Abstract
We study the finite temperature properties of a recently introduced string bit model designed to capture some features of the emergent string in the tensionless limit. The model consists of a pair of bosonic and fermionic bit operators transforming in the adjoint representation of the color group SU(N). Color confinement is not achieved as a dynamical effect, but instead is enforced by an explicit singlet projection. At large N and finite temperature, the model has a non trivial thermodynamics. In particular, there is a Hagedorn type transition at a finite temperature T = T H where the string degrees of freedom are liberated and the free energy gets a large contribution ∼ N 2 that plays the role of an order parameter. For T > T H, the low temperature phase becomes unstable. In the new phase, the thermodynamically favoured configurations are characterized by a non-trivial gapped density of the SU(N) angles associated with the singlet projection. We present an accurate algorithm for the determination of the density profile at N = ∞. In particular, we determine the gap endpoint at generic temperature and analytical expansions valid near the Hagedorn transition as well as at high temperature. The leading order corrections are characterized by non-trivial exponents that are determined analytically and compared with explicit numerical calculations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Giles and C.B. Thorn, A Lattice Approach to String Theory, Phys. Rev. D 16 (1977) 366 [INSPIRE].
C.B. Thorn, Reformulating string theory with the 1/N expansion, in The First International A.D. Sakharov Conference on Physics, Moscow, USSR, 27-31 May 1991, pp. 447-454 [hep-th/9405069] [INSPIRE].
O. Bergman and C.B. Thorn, String bit models for superstring, Phys. Rev. D 52 (1995) 5980 [hep-th/9506125] [INSPIRE].
S. Sun and C.B. Thorn, Stable String Bit Models, Phys. Rev. D 89 (2014) 105002 [arXiv:1402.7362] [INSPIRE].
C.B. Thorn, Space from String Bits, JHEP 11 (2014) 110 [arXiv:1407.8144] [INSPIRE].
G. Chen and S. Sun, Numerical Study of the Simplest String Bit Model, Phys. Rev. D 93 (2016) 106004 [arXiv:1602.02166] [INSPIRE].
R. Hagedorn, Statistical thermodynamics of strong interactions at high-energies, Nuovo Cim. Suppl. 3 (1965) 147 [INSPIRE].
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
C.B. Thorn, Infinite N c QCD at finite temperature: is there an ultimate temperature?, Phys. Lett. B 99 (1981) 458 [INSPIRE].
S. Fubini and G. Veneziano, Level structure of dual-resonance models, Nuovo Cim. A 64 (1969) 811 [INSPIRE].
J.J. Atick and E. Witten, The Hagedorn Transition and the Number of Degrees of Freedom of String Theory, Nucl. Phys. B 310 (1988) 291 [INSPIRE].
C.B. Thorn, String Bits at Finite Temperature and the Hagedorn Phase, Phys. Rev. D 92 (2015) 066007 [arXiv:1507.03036] [INSPIRE].
S. Raha, Hagedorn temperature in superstring bit model and SU(N) characters, Phys. Rev. D 96 (2017) 086006 [arXiv:1706.09951] [INSPIRE].
T.L. Curtright, S. Raha and C.B. Thorn, Color Characters for White Hot String Bits, arXiv:1708.03342 [INSPIRE].
P. Goddard, J. Goldstone, C. Rebbi and C.B. Thorn, Quantum dynamics of a massless relativistic string, Nucl. Phys. B 56 (1973) 109 [INSPIRE].
G. ’t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
D.J. Gross and E. Witten, Possible Third Order Phase Transition in the Large-N Lattice Gauge Theory, Phys. Rev. D 21 (1980) 446 [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn/deconfinement phase transition in weakly coupled large-N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].
B.S. Skagerstam, On the Large-N c Limit of the SU(N c ) Color quark-gluon Partition Function, Z. Phys. C 24 (1984) 97 [INSPIRE].
H.J. Schnitzer, Confinement/deconfinement transition of large-N gauge theories with N f fundamentals: N f /N finite, Nucl. Phys. B 695 (2004) 267 [hep-th/0402219] [INSPIRE].
H.J. Schnitzer, Confinement/deconfinement transition of large-N gauge theories in perturbation theory with N f fundamentals: N f /N finite, hep-th/0612099 [INSPIRE].
S.H. Shenker and X. Yin, Vector Models in the Singlet Sector at Finite Temperature, arXiv:1109.3519 [INSPIRE].
M. Beccaria and A.A. Tseytlin, Partition function of free conformal fields in 3-plet representation, JHEP 05 (2017) 053 [arXiv:1703.04460] [INSPIRE].
J. Jurkiewicz and K. Zalewski, Vacuum Structure of the U(N → ∞) Gauge Theory on a Two-dimensional Lattice for a Broad Class of Variant Actions, Nucl. Phys. B 220 (1983) 167 [INSPIRE].
C.M. Bender and S.A. Orszag, Advanced mathematical methods for scientists and engineers I: asymptotic methods and perturbation theory, Springer Science & Business Media (2013).
D.A. Lowe and L. Thorlacius, Hot string soup, Phys. Rev. D 51 (1995) 665 [hep-th/9408134] [INSPIRE].
H. Liu, Fine structure of Hagedorn transitions, hep-th/0408001 [INSPIRE].
L. Álvarez-Gaumé, C. Gomez, H. Liu and S. Wadia, Finite temperature effective action, AdS 5 black holes and 1/N expansion, Phys. Rev. D 71 (2005) 124023 [hep-th/0502227] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1709.01801
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Beccaria, M. Thermal properties of a string bit model at large N . J. High Energ. Phys. 2017, 200 (2017). https://doi.org/10.1007/JHEP10(2017)200
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2017)200