Journal of High Energy Physics

, 2014:157 | Cite as

Accidents in (0,2) Landau-Ginzburg theories

  • Marco Bertolini
  • Ilarion V. Melnikov
  • M. Ronen Plesser
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Field Theories in Lower Dimensions Superstrings and Heterotic Strings 

References

  1. [1]
    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].ADSCrossRefMathSciNetGoogle Scholar
  2. [2]
    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].
  3. [3]
    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].ADSGoogle Scholar
  4. [4]
    A.B. Zamolodchikov, Conformal Symmetry and Multicritical Points in Two-Dimensional Quantum Field Theory. (In Russian), Sov. J. Nucl. Phys. 44 (1986) 529 [INSPIRE].MathSciNetGoogle Scholar
  5. [5]
    D.A. Kastor, E.J. Martinec and S.H. Shenker, RG Flow in N = 1 Discrete Series, Nucl. Phys. B 316 (1989) 590 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  6. [6]
    E.J. Martinec, Algebraic Geometry and Effective Lagrangians, Phys. Lett. B 217 (1989) 431 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  7. [7]
    C. Vafa and N.P. Warner, Catastrophes and the Classification of Conformal Theories, Phys. Lett. B 218 (1989) 51 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  8. [8]
    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.Google Scholar
  9. [9]
    E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  10. [10]
    J. Distler and S. Kachru, (0,2) Landau-Ginzburg theory, Nucl. Phys. B 413 (1994) 213 [hep-th/9309110] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  11. [11]
    E. Silverstein and E. Witten, Criteria for conformal invariance of (0,2) models, Nucl. Phys. B 444 (1995) 161 [hep-th/9503212] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  12. [12]
    J. Distler, Notes on (0,2) superconformal field theories, hep-th/9502012 [INSPIRE].
  13. [13]
    P.S. Aspinwall, B.R. Greene and D.R. Morrison, The Monomial divisor mirror map, alg-geom/9309007 [INSPIRE].
  14. [14]
    D. A. Cox and S. Katz, Mirror symmetry and algebraic geometry, Providence, U.S.A.: AMS, 2000, pg. 469.Google Scholar
  15. [15]
    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].ADSMathSciNetGoogle Scholar
  16. [16]
    I.V. Melnikov, (0,2) Landau-Ginzburg Models and Residues, JHEP 09 (2009) 118 [arXiv:0902.3908] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    C. Beasley and E. Witten, New instanton effects in supersymmetric QCD, JHEP 01 (2005) 056 [hep-th/0409149] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  18. [18]
    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].ADSCrossRefMathSciNetGoogle Scholar
  19. [19]
    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].ADSCrossRefMathSciNetGoogle Scholar
  20. [20]
    K.A. Intriligator and B. Wecht, The Exact superconformal R symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  21. [21]
    F. Benini and N. Bobev, Exact two-dimensional superconformal R-symmetry and c-extremization, Phys. Rev. Lett. 110 (2013) 061601 [arXiv:1211.4030] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    M. Kreuzer and H. Skarke, No mirror symmetry in Landau-Ginzburg spectra!, Nucl. Phys. B 388 (1992) 113 [hep-th/9205004] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  23. [23]
    A. Klemm and R. Schimmrigk, Landau-Ginzburg string vacua, Nucl. Phys. B 411 (1994) 559 [hep-th/9204060] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  24. [24]
    N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  25. [25]
    M. Kreuzer and H. Skarke, On the classification of quasihomogeneous functions, Commun. Math. Phys. 150 (1992) 137 [hep-th/9202039] [INSPIRE].ADSCrossRefMathSciNetMATHGoogle Scholar
  26. [26]
    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.Google Scholar
  27. [27]
    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].ADSCrossRefMathSciNetGoogle Scholar
  28. [28]
    J. Polchinski, Scale and Conformal Invariance in Quantum Field Theory, Nucl. Phys. B 303 (1988) 226 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  29. [29]
    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].ADSCrossRefMathSciNetGoogle Scholar
  30. [30]
    M. Dine, I. Ichinose and N. Seiberg, F terms and d Terms in String Theory, Nucl. Phys. B 293 (1987)253 [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    V. Periwal and A. Strominger, Kähler Geometry of the Space of N = 2 Superconformal Field Theories, Phys. Lett. B 235 (1990) 261 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  32. [32]
    M. Dine, N. Seiberg, X.G. Wen and E. Witten, Nonperturbative Effects on the String World Sheet, Nucl. Phys. B 278 (1986) 769 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  33. [33]
    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].ADSCrossRefMathSciNetGoogle Scholar
  34. [34]
    I.V. Melnikov, R. Minasian and S. Theisen, Heterotic flux backgrounds and their IIA duals, JHEP 07 (2014) 023 [arXiv:1206.1417] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    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].ADSCrossRefMathSciNetGoogle Scholar
  36. [36]
    I.V. Melnikov and M.R. Plesser, A (0,2) Mirror Map, JHEP 02 (2011) 001 [arXiv:1003.1303] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  37. [37]
    D. Kutasov, New results on thea theoremin four-dimensional supersymmetric field theory, hep-th/0312098 [INSPIRE].
  38. [38]
    D. Kutasov and A. Schwimmer, Lagrange multipliers and couplings in supersymmetric field theory, Nucl. Phys. B 702 (2004) 369 [hep-th/0409029] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  39. [39]
    D. Erkal and D. Kutasov, a-Maximization, Global Symmetries and RG Flows, arXiv:1007.2176 [INSPIRE].
  40. [40]
    M. Bertolini, I.V. Melnikov and M.R. Plesser, Hybrid conformal field theories, JHEP 05 (2014) 043 [arXiv:1307.7063] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  41. [41]
    N. Behr and A. Konechny, Renormalization and redundancy in 2d quantum field theories, JHEP 02 (2014) 001 [arXiv:1310.4185] [INSPIRE].CrossRefMathSciNetGoogle Scholar
  42. [42]
    P.S. Aspinwall, I.V. Melnikov and M.R. Plesser, (0,2) Elephants, JHEP 01 (2012) 060 [arXiv:1008.2156] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  43. [43]
    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].ADSCrossRefMathSciNetGoogle Scholar
  44. [44]
    J. McOrist and I.V. Melnikov, Old issues and linear σ-models, Adv. Theor. Math. Phys. 16 (2012) 251 [arXiv:1103.1322] [INSPIRE].CrossRefMathSciNetMATHGoogle Scholar
  45. [45]
    M. Dine and N. Seiberg, Are (0,2) models string miracles?, Nucl. Phys. B 306 (1988) 137 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Marco Bertolini
    • 1
    • 2
  • Ilarion V. Melnikov
    • 3
  • M. Ronen Plesser
    • 1
  1. 1.Center for Geometry and Theoretical Physics, Box 90318Duke UniversityDurhamU.S.A.
  2. 2.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  3. 3.George P. and Cynthia W. Mitchell Institute for Fundamental Physics and AstronomyTexas A&M UniversityCollege StationU.S.A.

Personalised recommendations