Abstract
We study the role of accidental symmetries in two-dimensional (0,2) superconformal field theories obtained by RG flow from (0,2) Landau-Ginzburg theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) Landau-Ginzburg models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. We also give a self-contained discussion of aspects of (0,2) conformal perturbation theory.
Article PDF
Similar content being viewed by others
References
A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory, Nucl. Phys. B 241 (1984) 333 [INSPIRE].
S. El-Showk, M.F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin et al., Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents, J. Stat. Phys. xx (2014) xx [arXiv:1403.4545] [INSPIRE].
S. El-Showk, M.F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin et al., Solving the 3D Ising Model with the Conformal Bootstrap, Phys. Rev. D 86 (2012) 025022 [arXiv:1203.6064] [INSPIRE].
A.B. Zamolodchikov, Conformal Symmetry and Multicritical Points in Two-Dimensional Quantum Field Theory. (In Russian), Sov. J. Nucl. Phys. 44 (1986) 529 [INSPIRE].
D.A. Kastor, E.J. Martinec and S.H. Shenker, RG Flow in N = 1 Discrete Series, Nucl. Phys. B 316 (1989) 590 [INSPIRE].
E.J. Martinec, Algebraic Geometry and Effective Lagrangians, Phys. Lett. B 217 (1989) 431 [INSPIRE].
C. Vafa and N.P. Warner, Catastrophes and the Classification of Conformal Theories, Phys. Lett. B 218 (1989) 51 [INSPIRE].
K. Hori, S. Katz, A. Klemm, R. Pandharipande, R. Thomas, C. Vafa, R. Vakil, and E. Zaslow, Mirror symmetry, vol. 1 of Clay Mathematics Monographs, American Mathematical Society, Providence, RI, 2003, with a preface by Vafa.
E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].
J. Distler and S. Kachru, (0,2) Landau-Ginzburg theory, Nucl. Phys. B 413 (1994) 213 [hep-th/9309110] [INSPIRE].
E. Silverstein and E. Witten, Criteria for conformal invariance of (0,2) models, Nucl. Phys. B 444 (1995) 161 [hep-th/9503212] [INSPIRE].
J. Distler, Notes on (0,2) superconformal field theories, hep-th/9502012 [INSPIRE].
P.S. Aspinwall, B.R. Greene and D.R. Morrison, The Monomial divisor mirror map, alg-geom/9309007 [INSPIRE].
D. A. Cox and S. Katz, Mirror symmetry and algebraic geometry, Providence, U.S.A.: AMS, 2000, pg. 469.
T. Kawai, Y. Yamada and S.-K. Yang, Elliptic genera and N = 2 superconformal field theory, Nucl. Phys. B 414 (1994) 191 [hep-th/9306096] [INSPIRE].
I.V. Melnikov, (0,2) Landau-Ginzburg Models and Residues, JHEP 09 (2009) 118 [arXiv:0902.3908] [INSPIRE].
C. Beasley and E. Witten, New instanton effects in supersymmetric QCD, JHEP 01 (2005) 056 [hep-th/0409149] [INSPIRE].
I.V. Melnikov and E. Sharpe, On marginal deformations of (0,2) non-linear σ-models, Phys. Lett. B 705 (2011) 529 [arXiv:1110.1886] [INSPIRE].
R. Blumenhagen, R. Schimmrigk and A. Wisskirchen, The (0,2) exactly solvable structure of chiral rings, Landau-Ginzburg theories and Calabi-Yau manifolds, Nucl. Phys. B 461 (1996) 460 [hep-th/9510055] [INSPIRE].
K.A. Intriligator and B. Wecht, The Exact superconformal R symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].
F. Benini and N. Bobev, Exact two-dimensional superconformal R-symmetry and c-extremization, Phys. Rev. Lett. 110 (2013) 061601 [arXiv:1211.4030] [INSPIRE].
M. Kreuzer and H. Skarke, No mirror symmetry in Landau-Ginzburg spectra!, Nucl. Phys. B 388 (1992) 113 [hep-th/9205004] [INSPIRE].
A. Klemm and R. Schimmrigk, Landau-Ginzburg string vacua, Nucl. Phys. B 411 (1994) 559 [hep-th/9204060] [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
M. Kreuzer and H. Skarke, On the classification of quasihomogeneous functions, Commun. Math. Phys. 150 (1992) 137 [hep-th/9202039] [INSPIRE].
L.J. Dixon, Some world sheet properties of superstring compactifications, on orbifolds and otherwise, lectures given at the 1987 ICTP Summer Workshop in High Energy Phsyics and Cosmology, Trieste, Italy, Jun 29 - Aug 7, 1987.
D. Green, Z. Komargodski, N. Seiberg, Y. Tachikawa and B. Wecht, Exactly Marginal Deformations and Global Symmetries, JHEP 06 (2010) 106 [arXiv:1005.3546] [INSPIRE].
J. Polchinski, Scale and Conformal Invariance in Quantum Field Theory, Nucl. Phys. B 303 (1988) 226 [INSPIRE].
J.J. Atick, L.J. Dixon and A. Sen, String Calculation of Fayet-Iliopoulos d Terms in Arbitrary Supersymmetric Compactifications, Nucl. Phys. B 292 (1987) 109 [INSPIRE].
M. Dine, I. Ichinose and N. Seiberg, F terms and d Terms in String Theory, Nucl. Phys. B 293 (1987)253 [INSPIRE].
V. Periwal and A. Strominger, Kähler Geometry of the Space of N = 2 Superconformal Field Theories, Phys. Lett. B 235 (1990) 261 [INSPIRE].
M. Dine, N. Seiberg, X.G. Wen and E. Witten, Nonperturbative Effects on the String World Sheet, Nucl. Phys. B 278 (1986) 769 [INSPIRE].
K. Becker, M. Becker, J.-X. Fu, L.-S. Tseng and S.-T. Yau, Anomaly cancellation and smooth non-Kähler solutions in heterotic string theory, Nucl. Phys. B 751 (2006) 108 [hep-th/0604137] [INSPIRE].
I.V. Melnikov, R. Minasian and S. Theisen, Heterotic flux backgrounds and their IIA duals, JHEP 07 (2014) 023 [arXiv:1206.1417] [INSPIRE].
M. Kreuzer, J. McOrist, I.V. Melnikov and M.R. Plesser, (0,2) Deformations of Linear σ-models, JHEP 07 (2011) 044 [arXiv:1001.2104] [INSPIRE].
I.V. Melnikov and M.R. Plesser, A (0,2) Mirror Map, JHEP 02 (2011) 001 [arXiv:1003.1303] [INSPIRE].
D. Kutasov, New results on the ‘a theorem’ in four-dimensional supersymmetric field theory, hep-th/0312098 [INSPIRE].
D. Kutasov and A. Schwimmer, Lagrange multipliers and couplings in supersymmetric field theory, Nucl. Phys. B 702 (2004) 369 [hep-th/0409029] [INSPIRE].
D. Erkal and D. Kutasov, a-Maximization, Global Symmetries and RG Flows, arXiv:1007.2176 [INSPIRE].
M. Bertolini, I.V. Melnikov and M.R. Plesser, Hybrid conformal field theories, JHEP 05 (2014) 043 [arXiv:1307.7063] [INSPIRE].
N. Behr and A. Konechny, Renormalization and redundancy in 2d quantum field theories, JHEP 02 (2014) 001 [arXiv:1310.4185] [INSPIRE].
P.S. Aspinwall, I.V. Melnikov and M.R. Plesser, (0,2) Elephants, JHEP 01 (2012) 060 [arXiv:1008.2156] [INSPIRE].
S. Kachru and E. Witten, Computing the complete massless spectrum of a Landau-Ginzburg orbifold, Nucl. Phys. B 407 (1993) 637 [hep-th/9307038] [INSPIRE].
J. McOrist and I.V. Melnikov, Old issues and linear σ-models, Adv. Theor. Math. Phys. 16 (2012) 251 [arXiv:1103.1322] [INSPIRE].
M. Dine and N. Seiberg, Are (0,2) models string miracles?, Nucl. Phys. B 306 (1988) 137 [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1405.4266
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Bertolini, M., Melnikov, I.V. & Plesser, M.R. Accidents in (0,2) Landau-Ginzburg theories. J. High Energ. Phys. 2014, 157 (2014). https://doi.org/10.1007/JHEP12(2014)157
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2014)157