Abstract
Stochastic quantization provides an alternate approach to the computation of quantum observables, by stochastically sampling phase space in a path integral. Furthermore, the stochastic variational method can provide analytical control over the strong coupling regime of a quantum field theory -- provided one has a decent qualitative guess at the form of certain observables at strong coupling. In the context of the holographic duality, the strong coupling regime of a Yang-Mills theory can capture gravitational dynamics. This can provide enough insight to guide a stochastic variational ansatz. We demonstrate this in the bosonic Banks-Fischler-Shenker-Susskind Matrix theory. We compute a two-point function at all values of coupling using the variational method showing agreement with lattice numerical computations and capturing the confinement-deconfinement phase transition at strong coupling. This opens up a new realm of possibilities for exploring the holographic duality and emergent geometry.
Highlights
AND HIGHLIGHTSIn the context of holographic dualities [1,2,3,4,5], one can use a nongravitational theory—typically a Yang-Mills theory of rank N and effective coupling λ, to describe gravitational dynamics in a regime where N is large and λ > 1
We focus on the Banks-Fischler-Shenker-Susskind (BFSS) matrix theory [1], which describes M-theory through a matrix model that is the dimensional reduction of 10D N 1⁄4 1 Super Yang-Mills (SYM)
We review alternate numerical techniques based on stochastic quantization that can be used for computing zero temperature dynamics
Summary
In the context of holographic dualities [1,2,3,4,5], one can use a nongravitational theory—typically a Yang-Mills theory of rank N and effective coupling λ, to describe gravitational dynamics in a regime where N is large and λ > 1. BFSS theory is known to be chaotic and, at strong coupling, can be described by random matrices with a couplingdependent effective mass We will use this knowledge to employ a robust ansatz and access strong coupling dynamics. We employ a perturbative approach in the effective coupling, deriving stochastic Feynman diagrams to compute any observable We use this perturbative approach to compute the vev of R2 ≡ TrXi2=N, which is a gauge invariant operator measuring the size of the matrix configuration in the vacuum. We proceed to developing the variational approach of the stochastic quantization of bosonic BFSS theory to access the strong coupling regime. VI we summarize the results and suggest directions for the future
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