Thermal phase transition in Yang-Mills matrix model
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Received: November 2, 2019 Accepted: December 22, 2019 Published: January 10, 2020
Thermal phase transition in Yang-Mills matrix model Georg Bergner,a Norbert Bodendorfer,b Masanori Hanada,c Enrico Rinaldi,d,e Andreas Sch¨ aferb and Pavlos Vranasf,g Institute for Theoretical Physics, University of Jena, Max-Wien-Platz 1, D-07743 Jena, Germany b Institute of Theoretical Physics, University of Regensburg, Universit¨ atsstrasse 31, D-93053, Germany c School of Physics and Astronomy and STAG Research Centre, University of Southampton, Southampton, SO17 1BJ, U.K. d R&D Headquarters, Arithmer Inc., Minato, Tokyo 106-6040, Japan e Interdisciplinary Theoretical and Mathematical Sciences Program, RIKEN, Wako, Saitama 351-0198, Japan f Nuclear and Chemical Sciences Division, Lawrence Livermore National Laboratory, Livermore, CA 94550, U.S.A. g Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, U.S.A.
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: We study the bosonic matrix model obtained as the high-temperature limit of two-dimensional maximally supersymmetric SU(N ) Yang-Mills theory. So far, no consensus about the order of the deconfinement transition in this theory has been reached and this hinders progress in understanding the nature of the black hole/black string topology change from the gauge/gravity duality perspective. On the one hand, previous works considered the deconfinement transition consistent with two transitions which are of second and third order. On the other hand, evidence for a first order transition was put forward more recently. We perform high-statistics lattice Monte Carlo simulations at large N and small lattice spacing to establish that the transition is really of first order. Our findings flag a warning that the required large-N and continuum limit might not have been reached in earlier publications, and that was the source of the discrepancy. Moreover, our detailed results confirm the existence of a new partially deconfined phase which describes nonuniform black strings via the gauge/gravity duality. This phase exhibits universal features already predicted in quantum field theory. Keywords: Gauge-gravity correspondence, Lattice Quantum Field Theory, M(atrix) Theories ArXiv ePrint: 1909.04592
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)053
JHEP01(2020)053
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Contents 1 Introduction
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2 Theoretical expectations 2.1 Partial deconfinement and possible phase structures 2.2 Large-D, large-N analysis 2.3 Finite-N effects
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4 Partial deconfinement
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5 Conclusion and future directions
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A Simulation details
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B Data for N = 32
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1
Introduction
Bosonic matrix models in one dimension have been studied in various contexts. Despite their simple structure, they display a rich non-trivial phase diagram that can be accesse
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