Review of Lattice Supersymmetry and Gauge-Gravity Duality

We review the status of recent investigations on validating the gauge-gravity duality conjecture through numerical simulations of strongly coupled maximally supersymmetric thermal gauge theories. In the simplest setting, the gauge-gravity duality connects systems of D0-branes and black hole geometries at finite temperature to maximally supersymmetric gauged quantum mechanics at the same temperature. Recent simulations show that non-perturbative gauge theory results give excellent agreement with the quantum gravity predictions, thus proving strong evidence for the validity of the duality conjecture and more insight into quantum black holes and gravity.Comment: v2: Minor comments and references added. Invited review for the International Journal of Modern Physics

Lattice Formulation of N=2∗{\cal N} = 2^* Yang-Mills

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.Comment: 22 pages, no figures. v3: Matches with published versio

Two-dimensional N=(2,2){\cal N} = (2, 2) Lattice Gauge Theories with Matter in Higher Representations

We construct two-dimensional ${\cal N} = (2, 2)$ supersymmetric gauge theories on a Euclidean spacetime lattice with matter in the two-index symmetric and anti-symmetric representations of SU($N_c$) color group. These lattice theories preserve a subset of the supercharges exact at finite lattice spacing. The method of topological twisting is used to construct such theories in the continuum and then the geometric discretization scheme is used to formulate them on the lattice. The lattice theories obtained this way are gauge-invariant, free from fermion doubling problem and exact supersymmetric at finite lattice spacing. We hope that these lattice constructions further motivate the nonperturbative explorations of models inspired by technicolor, orbifolding and orientifolding in string theories and the Corrigan-Ramond limit.Comment: 16 pages, 1 figure. v2: New section on fine tuning added. Slight modification in abstract. Version matches with the one accepted for publicatio

Lattice formulations of supersymmetric gauge theories with matter fields

Certain classes of supersymmetric gauge theories, including the well known N=4 supersymmetric Yang-Mills theory, that takes part in the AdS/CFT correspondence, can be formulated on a Euclidean spacetime lattice using the techniques of exact lattice supersymmetry. Great ideas such as topological field theories, Dirac-Kaehler fermions, geometric discretization all come together to create supersymmetric lattice theories that are gauge-invariant, doubler free, local and exact supersymmetric. We discuss the recent lattice constructions of supersymmetric Yang-Mills theories in two and three dimensions coupled to matter fields in various representations of the color group.Comment: 7 pages, 3 figures. Talk presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, Columbia University, New York, N

N=2∗{\cal N} = 2^* Yang-Mills on the Lattice

The ${\cal N} = 2^*$ Yang-Mills theory in four dimensions is a non-conformal theory that appears as a mass deformation of maximally supersymmetric ${\cal N} = 4$ Yang-Mills theory. This theory also takes part in the AdS/CFT correspondence and its gravity dual is type IIB supergravity on the Pilch-Warner background. The finite temperature properties of this theory have been studied recently in the literature. It has been argued that at large $N$ and strong coupling this theory exhibits no thermal phase transition at any non-zero temperature. The low temperature ${\cal N} = 2^*$ plasma can be compared to the QCD plasma. We provide a lattice construction of ${\cal N} = 2^*$ Yang-Mills on a hypercubic lattice starting from the ${\cal N} = 4$ gauge theory. The lattice construction is local, gauge-invariant, free from fermion doubling problem and preserves a part of the supersymmetry. This nonperturbative formulation of the theory can be used to provide a highly nontrivial check of the AdS/CFT correspondence in a non-conformal theory.Comment: 8 pages, 0 figures. Talk presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai

Gauge theory duals of black hole - black string transitions of gravitational theories on a circle

We study the black hole - black string phase transitions of gravitational theories compactified on a circle using the holographic duality conjecture. The gauge theory duals of these theories are maximally supersymmetric and strongly coupled 1 + 1 dimensional SU(N) Yang-Mills theories compactified on a circle, in the large $N$ limit. We perform the strongly coupled finite temperature gauge theory calculations on a lattice, using the recently developed exact lattice supersymmetry methods based on topological twisting and orbifolding. The spatial Polyakov line serves as relevant order parameter of the confinement - deconfinement phase transitions in the gauge theory duals.Comment: v2: 8 pages, 2 figures. References added. Talk given at the 6th International Symposium on Quantum Theory and Symmetries (QTS6), Lexington, Kentucky, 20-25 Jul 200