Two-dimensional lattice for four-dimensional N=4 supersymmetric Yang-Mills

Fumihiko Sugino; Masanori Hanada; So Matsuura

Two-dimensional lattice for four-dimensional N=4 supersymmetric Yang-Mills

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arxiv 1004.5513 v3 pith:JYJLV35G submitted 2010-04-30 hep-lat hep-th

Masanori Hanada , So Matsuura , Fumihiko Sugino This is my paper · ORCID

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We construct a lattice formulation of a mass-deformed two-dimensional N=(8,8) super Yang-Mills theory with preserving two supercharges exactly. Gauge fields are represented by compact unitary link variables, and the exact supercharges on the lattice are nilpotent up to gauge transformations and SU(2)_R rotations. Due to the mass deformation, the lattice model is free from the vacuum degeneracy problem, which was encountered in earlier approaches, and flat directions of scalar fields are stabilized giving discrete minima representing fuzzy S^2. Around the trivial minimum, quantum continuum theory is obtained with no tuning, which serves a nonperturbative construction of the IIA matrix string theory. Moreover, around the minimum of k-coincident fuzzy spheres, four-dimensional N=4 U(k) super Yang-Mills theory with two commutative and two noncommutative directions emerges. In this theory, sixteen supersymmetries are broken by the mass deformation to two. Assuming the breaking is soft, we give a scenario leading to undeformed N=4 super Yang-Mills on R^4 without any fine tuning. As an evidence for the validity of the assumption, some computation of 1-loop radiative corrections is presented.

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Novel first-order phase transition and critical points on $SU(3)$ Yang-Mills theory in $\mathbb{T}^2\times\mathbb{R}^2$
hep-lat 2025-02 conditional novelty 2.0 of 10

An effective model fitted to lattice data predicts a first-order phase transition with critical endpoints inside the deconfined phase of SU(3) Yang-Mills theory on a squeezed torus.

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