$ \mathcal{N} $ = 4 supersymmetric Yang-Mills thermodynamics to order λ2

Du, Qianqian; Strickland, Michael; Tantary, Ubaid

doi:10.1007/jhep08(2021)064

Title: $ \mathcal{N} $ = 4 supersymmetric Yang-Mills thermodynamics to order λ²

Abstract

We calculate the resummed perturbative free energy of $ \mathcal{N} $ = 4 supersymmetric Yang-Mills in four spacetime dimensions (SYM_4,4) through second order in the ’t Hooft coupling λ at finite temperature and zero chemical potential. Our final result is ultraviolet finite and all infrared divergences generated at three-loop level are canceled by summing over SYM_4,4 ring diagrams. Non-analytic terms at $ \mathcal{O} $(λ^3/2) and $ \mathcal{O} $(λ² log λ) are generated by dressing the A₀ and scalar propagators. The gauge-field Debye mass m_D and the scalar thermal mass M_D are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of SYM_4,4 to $ \mathcal{O} $(λ²). We compare our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Padé approximant that interpolates between the weak-coupling result and the large-N_c strong-coupling result. Our results suggest that the $ \mathcal{O} $(λ²) weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2.

Authors:

Du, Qianqian ^[1];

^[2]; Tantary, Ubaid ^[2]

Central China Normal Univ., Wuhan (China); Kent State Univ., Kent, OH (United States)
Kent State Univ., Kent, OH (United States)

Publication Date:: Mon Aug 16 00:00:00 EDT 2021

Research Org.:: Kent State Univ., Kent, OH (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); Chinese Scholarship Council; National Natural Science Foundation of China (NSFC); Guangdong Major Project of Basic and Applied Basic Research

OSTI Identifier:: 1851803

Grant/Contract Number:: SC0013470; 201906770021; 11935007; 2020B0301030008

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2021; Journal Issue: 8; Journal ID: ISSN 1029-8479

Publisher:: Springer Nature

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; physics; resummation; supersymmetric gauge theory

Citation Formats


                    Du, Qianqian, Strickland, Michael, and Tantary, Ubaid. \( \mathcal{N} \) = 4 supersymmetric Yang-Mills thermodynamics to order λ2.  United States: N. p., 2021. 
Web.  doi:10.1007/jhep08(2021)064.

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                    Du, Qianqian, Strickland, Michael, & Tantary, Ubaid. \( \mathcal{N} \) = 4 supersymmetric Yang-Mills thermodynamics to order λ2.  United States.  https://doi.org/10.1007/jhep08(2021)064

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                    Du, Qianqian, Strickland, Michael, and Tantary, Ubaid. Mon .  
"\( \mathcal{N} \) = 4 supersymmetric Yang-Mills thermodynamics to order λ2".  United States.  https://doi.org/10.1007/jhep08(2021)064.  https://www.osti.gov/servlets/purl/1851803.

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@article{osti_1851803,

  title        = {\( \mathcal{N} \) = 4 supersymmetric Yang-Mills thermodynamics to order λ2},

  author       = {Du, Qianqian and Strickland, Michael and Tantary, Ubaid},

  abstractNote = {We calculate the resummed perturbative free energy of \( \mathcal{N} \) = 4 supersymmetric Yang-Mills in four spacetime dimensions (SYM4,4) through second order in the ’t Hooft coupling λ at finite temperature and zero chemical potential. Our final result is ultraviolet finite and all infrared divergences generated at three-loop level are canceled by summing over SYM4,4 ring diagrams. Non-analytic terms at \( \mathcal{O} \)(λ3/2) and \( \mathcal{O} \)(λ2 log λ) are generated by dressing the A0 and scalar propagators. The gauge-field Debye mass mD and the scalar thermal mass MD are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of SYM4,4 to \( \mathcal{O} \)(λ2). We compare our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Padé approximant that interpolates between the weak-coupling result and the large-Nc strong-coupling result. Our results suggest that the \( \mathcal{O} \)(λ2) weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2.},

  doi          = {10.1007/jhep08(2021)064},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 8,

  volume       = 2021,

  place        = {United States},

  year         = {Mon Aug 16 00:00:00 EDT 2021},

  month        = {Mon Aug 16 00:00:00 EDT 2021}

}

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Title: \( \mathcal{N} \) = 4 supersymmetric Yang-Mills thermodynamics to order λ2

Abstract

Citation Formats

Resummation in hot field theories journal, June 2005

Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory journal, November 1998

Inconsistency of supersymmetric dimensional regularization journal, July 1980

Three-loop free energy for pure gauge QCD journal, December 1994

Perturbative thermal QCD: Formalism and applications journal, October 2020

Phase diagram of Script N = 4 super-Yang-Mills theory with R -symmetry chemical potentials journal, September 2006

Two-loop hard-thermal-loop thermodynamics with quarks journal, August 2004

Supersymmetry, supergravity theories and the dual spinor model journal, April 1977

Hard thermal loops and the entropy of supersymmetric Yang-Mills theories journal, June 2007

Dimensional regularization and supersymmetry journal, November 1984

Free energy of QCD at high temperature journal, March 1996

Regularization by Dimensional Reduction: Consistency, Quantum Action Principle, and Supersymmetry journal, March 2005

Supersymmetric Yang-Mills theories journal, March 1977

The Large-N Limit of Superconformal Field Theories and Supergravity journal, January 1999

Three-loop HTL QCD thermodynamics journal, August 2011

Free energy of hot gauge theories with fermions through g 5 journal, December 1995

QCD and instantons at finite temperature journal, January 1981

Quantum corrections to η / s journal, February 2009

Regularization and renormalization of gauge fields journal, July 1972

Hard-Thermal-Loop Resummation of the Free Energy of a Hot Gluon Plasma journal, September 1999

Two-loop HTL-resummed thermodynamics for $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory journal, September 2020

Remarks on two-loop free energy in N = 4 supersymmetric Yang-Mills theory at finite temperature journal, February 1999

Dimensional regularization and supersymmetry journal, June 1983

Self-consistent hard-thermal-loop thermodynamics for the quark-gluon plasma journal, December 1999

Note on supersymmetric Yang-Mills thermodynamics journal, October 1999

Regularization by dimensional reduction of supersymmetric and non-supersymmetric gauge theories journal, May 1980

Pressure of hot QCD up to g 6 ln ( 1 / g ) journal, May 2003

Hard-thermal-loop perturbation theory to two loops journal, October 2002

Regularization of supersymmetric theories — recent progress journal, July 2006

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Finite-Temperature Conformal Field Theory Results for All Couplings: O ( N ) Model in 2 + 1 Dimensions journal, June 2019

Three-loop HTL gluon thermodynamics at intermediate coupling journal, August 2010

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Supersymmetric dimensional regularization via dimensional reduction journal, June 1979

Dimensional renorinalization : The number of dimensions as a regularizing parameter journal, November 1972

Title: \( \mathcal{N} \) = 4 supersymmetric Yang-Mills thermodynamics to order λ²

Resummation in hot field theories
journal, June 2005

Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory
journal, November 1998

Inconsistency of supersymmetric dimensional regularization
journal, July 1980

Three-loop free energy for pure gauge QCD
journal, December 1994

Perturbative thermal QCD: Formalism and applications
journal, October 2020

Phase diagram of Script N = 4 super-Yang-Mills theory with R -symmetry chemical potentials
journal, September 2006

Two-loop hard-thermal-loop thermodynamics with quarks
journal, August 2004

Supersymmetry, supergravity theories and the dual spinor model
journal, April 1977

Hard thermal loops and the entropy of supersymmetric Yang-Mills theories
journal, June 2007

Dimensional regularization and supersymmetry
journal, November 1984

Free energy of QCD at high temperature
journal, March 1996

Regularization by Dimensional Reduction: Consistency, Quantum Action Principle, and Supersymmetry
journal, March 2005

Supersymmetric Yang-Mills theories
journal, March 1977

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

Three-loop HTL QCD thermodynamics
journal, August 2011

Free energy of hot gauge theories with fermions through $g^{5}$
journal, December 1995

QCD and instantons at finite temperature
journal, January 1981

Quantum corrections to $η / s$
journal, February 2009

Regularization and renormalization of gauge fields
journal, July 1972

Hard-Thermal-Loop Resummation of the Free Energy of a Hot Gluon Plasma
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Two-loop HTL-resummed thermodynamics for $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory
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Remarks on two-loop free energy in $N = 4$ supersymmetric Yang-Mills theory at finite temperature
journal, February 1999

Dimensional regularization and supersymmetry
journal, June 1983

Self-consistent hard-thermal-loop thermodynamics for the quark-gluon plasma
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Note on supersymmetric Yang-Mills thermodynamics
journal, October 1999

Regularization by dimensional reduction of supersymmetric and non-supersymmetric gauge theories
journal, May 1980

Pressure of hot QCD up to $g^{6} \ln (1 / g)$
journal, May 2003

Hard-thermal-loop perturbation theory to two loops
journal, October 2002

Regularization of supersymmetric theories — recent progress
journal, July 2006

Approximately self-consistent resummations for the thermodynamics of the quark-gluon plasma: Entropy and density
journal, February 2001

Finite-Temperature Conformal Field Theory Results for All Couplings: $O (N)$ Model in $2 + 1$ Dimensions
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Three-loop HTL gluon thermodynamics at intermediate coupling
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A method of gauge-invariant regularization
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Three-loop free energy for high-temperature QED and QCD with fermions
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Thermodynamics of large-N super Yang–Mills theory AdS/CFT correspondence
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Supersymmetric dimensional regularization via dimensional reduction
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