Abstract
We study dynamics of two-dimensional non-abelian gauge theories with \( \mathcal{N} \) = (0, 2) supersymmetry that include \( \mathcal{N} \) = (0, 2) supersymmetric QCD and its generaliza- tions. In particular, we present the phase diagram of \( \mathcal{N} \) = (0, 2) SQCD and determine its massive and low-energy spectrum. We find that the theory has no mass gap, a nearly constant distribution of massive states, and lots of massless states that in general flow to an interacting CFT. For a range of parameters where supersymmetry is not dynamically broken at low energies, we give a complete description of the low-energy physics in terms of 2d \( \mathcal{N} \) = (0, 2) SCFTs using anomaly matching and modular invariance. Our construction provides a vast landscape of new \( \mathcal{N} \) = (0, 2) SCFTs which, for small values of the central charge, could be used for building novel heterotic models with no moduli and, for large values of the central charge, could be dual to AdS3 string vacua.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Gadde, S. Gukov and P. Putrov, (0, 2) trialities, JHEP 03 (2014) 076 [arXiv:1310.0818] [INSPIRE].
Y. Frishman and J. Sonnenschein, Bosonization and QCD in two-dimensions, Phys. Rept. 223 (1993) 309 [hep-th/9207017] [INSPIRE].
D. Kutasov and A. Schwimmer, Universality in two-dimensional gauge theory, Nucl. Phys. B 442 (1995) 447 [hep-th/9501024] [INSPIRE].
E. Witten, Two-dimensional models with (0, 2) supersymmetry: Perturbative aspects, Adv. Theor. Math. Phys. 11 (2007) 1 [hep-th/0504078] [INSPIRE].
N.A. Nekrasov, Lectures on curved beta-gamma systems, pure spinors and anomalies, hep-th/0511008 [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].
D. Kutasov, Two-dimensional QCD coupled to adjoint matter and string theory, Nucl. Phys. B 414 (1994) 33 [hep-th/9306013] [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].
F. Antonuccio, O. Lunin, S. Pinsky, H.C. Pauli and S. Tsujimaru, The DLCQ spectrum of N = (8, 8) superYang-Mills, Phys. Rev. D 58 (1998) 105024 [hep-th/9806133] [INSPIRE].
K. Aoki and T. Ichihara, (1 + 1)-dimensional QCD with fundamental bosons and fermions, Phys. Rev. D 52 (1995) 6435 [hep-th/9506058] [INSPIRE].
F. Antonuccio, O. Lunin and S.S. Pinsky, Bound states of dimensionally reduced SYM(2 + 1) at finite N, Phys. Lett. B 429 (1998) 327 [hep-th/9803027] [INSPIRE].
F. Antonuccio, O. Lunin and S. Pinsky, Nonperturbative spectrum of two-dimensional (1, 1) superYang-Mills at finite and large N, Phys. Rev. D 58 (1998) 085009 [hep-th/9803170] [INSPIRE].
D. Gepner, Exactly Solvable String Compactifications on Manifolds of SU(N ) Holonomy, Phys. Lett. B 199 (1987) 380 [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].
A.B. Zamolodchikov, Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory, JETP Lett. 43 (1986) 730 [INSPIRE].
B. Jia, E. Sharpe and R. Wu, Notes on nonabelian (0, 2) theories and dualities, JHEP 08 (2014) 017 [arXiv:1401.1511] [INSPIRE].
D. Gaiotto, Kazama-Suzuki models and BPS domain wall junctions in N = 1 SU(N ) Super Yang-Mills, arXiv:1306.5661 [INSPIRE].
Y. Kazama and H. Suzuki, New N = 2 Superconformal Field Theories and Superstring Compactification, Nucl. Phys. B 321 (1989) 232 [INSPIRE].
G. Veneziano, Some Aspects of a Unified Approach to Gauge, Dual and Gribov Theories, Nucl. Phys. B 117 (1976) 519 [INSPIRE].
D.B. Kaplan, J.-W. Lee, D.T. Son and M.A. Stephanov, Conformality Lost, Phys. Rev. D 80 (2009) 125005 [arXiv:0905.4752] [INSPIRE].
M. Jarvinen and E. Kiritsis, Holographic Models for QCD in the Veneziano Limit, JHEP 03 (2012) 002 [arXiv:1112.1261] [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. Armoni, Y. Frishman and J. Sonnenschein, Screening in supersymmetric gauge theories in two-dimensions, Phys. Lett. B 449 (1999) 76 [hep-th/9807022] [INSPIRE].
F. Antonuccio, H.C. Pauli, S. Pinsky and S. Tsujimaru, DLCQ bound states of N = (2, 2) superYang-Mills at finite and large N , Phys. Rev. D 58 (1998) 125006 [hep-th/9808120] [INSPIRE].
S. Gusken, Flavor singlet phenomena in lattice QCD, hep-lat/9906034 [INSPIRE].
M. Beneke and M. Neubert, Flavor singlet B decay amplitudes in QCD factorization, Nucl. Phys. B 651 (2003) 225 [hep-ph/0210085] [INSPIRE].
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
A. Gadde, E. Pomoni and L. Rastelli, The Veneziano Limit of N = 2 Superconformal QCD: Towards the String Dual of N = 2 SU(Nc) SYM with Nf = 2Nc, arXiv:0912.4918 [INSPIRE].
O. Lunin and S. Pinsky, Mesonic spectrum of two-dimensional supersymmetric theories, Phys. Rev. D 63 (2001) 045019 [hep-th/0005282] [INSPIRE].
A. Armoni and J. Sonnenschein, Screening and confinement in large Nf QCD2 and N = 1 SYM2, Nucl. Phys. B 502 (1997) 516 [hep-th/9703114] [INSPIRE].
A. Armoni, Y. Frishman, J. Sonnenschein and U. Trittmann, The Spectrum of multiflavor QCD in two-dimensions and the nonAbelian Schwinger equation, Nucl. Phys. B 537 (1999) 503 [hep-th/9805155] [INSPIRE].
S. Dalley, Adjoint QCD in two-dimensions and the nonAbelian Schwinger mechanism, Phys. Lett. B 418 (1998) 160 [hep-th/9708115] [INSPIRE].
V.G. Kač and D.H. Peterson, Infinite dimensional Lie algebras, theta functions and modular forms, Adv. Math. 53 (1984) 125 [INSPIRE].
I. Frenkel, Representations of affine lie algebras, hecke modular forms and Korteweg-de Vries type equations, in Lie algebras and related topics, Springer (1982), pp. 71–110.
M. Jimbo and T. Miwa, On a duality of branching rules for affine Lie algebras, Adv. Stud. Pure Math 6 (1985) 17.
K. Hasegawa, Spin module versions of Weyl’s reciprocity theorem for classical Kac-Moody Lie algebras: an application to branching rule duality, Publ. Res. Inst. Math. Sci. 25 (1989) 741.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1404.5314
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
Gadde, A., Gukov, S. & Putrov, P. Exact solutions of 2d supersymmetric gauge theories. J. High Energ. Phys. 2019, 174 (2019). https://doi.org/10.1007/JHEP11(2019)174
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2019)174