Abstract
We carry out a systematic study of the effective bosonic string describing confining flux tubes in SU(N) Yang-Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu-Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare the results of novel lattice simulations for theories with N = 3 and 6 color charges, and report an improved estimate for the N = 2 case, discussing the approach to the large-N limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. In addition, we also present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions, finding that the lattice results for the Polyakov-loop correlation function are in excellent agreement with the predictions of the Svetitsky-Yaffe mapping, which are worked out quantitatively applying conformal perturbation theory to the three-state Potts model in two dimensions. The implications of these results are discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Lüscher, Symmetry Breaking Aspects of the Roughening Transition in Gauge Theories, Nucl. Phys. B 180 (1981) 317 [INSPIRE].
M. Lüscher, K. Symanzik and P. Weisz, Anomalies of the Free Loop Wave Equation in the WKB Approximation, Nucl. Phys. B 173 (1980) 365 [INSPIRE].
Y. Nambu, Quark model and the factorization of the Veneziano amplitude, in Broken Symmetry, T. Eguchi and K. Nishijima eds., World Scientific (1995), p. 258–267 [https://doi.org/10.1142/9789812795823_0024].
Y. Nambu, Strings, Monopoles and Gauge Fields, Phys. Rev. D 10 (1974) 4262 [INSPIRE].
T. Gotō, Relativistic quantum mechanics of one-dimensional mechanical continuum and subsidiary condition of dual resonance model, Prog. Theor. Phys. 46 (1971) 1560 [INSPIRE].
M. Lüscher and P. Weisz, String excitation energies in SU(N) gauge theories beyond the free-string approximation, JHEP 07 (2004) 014 [hep-th/0406205] [INSPIRE].
H.B. Meyer, Poincaré invariance in effective string theories, JHEP 05 (2006) 066 [hep-th/0602281] [INSPIRE].
O. Aharony and E. Karzbrun, On the effective action of confining strings, JHEP 06 (2009) 012 [arXiv:0903.1927] [INSPIRE].
O. Aharony and M. Dodelson, Effective String Theory and Nonlinear Lorentz Invariance, JHEP 02 (2012) 008 [arXiv:1111.5758] [INSPIRE].
F. Gliozzi, Dirac-Born-Infeld action from spontaneous breakdown of Lorentz symmetry in brane-world scenarios, Phys. Rev. D 84 (2011) 027702 [arXiv:1103.5377] [INSPIRE].
F. Gliozzi and M. Meineri, Lorentz completion of effective string (and p-brane) action, JHEP 08 (2012) 056 [arXiv:1207.2912] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Effective String Theory Revisited, JHEP 09 (2012) 044 [arXiv:1203.1054] [INSPIRE].
O. Aharony and Z. Komargodski, The Effective Theory of Long Strings, JHEP 05 (2013) 118 [arXiv:1302.6257] [INSPIRE].
B.B. Brandt and M. Meineri, Effective string description of confining flux tubes, Int. J. Mod. Phys. A 31 (2016) 1643001 [arXiv:1603.06969] [INSPIRE].
M. Caselle, Effective String Description of the Confining Flux Tube at Finite Temperature, Universe 7 (2021) 170 [arXiv:2104.10486] [INSPIRE].
J. Polchinski, String theory. Volume 1: An introduction to the bosonic string, Cambridge University Press (2007) [https://doi.org/10.1017/CBO9780511816079] [INSPIRE].
M. Caselle, E. Cellini and A. Nada, Sampling the lattice Nambu-Gotō string using Continuous Normalizing Flows, JHEP 02 (2024) 048 [arXiv:2307.01107] [INSPIRE].
F. Caristo et al., Fine corrections in the effective string describing SU(2) Yang-Mills theory in three dimensions, JHEP 03 (2022) 115 [arXiv:2109.06212] [INSPIRE].
P. Białas, L. Daniel, A. Morel and B. Petersson, Three dimensional finite temperature SU(3) gauge theory in the confined region and the string picture, Nucl. Phys. B 836 (2010) 91 [arXiv:0912.0206] [INSPIRE].
K. Holland, M. Pepe and U.-J. Wiese, Revisiting the deconfinement phase transition in SU(4) Yang-Mills theory in 2 + 1 dimensions, JHEP 02 (2008) 041 [arXiv:0712.1216] [INSPIRE].
K. Holland, Another weak first order deconfinement transition: Three-dimensional SU(5) gauge theory, JHEP 01 (2006) 023 [hep-lat/0509041] [INSPIRE].
B. Svetitsky and L.G. Yaffe, Critical Behavior at Finite Temperature Confinement Transitions, Nucl. Phys. B 210 (1982) 423 [INSPIRE].
J. Christensen, G. Thorleifsson, P.H. Damgaard and J.F. Wheater, Three-dimensional deconfinement transitions and conformal symmetry, Phys. Lett. B 276 (1992) 472 [INSPIRE].
J. Engels et al., A study of finite temperature gauge theory in (2 + 1)-dimensions, Nucl. Phys. B Proc. Suppl. 53 (1997) 420 [hep-lat/9608099] [INSPIRE].
G. Aarts et al., Phase Transitions in Particle Physics: Results and Perspectives from Lattice Quantum Chromo-Dynamics, Prog. Part. Nucl. Phys. 133 (2023) 104070 [arXiv:2301.04382] [INSPIRE].
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
D. Karabali and V.P. Nair, A Gauge invariant Hamiltonian analysis for nonAbelian gauge theories in (2 + 1)-dimensions, Nucl. Phys. B 464 (1996) 135 [hep-th/9510157] [INSPIRE].
D. Karabali, C.-J. Kim and V.P. Nair, Planar Yang-Mills theory: Hamiltonian, regulators and mass gap, Nucl. Phys. B 524 (1998) 661 [hep-th/9705087] [INSPIRE].
D. Karabali, C.-J. Kim and V.P. Nair, On the vacuum wave function and string tension of Yang-Mills theories in (2 + 1)-dimensions, Phys. Lett. B 434 (1998) 103 [hep-th/9804132] [INSPIRE].
D. Karabali, C.-J. Kim and V.P. Nair, Manifest covariance and the Hamiltonian approach to mass gap in (2 + 1)-dimensional Yang-Mills theory, Phys. Rev. D 64 (2001) 025011 [hep-th/0007188] [INSPIRE].
R.G. Leigh, D. Minic and A. Yelnikov, Solving pure QCD in 2 + 1 dimensions, Phys. Rev. Lett. 96 (2006) 222001 [hep-th/0512111] [INSPIRE].
R.G. Leigh, D. Minic and A. Yelnikov, On the Glueball Spectrum of Pure Yang-Mills Theory in 2 + 1 Dimensions, Phys. Rev. D 76 (2007) 065018 [hep-th/0604060] [INSPIRE].
D. Karabali, V.P. Nair and A. Yelnikov, The Hamiltonian Approach to Yang-Mills (2 + 1): An Expansion Scheme and Corrections to String Tension, Nucl. Phys. B 824 (2010) 387 [arXiv:0906.0783] [INSPIRE].
P. Bicudo, R.D. Pisarski and E. Seel, Matrix model for deconfinement in a SU(2) gauge theory in 2 + 1 dimensions, Phys. Rev. D 88 (2013) 034007 [arXiv:1306.2943] [INSPIRE].
P. Bicudo, R.D. Pisarski and E. Seel, Matrix model for deconfinement in a SU(Nc) gauge theory in 2 + 1 dimensions, Phys. Rev. D 89 (2014) 085020 [arXiv:1402.5137] [INSPIRE].
M. Frasca, Confinement in a three-dimensional Yang-Mills theory, Eur. Phys. J. C 77 (2017) 255 [arXiv:1611.08182] [INSPIRE].
M.J. Teper, SU(N) gauge theories in (2 + 1)-dimensions, Phys. Rev. D 59 (1999) 014512 [hep-lat/9804008] [INSPIRE].
R.W. Johnson and M.J. Teper, String models of glueballs and the spectrum of SU(N) gauge theories in (2 + 1)-dimensions, Phys. Rev. D 66 (2002) 036006 [hep-ph/0012287] [INSPIRE].
B. Lucini and M. Teper, SU(N) gauge theories in (2 + 1)-dimensions: Further results, Phys. Rev. D 66 (2002) 097502 [hep-lat/0206027] [INSPIRE].
H.B. Meyer and M.J. Teper, Glueball Regge trajectories in (2 + 1)-dimensional gauge theories, Nucl. Phys. B 668 (2003) 111 [hep-lat/0306019] [INSPIRE].
H.B. Meyer and M.J. Teper, Glueball Regge trajectories and the pomeron: A Lattice study, Phys. Lett. B 605 (2005) 344 [hep-ph/0409183] [INSPIRE].
F. Bursa and M. Teper, Strong to weak coupling transitions of SU(N) gauge theories in 2 + 1 dimensions, Phys. Rev. D 74 (2006) 125010 [hep-th/0511081] [INSPIRE].
B. Bringoltz and M. Teper, A precise calculation of the fundamental string tension in SU(N) gauge theories in 2 + 1 dimensions, Phys. Lett. B 645 (2007) 383 [hep-th/0611286] [INSPIRE].
A. Athenodorou, B. Bringoltz and M. Teper, The closed string spectrum of SU(N) gauge theories in 2 + 1 dimensions, Phys. Lett. B 656 (2007) 132 [arXiv:0709.0693] [INSPIRE].
J. Liddle and M. Teper, The deconfining phase transition in D = 2 + 1 SU(N) gauge theories, arXiv:0803.2128 [INSPIRE].
B. Bringoltz and M. Teper, Closed k-strings in SU(N) gauge theories: 2 + 1 dimensions, Phys. Lett. B 663 (2008) 429 [arXiv:0802.1490] [INSPIRE].
A. Athenodorou, B. Bringoltz and M. Teper, On the spectrum of closed k = 2 flux tubes in D = 2 + 1 SU(N) gauge theories, JHEP 05 (2009) 019 [arXiv:0812.0334] [INSPIRE].
A. Athenodorou, B. Bringoltz and M. Teper, Closed flux tubes and their string description in D = 2 + 1 SU(N) gauge theories, JHEP 05 (2011) 042 [arXiv:1103.5854] [INSPIRE].
M. Caselle et al., Thermodynamics of SU(N) Yang-Mills theories in 2 + 1 dimensions I. The confining phase, JHEP 06 (2011) 142 [arXiv:1105.0359] [INSPIRE].
M. Caselle et al., Thermodynamics of SU(N ) Yang-Mills theories in 2 + 1 dimensions II. The Deconfined phase, JHEP 05 (2012) 135 [arXiv:1111.0580] [INSPIRE].
F. Bursa, R. Lau and M. Teper, SO(2N) and SU(N) gauge theories in 2 + 1 dimensions, JHEP 05 (2013) 025 [arXiv:1208.4547] [INSPIRE].
P. Białas, L. Daniel, A. Morel and B. Petersson, Three dimensional finite temperature SU(3) gauge theory near the phase transition, Nucl. Phys. B 871 (2013) 111 [arXiv:1211.3304] [INSPIRE].
A. Athenodorou and M. Teper, Closed flux tubes in higher representations and their string description in D = 2 + 1 SU(N) gauge theories, JHEP 06 (2013) 053 [arXiv:1303.5946] [INSPIRE].
A. Athenodorou, R. Lau and M. Teper, On the weak N-dependence of SO(N) and SU(N ) gauge theories in 2 + 1 dimensions, Phys. Lett. B 749 (2015) 448 [arXiv:1504.08126] [INSPIRE].
R. Lau and M. Teper, The deconfining phase transition of SO(N) gauge theories in 2 + 1 dimensions, JHEP 03 (2016) 072 [arXiv:1510.07841] [INSPIRE].
A. Athenodorou and M. Teper, SU(N) gauge theories in 2 + 1 dimensions: glueball spectra and k-string tensions, JHEP 02 (2017) 015 [arXiv:1609.03873] [INSPIRE].
A. Athenodorou and M. Teper, Closed flux tubes in D = 2 + 1 SU(N) gauge theories: dynamics and effective string description, JHEP 10 (2016) 093 [arXiv:1602.07634] [INSPIRE].
P. Conkey, S. Dubovsky and M. Teper, Glueball spins in D = 3 Yang-Mills, JHEP 10 (2019) 175 [arXiv:1909.07430] [INSPIRE].
M. Caselle, D. Fioravanti, F. Gliozzi and R. Tateo, Quantisation of the effective string with TBA, JHEP 07 (2013) 071 [arXiv:1305.1278] [INSPIRE].
S. Dubovsky, V. Gorbenko and M. Mirbabayi, Asymptotic fragility, near AdS2 holography and \( T\overline{T} \), JHEP 09 (2017) 136 [arXiv:1706.06604] [INSPIRE].
S. Dubovsky, V. Gorbenko and G. Hernández-Chifflet, \( T\overline{T} \) partition function from topological gravity, JHEP 09 (2018) 158 [arXiv:1805.07386] [INSPIRE].
C. Chen, P. Conkey, S. Dubovsky and G. Hernández-Chifflet, Undressing Confining Flux Tubes with \( T\overline{T} \), Phys. Rev. D 98 (2018) 114024 [arXiv:1808.01339] [INSPIRE].
A.B. Zamolodchikov, Expectation value of composite field \( T\overline{T} \) in two-dimensional quantum field theory, hep-th/0401146 [INSPIRE].
F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].
A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo, \( T\overline{T} \)-deformed 2D Quantum Field Theories, JHEP 10 (2016) 112 [arXiv:1608.05534] [INSPIRE].
R. Conti, L. Iannella, S. Negro and R. Tateo, Generalised Born-Infeld models, Lax operators and the \( T\overline{T} \) perturbation, JHEP 11 (2018) 007 [arXiv:1806.11515] [INSPIRE].
R. Conti, S. Negro and R. Tateo, The \( T\overline{T} \) perturbation and its geometric interpretation, JHEP 02 (2019) 085 [arXiv:1809.09593] [INSPIRE].
R. Conti, S. Negro and R. Tateo, Conserved currents and \( T{\overline{T}}_s \) irrelevant deformations of 2D integrable field theories, JHEP 11 (2019) 120 [arXiv:1904.09141] [INSPIRE].
L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \( T\overline{T} \), JHEP 04 (2018) 010 [arXiv:1611.03470] [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, \( T\overline{T} \) and LST, JHEP 07 (2017) 122 [arXiv:1701.05576] [INSPIRE].
S. Datta and Y. Jiang, \( T\overline{T} \) deformed partition functions, JHEP 08 (2018) 106 [arXiv:1806.07426] [INSPIRE].
O. Aharony et al., Modular invariance and uniqueness of \( T\overline{T} \) deformed CFT, JHEP 01 (2019) 086 [arXiv:1808.02492] [INSPIRE].
P. Kraus, J. Liu and D. Marolf, Cutoff AdS3 versus the \( T\overline{T} \) deformation, JHEP 07 (2018) 027 [arXiv:1801.02714] [INSPIRE].
T. Hartman, J. Kruthoff, E. Shaghoulian and A. Tajdini, Holography at finite cutoff with a T2 deformation, JHEP 03 (2019) 004 [arXiv:1807.11401] [INSPIRE].
G. Bonelli, N. Doroud and M. Zhu, \( T\overline{T} \)-deformations in closed form, JHEP 06 (2018) 149 [arXiv:1804.10967] [INSPIRE].
V. Gorbenko, E. Silverstein and G. Torroba, dS/dS and \( T\overline{T} \), JHEP 03 (2019) 085 [arXiv:1811.07965] [INSPIRE].
X. Dong, E. Silverstein and G. Torroba, De Sitter Holography and Entanglement Entropy, JHEP 07 (2018) 050 [arXiv:1804.08623] [INSPIRE].
J. Cardy, The \( T\overline{T} \) deformation of quantum field theory as random geometry, JHEP 10 (2018) 186 [arXiv:1801.06895] [INSPIRE].
J. Cardy, \( T\overline{T} \) deformation of correlation functions, JHEP 12 (2019) 160 [arXiv:1907.03394] [INSPIRE].
M. Billò and M. Caselle, Polyakov loop correlators from D0-brane interactions in bosonic string theory, JHEP 07 (2005) 038 [hep-th/0505201] [INSPIRE].
R.D. Pisarski and O. Alvarez, Strings at Finite Temperature and Deconfinement, Phys. Rev. D 26 (1982) 3735 [INSPIRE].
P. Olesen, Strings, Tachyons and Deconfinement, Phys. Lett. B 160 (1985) 408 [INSPIRE].
J. Elias Miró et al., Flux Tube S-matrix Bootstrap, Phys. Rev. Lett. 123 (2019) 221602 [arXiv:1906.08098] [INSPIRE].
A. Baffigo and M. Caselle, Ising string beyond the Nambu-Gotō action, Phys. Rev. D 109 (2024) 034520 [arXiv:2306.06966] [INSPIRE].
J. Elias Miró and A. Guerrieri, Dual EFT bootstrap: QCD flux tubes, JHEP 10 (2021) 126 [arXiv:2106.07957] [INSPIRE].
K.G. Wilson, Confinement of Quarks, Phys. Rev. D 10 (1974) 2445 [INSPIRE].
L. Onsager, Crystal statistics. I. A Two-dimensional model with an order disorder transition, Phys. Rev. 65 (1944) 117 [INSPIRE].
B. Kaufman, Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis, Phys. Rev. 76 (1949) 1232 [INSPIRE].
M. Kac and J.C. Ward, A combinatorial solution of the two-dimensional Ising model, Phys. Rev. 88 (1952) 1332 [INSPIRE].
C.A. Hurst and H.S. Green, New Solution of the Ising Problem for a Rectangular Lattice, J. Chem. Phys. 33 (1960) 1059 [INSPIRE].
T.D. Schultz, D.C. Mattis and E.H. Lieb, Two-dimensional Ising model as a soluble problem of many fermions, Rev. Mod. Phys. 36 (1964) 856 [INSPIRE].
M. Caselle et al., Potts correlators and the static three-quark potential, J. Stat. Mech. 0603 (2006) P03008 [hep-th/0511168] [INSPIRE].
A.B. Zamolodchikov, Integrable field theory from conformal field theory, Adv. Stud. Pure Math. 19 (1989) 641 [INSPIRE].
A.B. Zamolodchikov, Two point correlation function in scaling Lee-Yang model, Nucl. Phys. B 348 (1991) 619 [INSPIRE].
R. Guida and N. Magnoli, All order IR finite expansion for short distance behavior of massless theories perturbed by a relevant operator, Nucl. Phys. B 471 (1996) 361 [hep-th/9511209] [INSPIRE].
R. Guida and N. Magnoli, On the short distance behavior of the critical Ising model perturbed by a magnetic field, Nucl. Phys. B 483 (1997) 563 [hep-th/9606072] [INSPIRE].
R. Guida and N. Magnoli, Tricritical Ising model near criticality, Int. J. Mod. Phys. A 13 (1998) 1145 [hep-th/9612154] [INSPIRE].
S.L. Lukyanov and A.B. Zamolodchikov, Exact expectation values of local fields in quantum sine-Gordon model, Nucl. Phys. B 493 (1997) 571 [hep-th/9611238] [INSPIRE].
V. Fateev, S.L. Lukyanov, A.B. Zamolodchikov and A.B. Zamolodchikov, Expectation values of local fields in Bullough-Dodd model and integrable perturbed conformal field theories, Nucl. Phys. B 516 (1998) 652 [hep-th/9709034] [INSPIRE].
V. Fateev et al., Expectation values of descendent fields in the sine-Gordon model, Nucl. Phys. B 540 (1999) 587 [hep-th/9807236] [INSPIRE].
V.S. Dotsenko and V.A. Fateev, Operator Algebra of Two-Dimensional Conformal Theories with Central Charge C <= 1, Phys. Lett. B 154 (1985) 291 [INSPIRE].
T.R. Klassen and E. Melzer, RG flows in the D series of minimal CFTs, Nucl. Phys. B 400 (1993) 547 [hep-th/9110047] [INSPIRE].
J. McCabe and T. Wydro, Critical Correlation Functions of the 2-Dimensional, 3-State Potts Model, Int. J. Mod. Phys. A 13 (1998) 1013 [cond-mat/9507033] [INSPIRE].
V.A. Fateev, The exact relations between the coupling constants and the masses of particles for the integrable perturbed conformal field theories, Phys. Lett. B 324 (1994) 45 [INSPIRE].
A.B. Zamolodchikov, Thermodynamic Bethe Ansatz in Relativistic Models. Scaling Three State Potts and Lee-yang Models, Nucl. Phys. B 342 (1990) 695 [INSPIRE].
C. Bonati, M. Caselle and S. Morlacchi, The unreasonable effectiveness of effective string theory: The case of the 3D SU(2) Higgs model, Phys. Rev. D 104 (2021) 054501 [arXiv:2106.08784] [INSPIRE].
M. Panero, Thermodynamics of the QCD plasma and the large-N limit, Phys. Rev. Lett. 103 (2009) 232001 [arXiv:0907.3719] [INSPIRE].
A. Mykkänen, M. Panero and K. Rummukainen, Casimir scaling and renormalization of Polyakov loops in large-N gauge theories, JHEP 05 (2012) 069 [arXiv:1202.2762] [INSPIRE].
A. Guerrieri, A. Homrich and P. Vieira, Multiparticle Flux Tube S-matrix Bootstrap, arXiv:2404.10812 [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Flux Tube Spectra from Approximate Integrability at Low Energies, J. Exp. Theor. Phys. 120 (2015) 399 [arXiv:1404.0037] [INSPIRE].
B. Lucini and M. Panero, SU(N) gauge theories at large N, Phys. Rept. 526 (2013) 93 [arXiv:1210.4997] [INSPIRE].
M. Panero, Recent results in large-N lattice gauge theories, PoS LATTICE2012 (2012) 010 [arXiv:1210.5510] [INSPIRE].
A.M. Halasz et al., On the phase diagram of QCD, Phys. Rev. D 58 (1998) 096007 [hep-ph/9804290] [INSPIRE].
J. Berges and K. Rajagopal, Color superconductivity and chiral symmetry restoration at nonzero baryon density and temperature, Nucl. Phys. B 538 (1999) 215 [hep-ph/9804233] [INSPIRE].
M. Caselle et al., Conformal perturbation theory confronts lattice results in the vicinity of a critical point, Phys. Rev. D 100 (2019) 034512 [arXiv:1904.12749] [INSPIRE].
S. El-Showk et al., Solving the 3D Ising Model with the Conformal Bootstrap, Phys. Rev. D 86 (2012) 025022 [arXiv:1203.6064] [INSPIRE].
S. El-Showk et al., Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents, J. Stat. Phys. 157 (2014) 869 [arXiv:1403.4545] [INSPIRE].
F. Gliozzi and A. Rago, Critical exponents of the 3d Ising and related models from Conformal Bootstrap, JHEP 10 (2014) 042 [arXiv:1403.6003] [INSPIRE].
A.B. Zamolodchikov, Renormalization Group and Perturbation Theory Near Fixed Points in Two-Dimensional Field Theory, Sov. J. Nucl. Phys. 46 (1987) 1090 [INSPIRE].
M.R. Gaberdiel, A. Konechny and C. Schmidt-Colinet, Conformal perturbation theory beyond the leading order, J. Phys. A 42 (2009) 105402 [arXiv:0811.3149] [INSPIRE].
M. Caselle, G. Costagliola and N. Magnoli, Conformal perturbation of off-critical correlators in the 3D Ising universality class, Phys. Rev. D 94 (2016) 026005 [arXiv:1605.05133] [INSPIRE].
A. Amoretti and N. Magnoli, Conformal perturbation theory, Phys. Rev. D 96 (2017) 045016 [arXiv:1705.03502] [INSPIRE].
Y. Fujimoto and S. Reddy, Bounds on the equation of state from QCD inequalities and lattice QCD, Phys. Rev. D 109 (2024) 014020 [arXiv:2310.09427] [INSPIRE].
R. Chiba and T. Kojo, Sound velocity peak and conformality in isospin QCD, Phys. Rev. D 109 (2024) 076006 [arXiv:2304.13920] [INSPIRE].
G.D. Moore and T. Gorda, Bounding the QCD Equation of State with the Lattice, JHEP 12 (2023) 133 [arXiv:2309.15149] [INSPIRE].
P. Navarrete, R. Paatelainen and K. Seppänen, Perturbative QCD meets phase quenching: The pressure of cold Quark Matter, arXiv:2403.02180 [INSPIRE].
R. Abbott et al., QCD constraints on isospin-dense matter and the nuclear equation of state, arXiv:2406.09273 [INSPIRE].
T. Kojo, D. Suenaga and R. Chiba, Isospin QCD as a laboratory for dense QCD, arXiv:2406.11059 [INSPIRE].
O. Philipsen, The QCD phase diagram at zero and small baryon density, PoS LAT2005 (2006) 016 [hep-lat/0510077] [INSPIRE].
P. de Forcrand, Simulating QCD at finite density, PoS LAT2009 (2009) 010 [arXiv:1005.0539] [INSPIRE].
G. Aarts, Introductory lectures on lattice QCD at nonzero baryon number, J. Phys. Conf. Ser. 706 (2016) 022004 [arXiv:1512.05145] [INSPIRE].
C. Gattringer and K. Langfeld, Approaches to the sign problem in lattice field theory, Int. J. Mod. Phys. A 31 (2016) 1643007 [arXiv:1603.09517] [INSPIRE].
M. Caselle and M. Sorba, Charting the scaling region of the Ising universality class in two and three dimensions, Phys. Rev. D 102 (2020) 014505 [arXiv:2003.12332] [INSPIRE].
C. Nonaka and M. Asakawa, Hydrodynamical evolution near the QCD critical end point, Phys. Rev. C 71 (2005) 044904 [nucl-th/0410078] [INSPIRE].
B. Kämpfer et al., QCD matter within a quasi-particle model and the critical end point, Nucl. Phys. A 774 (2006) 757 [hep-ph/0509146] [INSPIRE].
P. Parotto et al., QCD equation of state matched to lattice data and exhibiting a critical point singularity, Phys. Rev. C 101 (2020) 034901 [arXiv:1805.05249] [INSPIRE].
X. An et al., The BEST framework for the search for the QCD critical point and the chiral magnetic effect, Nucl. Phys. A 1017 (2022) 122343 [arXiv:2108.13867] [INSPIRE].
Acknowledgments
We thank A. Bulgarelli and E. Cellini for helpful discussions. This work of has been partially supported by the Italian PRIN “Progetti di Ricerca di Rilevante Interesse Nazionale — Bando 2022”, prot. 2022TJFCYB, and by the “Simons Collaboration on Confinement and QCD Strings” funded by the Simons Foundation. The simulations were run on CINECA computers. We acknowledge support from the SFT Scientific Initiative of the Italian Nuclear Physics Institute (INFN).
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: 2407.10678
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
Caselle, M., Magnoli, N., Nada, A. et al. Confining strings in three-dimensional gauge theories beyond the Nambu-Gotō approximation. J. High Energ. Phys. 2024, 198 (2024). https://doi.org/10.1007/JHEP08(2024)198
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2024)198