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High temperature expansion in supersymmetric matrix quantum mechanics

Naoyuki Kawahara1,2, Jun Nishimura1,3 and Shingo Takeuchi3

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We formulate the high temperature expansion in supersymmetric matrix quantum mechanics with 4, 8 and 16 supercharges. The models can be obtained by dimensionally reducing Script N = 1 U(N) super Yang-Mills theory in D = 4,6,10 to 1 dimension, respectively. While the non-zero frequency modes become weakly coupled at high temperature, the zero modes remain strongly coupled. We find, however, that the integration over the zero modes that remains after integrating out all the non-zero modes perturbatively, reduces to the evaluation of connected Green's functions in the bosonic IKKT model. We perform Monte Carlo simulation to compute these Green's functions, which are then used to obtain the coefficients of the high temperature expansion for various quantities up to the next-leading order. Our results nicely reproduce the asymptotic behaviors of the recent simulation results at finite temperature. In particular, the fermionic matrices, which decouple at the leading order, give rise to substantial effects at the next-leading order, reflecting finite temperature behaviors qualitatively different from the corresponding models without fermions.

Keywords

Thermal Field Theory

Matrix Models

 

E-print Number: 0710.2188

Cited: by |

Refers: to

PACS

11.30.Pb Supersymmetry

11.30.Ly Other internal and higher symmetries

11.10.Wx Finite-temperature field theory

11.25.Yb M theory

11.15.Pg Expansions for large numbers of components (e.g., 1/Nc expansions)

Subjects

Particle physics and field theory

Dates

Issue 12 (December 2007)

Received 8 November 2007, accepted for publication 11 December 2007

Published 31 December 2007



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