Abstract
Two-dimensional SU(N) gauge theory coupled to a Majorana fermion in the adjoint representation is a nice toy model for higher-dimensional gauge dynamics. It possesses a multitude of “gluinoball” bound states whose spectrum has been studied using numerical diagonalizations of the light-cone Hamiltonian. We extend this model by coupling it to Nf flavors of fundamental Dirac fermions (quarks). The extended model also contains meson-like bound states, both bosonic and fermionic, which in the large-N limit decouple from the gluinoballs. We study the large-N meson spectrum using the Discretized Light-Cone Quantization (DLCQ). When all the fermions are massless, we exhibit an exact \( \mathfrak{osp} \)(1|4) symmetry algebra that leads to an infinite number of degeneracies in the DLCQ approach. More generally, we show that many single-trace states in the theory are threshold bound states that are degenerate with multi-trace states. These exact degeneracies can be explained using the Kac-Moody algebra of the SU(N) current. We also present strong numerical evidence that additional threshold states appear in the continuum limit. Finally, we make the quarks massive while keeping the adjoint fermion massless. In this case too, we observe some exact degeneracies that show that the spectrum of mesons becomes continuous above a certain threshold. This demonstrates quantitatively that the fundamental string tension vanishes in the massless adjoint QCD2 without explicit four-fermion operators.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.J. Gross and F. Wilczek, Ultraviolet Behavior of Nonabelian Gauge Theories, Phys. Rev. Lett. 30 (1973) 1343 [INSPIRE].
H.D. Politzer, Reliable Perturbative Results for Strong Interactions?, Phys. Rev. Lett. 30 (1973) 1346 [INSPIRE].
H. Fritzsch, M. Gell-Mann and H. Leutwyler, Advantages of the Color Octet Gluon Picture, Phys. Lett. B 47 (1973) 365 [INSPIRE].
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
G. ’t Hooft, A Two-Dimensional Model for Mesons, Nucl. Phys. B 75 (1974) 461 [INSPIRE].
E. Witten, θ Vacua in Two-dimensional Quantum Chromodynamics, Nuovo Cim. A 51 (1979) 325 [INSPIRE].
S. Dalley and I.R. Klebanov, String spectrum of (1+1)-dimensional large N QCD with adjoint matter, Phys. Rev. D 47 (1993) 2517 [hep-th/9209049] [INSPIRE].
K. Demeterfi, I.R. Klebanov and G. Bhanot, Glueball spectrum in a (1+1)-dimensional model for QCD, Nucl. Phys. B 418 (1994) 15 [hep-th/9311015] [INSPIRE].
Y. Matsumura, N. Sakai and T. Sakai, Mass spectra of supersymmetric Yang-Mills theories in (1+1)-dimensions, Phys. Rev. D 52 (1995) 2446 [hep-th/9504150] [INSPIRE].
A. Gadde, S. Gukov and P. Putrov, Exact Solutions of 2d Supersymmetric Gauge Theories, JHEP 11 (2019) 174 [arXiv:1404.5314] [INSPIRE].
H.C. Pauli and S.J. Brodsky, Discretized Light Cone Quantization: Solution to a Field Theory in One Space One Time Dimensions, Phys. Rev. D 32 (1985) 2001 [INSPIRE].
K. Hornbostel, S.J. Brodsky and H.C. Pauli, Light Cone Quantized QCD in (1+1)-Dimensions, Phys. Rev. D 41 (1990) 3814 [INSPIRE].
K. Hornbostel, The Application of Light Cone Quantization to Quantum Chromodynamics in (1 + 1) Dimensions, Ph.D. Thesis (1988), SLAC-0333, [INSPIRE].
S.J. Brodsky, H.-C. Pauli and S.S. Pinsky, Quantum chromodynamics and other field theories on the light cone, Phys. Rept. 301 (1998) 299 [hep-ph/9705477] [INSPIRE].
D. Kutasov, Two-dimensional QCD coupled to adjoint matter and string theory, Nucl. Phys. B 414 (1994) 33 [hep-th/9306013] [INSPIRE].
G. Bhanot, K. Demeterfi and I.R. Klebanov, (1+1)-dimensional large N QCD coupled to adjoint fermions, Phys. Rev. D 48 (1993) 4980 [hep-th/9307111] [INSPIRE].
A.V. Smilga, Instantons and fermion condensate in adjoint QCD in two-dimensions, Phys. Rev. D 49 (1994) 6836 [hep-th/9402066] [INSPIRE].
F. Lenz, M.A. Shifman and M. Thies, Quantum mechanics of the vacuum state in two-dimensional QCD with adjoint fermions, Phys. Rev. D 51 (1995) 7060 [hep-th/9412113] [INSPIRE].
D. Kutasov and A. Schwimmer, Universality in two-dimensional gauge theory, Nucl. Phys. B 442 (1995) 447 [hep-th/9501024] [INSPIRE].
D.J. Gross, I.R. Klebanov, A.V. Matytsin and A.V. Smilga, Screening versus confinement in (1+1)-dimensions, Nucl. Phys. B 461 (1996) 109 [hep-th/9511104] [INSPIRE].
A.V. Smilga, Two-dimensional instantons with bosonization and physics of adjoint QCD2, Phys. Rev. D 54 (1996) 7757 [hep-th/9607007] [INSPIRE].
A. Cherman, T. Jacobson, Y. Tanizaki and M. Ünsal, Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD, SciPost Phys. 8 (2020) 072 [arXiv:1908.09858] [INSPIRE].
Z. Komargodski, K. Ohmori, K. Roumpedakis and S. Seifnashri, Symmetries and strings of adjoint QCD2, JHEP 03 (2021) 103 [arXiv:2008.07567] [INSPIRE].
A. Smilga, A comment on instantons and their fermion zero modes in adjoint QCD_2, SciPost Phys. 10 (2021) 152 [arXiv:2104.06266] [INSPIRE].
V.G. Knizhnik and A.B. Zamolodchikov, Current Algebra and Wess-Zumino Model in Two-Dimensions, Nucl. Phys. B 247 (1984) 83 [INSPIRE].
D.J. Gross, A. Hashimoto and I.R. Klebanov, The Spectrum of a large N gauge theory near transition from confinement to screening, Phys. Rev. D 57 (1998) 6420 [hep-th/9710240] [INSPIRE].
U. Trittmann, On the bosonic spectrum of QCD(1+1) with SU(N) currents, Nucl. Phys. B 587 (2000) 311 [hep-th/0005075] [INSPIRE].
U. Trittmann, On the spectrum of QCD(1+1) with SU(Nc) currents, Phys. Rev. D 66 (2002) 025001 [hep-th/0110058] [INSPIRE].
U. Trittmann, Towards finding the single-particle content of two-dimensional adjoint QCD, Phys. Rev. D 92 (2015) 085021 [arXiv:1506.08119] [INSPIRE].
N. Anand, A.L. Fitzpatrick, E. Katz, Z.U. Khandker, M.T. Walters and Y. Xin, Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data, arXiv:2005.13544 [INSPIRE].
E. Katz, G. Marques Tavares and Y. Xu, Solving 2D QCD with an adjoint fermion analytically, JHEP 05 (2014) 143 [arXiv:1308.4980] [INSPIRE].
F. Antonuccio, O. Lunin and S. Pinsky, On exact supersymmetry in DLCQ, Phys. Lett. B 442 (1998) 173 [hep-th/9809165] [INSPIRE].
S. Dubovsky, A Simple Worldsheet Black Hole, JHEP 07 (2018) 011 [arXiv:1803.00577] [INSPIRE].
R. Gopakumar, A. Hashimoto, I.R. Klebanov, S. Sachdev and K. Schoutens, Strange Metals in One Spatial Dimension, Phys. Rev. D 86 (2012) 066003 [arXiv:1206.4719] [INSPIRE].
M. Isachenkov, I. Kirsch and V. Schomerus, Chiral Primaries in Strange Metals, Nucl. Phys. B 885 (2014) 679 [arXiv:1403.6857] [INSPIRE].
M. Isachenkov, I. Kirsch and V. Schomerus, Chiral Ring of Strange Metals: The Multicolor Limit, Nucl. Phys. B 897 (2015) 660 [arXiv:1410.4594] [INSPIRE].
E. Witten, Baryons in the 1/n Expansion, Nucl. Phys. B 160 (1979) 57.
R.F. Lebed, R.E. Mitchell and E.S. Swanson, Heavy-Quark QCD Exotica, Prog. Part. Nucl. Phys. 93 (2017) 143 [arXiv:1610.04528] [INSPIRE].
A. Esposito, A. Pilloni and A.D. Polosa, Multiquark Resonances, Phys. Rept. 668 (2017) 1 [arXiv:1611.07920] [INSPIRE].
F. Antonuccio and S. Pinsky, On the transition from confinement to screening in QCD(1+1) coupled to adjoint fermions at finite N, Phys. Lett. B 439 (1998) 142 [hep-th/9805188] [INSPIRE].
S. Balay et al., PETSc Users Manual, Tech. Rep. ANL-95/11 — Revision 3.11, Argonne National Laboratory, U.S.A. (2019).
S. Balay, W.D. Gropp, L.C. McInnes and B.F. Smith, Efficient Management of Parallelism in Object Oriented Numerical Software Libraries, in Modern Software Tools in Scientific Computing, E. Arge, A.M. Bruaset and H.P. Langtangen, eds., Birkhäuser Press, (1997), pp. 163–202.
V. Hernandez, J.E. Roman and V. Vidal, SLEPc: A Scalable and Flexible Toolkit for the Solution of Eigenvalue Problems, ACM Trans. Math. Software 31 (2005) 351.
J.E. Roman, C. Campos, E. Romero and A. Tomas, SLEPc Users Manual, Tech. Rep. DSIC-II/24/02 — Revision 3.13, D. Sistemes Informàtics i Computació, Universitat Politècnica de València, (2020).
E. Witten, Nonabelian Bosonization in Two-Dimensions, Commun. Math. Phys. 92 (1984) 455 [INSPIRE].
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: 2101.05432
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
Dempsey, R., Klebanov, I.R. & Pufu, S.S. Exact symmetries and threshold states in two-dimensional models for QCD. J. High Energ. Phys. 2021, 96 (2021). https://doi.org/10.1007/JHEP10(2021)096
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2021)096