Abstract
We propose a thermal scalar equation of motion (EOM) that takes into account curvature corrections for backgrounds supported by Ramond-Ramond fluxes. This can be used to obtain the Hagedorn temperature for type II string theory on AdS and pp-wave backgrounds. For Ramond-Ramond flux supported pp-waves we show that the proposed thermal scalar EOM reproduces the leading curvature correction in the Hagedorn temperature equation obtained from the type II string theory spectrum. Furthermore, we use the thermal scalar EOM to obtain curvature corrections to the Hagedorn temperature for the AdS5 × S5 and AdS4 × ℂP3 backgrounds. These corrections match with strong coupling results of the integrable dual field theories, recently obtained by the Quantum Spectral Curve technique.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Hagedorn, Statistical thermodynamics of strong interactions at high-energies, Nuovo Cim. Suppl. 3 (1965) 147 [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
B. Sundborg, The Hagedorn transition, deconfinement and \( \mathcal{N} \) = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].
O. Aharony et al., The Hagedorn-deconfinement phase transition in weakly coupled large N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
M. Spradlin and A. Volovich, A Pendant for Polya: The One-loop partition function of \( \mathcal{N} \) = 4 SYM on ℝ × S3, Nucl. Phys. B 711 (2005) 199 [hep-th/0408178] [INSPIRE].
T. Harmark and M. Wilhelm, Hagedorn Temperature of AdS5/CFT4 via Integrability, Phys. Rev. Lett. 120 (2018) 071605 [arXiv:1706.03074] [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
D. Bombardelli et al., An integrability primer for the gauge-gravity correspondence: An introduction, J. Phys. A 49 (2016) 320301 [arXiv:1606.02945] [INSPIRE].
T. Harmark and M. Orselli, Matching the Hagedorn temperature in AdS/CFT, Phys. Rev. D 74 (2006) 126009 [hep-th/0608115] [INSPIRE].
T. Harmark and M. Wilhelm, The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve, Phys. Lett. B 786 (2018) 53 [arXiv:1803.04416] [INSPIRE].
T. Harmark and M. Wilhelm, Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: chemical potentials and deformations, JHEP 07 (2022) 136 [arXiv:2109.09761] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum Spectral Curve for Planar \( \mathcal{N} \) = 4 Super-Yang-Mills Theory, Phys. Rev. Lett. 112 (2014) 011602 [arXiv:1305.1939] [INSPIRE].
N. Gromov, F. Levkovich-Maslyuk, G. Sizov and S. Valatka, Quantum spectral curve at work: from small spin to strong coupling in \( \mathcal{N} \) = 4 SYM, JHEP 07 (2014) 156 [arXiv:1402.0871] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for arbitrary state/operator in AdS5/CFT4, JHEP 09 (2015) 187 [arXiv:1405.4857] [INSPIRE].
S. Ekhammar, J.A. Minahan and C. Thull, The asymptotic form of the Hagedorn temperature in planar super Yang-Mills, J. Phys. A 56 (2023) 435401 [arXiv:2306.09883] [INSPIRE].
S. Ekhammar, J.A. Minahan and C. Thull, The ABJM Hagedorn Temperature from Integrability, JHEP 10 (2023) 066 [arXiv:2307.02350] [INSPIRE].
J. Maldacena, Correction to the hagedorn temperature in AdS5 × S5, unpublished note.
E.Y. Urbach, String stars in anti de Sitter space, JHEP 04 (2022) 072 [arXiv:2202.06966] [INSPIRE].
B. Sathiapalan, Vortices on the String World Sheet and Constraints on Toral Compactification, Phys. Rev. D 35 (1987) 3277 [INSPIRE].
Y.I. Kogan, Vortices on the World Sheet and String’s Critical Dynamics, JETP Lett. 45 (1987) 709 [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].
J.L.F. Barbon and E. Rabinovici, Touring the Hagedorn ridge, in the proceedings of the From Fields to Strings: Circumnavigating Theoretical Physics: A Conference in Tribute to Ian Kogan, Oxford, U.K., January 08–10 (2004) [https://doi.org/10.1142/9789812775344_0048] [hep-th/0407236] [INSPIRE].
M. Kruczenski and A. Lawrence, Random walks and the Hagedorn transition, JHEP 07 (2006) 031 [hep-th/0508148] [INSPIRE].
F. Bigazzi, T. Canneti and A.L. Cotrone, Higher order corrections to the Hagedorn temperature at strong coupling, JHEP 10 (2023) 056 [arXiv:2306.17126] [INSPIRE].
D. Mitchell and N. Turok, Statistical Mechanics of Cosmic Strings, Phys. Rev. Lett. 58 (1987) 1577 [INSPIRE].
D. Mitchell and N. Turok, Statistical Properties of Cosmic Strings, Nucl. Phys. B 294 (1987) 1138 [INSPIRE].
M.J. Bowick and S.B. Giddings, High temperature strings, Nucl. Phys. B 325 (1989) 631 [INSPIRE].
J. Polchinski, Evaluation of the One Loop String Path Integral, Commun. Math. Phys. 104 (1986) 37 [INSPIRE].
G.T. Horowitz and J. Polchinski, Selfgravitating fundamental strings, Phys. Rev. D 57 (1998) 2557 [hep-th/9707170] [INSPIRE].
T.G. Mertens, H. Verschelde and V.I. Zakharov, Near-Hagedorn Thermodynamics and Random Walks: a General Formalism in Curved Backgrounds, JHEP 02 (2014) 127 [arXiv:1305.7443] [INSPIRE].
T.G. Mertens, Hagedorn String Thermodynamics in Curved Spacetimes and near Black Hole Horizons, Ph.D. thesis, Gent University, Belgium (2015) [arXiv:1506.07798] [INSPIRE].
E.Y. Urbach, The black hole/string transition in AdS3 and confining backgrounds, JHEP 09 (2023) 156 [arXiv:2303.09567] [INSPIRE].
M. Blau, J.M. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, A new maximally supersymmetric background of IIB superstring theory, JHEP 01 (2002) 047 [hep-th/0110242] [INSPIRE].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 superYang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
K. Sugiyama and K. Yoshida, Type IIA string and matrix string on PP wave, Nucl. Phys. B 644 (2002) 128 [hep-th/0208029] [INSPIRE].
S.-J. Hyun and H.-J. Shin, N = (4, 4) type 2A string theory on PP wave background, JHEP 10 (2002) 070 [hep-th/0208074] [INSPIRE].
J.G. Russo and A.A. Tseytlin, On solvable models of type 2B superstring in NS NS and RR plane wave backgrounds, JHEP 04 (2002) 021 [hep-th/0202179] [INSPIRE].
G.T. Horowitz and A.R. Steif, Space-Time Singularities in String Theory, Phys. Rev. Lett. 64 (1990) 260 [INSPIRE].
R. Kallosh and A. Rajaraman, Vacua of M theory and string theory, Phys. Rev. D 58 (1998) 125003 [hep-th/9805041] [INSPIRE].
R.R. Metsaev, Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background, Nucl. Phys. B 625 (2002) 70 [hep-th/0112044] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Exactly solvable model of superstring in Ramond-Ramond plane wave background, Phys. Rev. D 65 (2002) 126004 [hep-th/0202109] [INSPIRE].
G. Grignani, M. Orselli, G.W. Semenoff and D. Trancanelli, The superstring Hagedorn temperature in a pp wave background, JHEP 06 (2003) 006 [hep-th/0301186] [INSPIRE].
L.A. Pando Zayas and D. Vaman, Strings in RR plane wave background at finite temperature, Phys. Rev. D 67 (2003) 106006 [hep-th/0208066] [INSPIRE].
B.R. Greene, K. Schalm and G. Shiu, On the Hagedorn behaviour of PP wave strings and \( \mathcal{N} \) = 4 SYM theory at finite R charge density, Nucl. Phys. B 652 (2003) 105 [hep-th/0208163] [INSPIRE].
Y. Sugawara, Thermal amplitudes in DLCQ superstrings on PP waves, Nucl. Phys. B 650 (2003) 75 [hep-th/0209145] [INSPIRE].
R.C. Brower, D.A. Lowe and C.-I. Tan, Hagedorn transition for strings on pp waves and tori with chemical potentials, Nucl. Phys. B 652 (2003) 127 [hep-th/0211201] [INSPIRE].
S.-J. Hyun, J.-D. Park and S.-H. Yi, Thermodynamic behavior of IIA string theory on a pp wave, JHEP 11 (2003) 006 [hep-th/0304239] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
O. Bergman and S. Hirano, Anomalous radius shift in AdS4/CFT3, JHEP 07 (2009) 016 [arXiv:0902.1743] [INSPIRE].
A. Cavaglià, D. Fioravanti, N. Gromov and R. Tateo, Quantum Spectral Curve of the \( \mathcal{N} \) = 6 Supersymmetric Chern-Simons Theory, Phys. Rev. Lett. 113 (2014) 021601 [arXiv:1403.1859] [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and W. Li, A holographic dual for string theory on AdS3 × S3 × S3 × S1, JHEP 08 (2017) 111 [arXiv:1707.02705] [INSPIRE].
A. Cavaglià, S. Ekhammar, N. Gromov and P. Ryan, Exploring the Quantum Spectral Curve for AdS3/CFT2, JHEP 12 (2023) 089 [arXiv:2211.07810] [INSPIRE].
A.A. Tseytlin, On field redefinitions and exact solutions in string theory, Phys. Lett. B 317 (1993) 559 [hep-th/9308042] [INSPIRE].
Acknowledgments
TH thanks Niels Obers, Bo Sundborg, Arkady Tseytlin and Kostya Zarembo for interesting and stimulating discussions and comments. TH also thanks an anonymous referee of JHEP for very useful feedback.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2402.06001
Rights and permissions
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.
About this article
Cite this article
Harmark, T. Hagedorn temperature from the thermal scalar in AdS and pp-wave backgrounds. J. High Energ. Phys. 2024, 140 (2024). https://doi.org/10.1007/JHEP06(2024)140
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2024)140