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Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature

Konstantinos N. Anagnostopoulos, Masanori Hanada, Jun Nishimura, Shingo Takeuchi

TL;DR

The Polyakov line asymptotes at low temperature to a characteristic behavior for a deconfined theory, suggesting the absence of a phase transition, providing highly nontrivial evidence for the gauge-gravity duality.

Abstract

We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature. The recently proposed non-lattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black hole geometry. The Polyakov line takes large values even at low temperature suggesting the absence of a phase transition in sharp contrast to the bosonic case. These results provide highly non-trivial evidences for the gauge/gravity duality.

Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature

TL;DR

The Polyakov line asymptotes at low temperature to a characteristic behavior for a deconfined theory, suggesting the absence of a phase transition, providing highly nontrivial evidence for the gauge-gravity duality.

Abstract

We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature. The recently proposed non-lattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black hole geometry. The Polyakov line takes large values even at low temperature suggesting the absence of a phase transition in sharp contrast to the bosonic case. These results provide highly non-trivial evidences for the gauge/gravity duality.

Paper Structure

This paper contains 6 sections, 8 equations, 3 figures.

Table of Contents

  1. Introduction.---
  2. Simulation techniques.---
  3. Infrared instability.---
  4. Results.---
  5. Summary.---
  6. Acknowledgments.---

Figures (3)

  • Figure 1: The "extent of space" is plotted against temperature. The dashed line represents the result obtained by HTE up to the next leading order for $N=8$HTE.
  • Figure 2: The absolute value of the Polyakov line is plotted against temperature. The dashed line represents the result obtained by HTE up to the next leading order for $N=8$HTE. The dotted line represents a fit to eq. (\ref{['polya-fit']}) with $a=0.15$ and $b=0.072$.
  • Figure 3: The energy is plotted against temperature. The dashed line represents the result obtained by HTE up to the next leading order for $N=8$HTE. The solid line represents the energy predicted at small $T$ by the gauge/gravity duality. The upper left panel zooms up the region, where the power-law behavior sets in.