nLab D=2 QCD

Idea

quantum chromodynamics in 2 spacetime dimensions

First considered in ‘t Hooft 74, whence also called the ‘t Hooft model.

Related concepts

• D=2 Yang-Mills theory

References

General

See also the references at D=2 Yang-Mills theory.

The original account is:

• Gerard ’t Hooft, A Two-Dimensional Model For Mesons, Nucl. Phys. B 75 (1974) 461-470 [doi:10.1016/0550-3213(74)90088-1]

Further discussion:

• Michael Douglas, Keke Li, Matthias Staudacher, Generalized Two-Dimensional QCD, Nucl.Phys. B 420 (1994) 118-140 [arXiv:hep-th/9401062, doi:10.1016/0550-3213(94)90377-8]

• Emanuel Katz, Gustavo Marques Tavares, Yiming Xu, A solution of 2D QCD at Finite $N$ using a conformal basis [arxiv:1405.6727]

See also:

• Jeremias Aguilera Damia, Giovanni Galati, Luigi Tizzano. Symmetries, Universes and Phases of $\text{QCD}_2$ with an Adjoint Dirac Fermion (2024). (arXiv:2409.17989).

As a string theory

The understanding of 2d QCD as the effective field theory of a string theory (“Gross-Taylor model”):

• David Gross. Two Dimensional QCD as a String Theory, Nuclear Physics B 400 1–3 (1993) 161-180 [hep-th/9212149, doi:10.1016/0550-3213(93)90402-B]

• David Gross, Washington Taylor, Two Dimensional QCD is a String Theory, Nucl. Phys. B 400 (1993) 181-210 [arxiv:hep-th/9301068, doi:10.1016/0550-3213(93)90403-C]

• David Gross, Washington Taylor, Twists and Wilson loops in the string theory of two-dimensional QCD, Nucl. Phys. B 403 (1993) 395-452 [hep-th/9303046, doi:10.1016/0550-3213(93)90042-N]

and the Hořava model:

• Petr Hořava, Topological Strings and QCD in Two Dimensions (1993) [hep-th/9311156, spire]

• Petr Hořava. Topological Rigid String Theory and Two Dimensional QCD, Nucl.Phys. B 463 (1996) 238-286 [hep-th/9507060, doi:10.1016/0550-3213(96)00036-3 ]

In Ads/CFT

In view of AdS/CFT duality and holographic entanglement entropy:

• William Donnelly, Sydney Timmerman, Nicolás Valdés-Meller, Entanglement entropy and the large $N$ expansion of two-dimensional Yang-Mills theory (arxiv:1911.09302)

On intersecting D-branes

Specifically geometric engineering of 2d QCD in intersecting D-brane models (AdS/QCD):

Top-down

top-down model building

construction of 2d QCD analogous to the Witten-Sakai-Sugimoto model for 4d QCD

• Yi-hong Gao, Weishui Xu, Ding-fang Zeng, NGN, $QCD_2$ and chiral phase transition from string theory, Nucl.Phys. B400:181-210, 1993 (arXiv:hep-th/0605138)

Specifically concerning the 3d Chern-Simons theory on the D8-branes:

• Ho-Ung Yee, Ismail Zahed, Holographic two dimensional QCD and Chern-Simons term, JHEP 1107:033, 2011 (arXiv:1103.6286)

and its relation to baryons:

• Hideo Suganuma, Yuya Nakagawa, Kohei Matsumoto, 1+1 Large $N_c$ QCD and its Holographic Dual $\sim$ Soliton Picture of Baryons in Single-Flavor World, JPS Conf. Proc. 13, 020013 (2017) (arXiv:1610.02074)

Bottom-up

bottom up model building

• Emanuel Katz, Takemichi Okui, The ‘t Hooft Model As A Hologram, JHEP 0901:013, 2009 (arXiv:0710.3402)

in terms of worldline formalism:

• Adi Armoni, Oded Mintakevich, Comments on Mesonic Correlators in the Worldline Formalism, Nuclear Physics B, Volume 852, Issue 1, 1 November 2011, Pages 61-70 (arxiv:1102.5318)

As a string theory

On D=2 Yang-Mills theory as the effective field theory of a string theory:

• Ofer Aharony, Suman Kundu, Tal Sheaffer, A String Theory for Two Dimensional Yang-Mills Theory I [arXiv:2312.12266]