74 research outputs found
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
Two-dimensional Lattice Gauge Theories with Matter in Higher Representations
We construct two-dimensional supersymmetric gauge
theories on a Euclidean spacetime lattice with matter in the two-index
symmetric and anti-symmetric representations of SU() 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
Yang-Mills on the Lattice
The Yang-Mills theory in four dimensions is a non-conformal
theory that appears as a mass deformation of maximally supersymmetric 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
and strong coupling this theory exhibits no thermal phase transition at any
non-zero temperature. The low temperature plasma can be
compared to the QCD plasma. We provide a lattice construction of Yang-Mills on a hypercubic lattice starting from the 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 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
Supersymmetric Yang-Mills theories on the lattice
This dissertation reviews the formulation of twisted supersymmetric Yang--Mills (SYM) theories in the continuum and also on the lattice. We focus on the maximally supersymmetric twisted SYM theories in four and two dimensions. The one-loop renormalization of the lattice four-dimensional SYM theory is investigated. We also study the thermal phase structure of the maximally supersymmetric SYM in two dimensions and possible black hole transitions in its dual gravitational theory, using numerical simulations of the lattice theory
Markov Chain Monte Carlo Methods in Quantum Field Theories: A Modern Primer
We introduce and discuss Monte Carlo methods in quantum field theories.
Methods of independent Monte Carlo, such as random sampling and importance
sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and
Hamiltonian Monte Carlo, are introduced. We review the underlying theoretical
foundations of Markov chain Monte Carlo. We provide several examples of Monte
Carlo simulations, including one-dimensional simple harmonic oscillator,
unitary matrix model exhibiting Gross-Witten-Wadia transition and a
supersymmetric model exhibiting dynamical supersymmetry breaking.Comment: v3: 125 pages, 33 figures, references updated. Based on the three
lectures given at the 2019 Joburg School in Theoretical Physics: Aspects of
Machine Learning, Mandelstam Institute for Theoretical Physics, The
University of the Witwatersrand, Johannesburg, South Africa (November 11 -
15, 2019). Published as part of Springer Briefs in Physics (2020). Author
version of the manuscrip
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