with the twisted supercharges Q, Qμ and Qμν, respectively
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