Journal of High Energy Physics

, 2013:152 | Cite as

Partition function of beta-gamma system on orbifolds

  • Chandrasekhar Bhamidipati
  • Koushik Ray


Partition function of beta-gamma systems on the orbifolds C 2/Z N and C 3/Z M × Z N are obtained as the invariant part of that on the respective affine spaces, by lifting the geometric action of the orbifold group to the fields. Interpreting the sum over roots of unity as an elementary contour integration, the partition function evaluates to a generalized Molien series counting invariant monomials composed of basic operators of the theory at each mass level.


Conformal Field Models in String Theory Differential and Algebraic Geometry Discrete and Finite Symmetries 


  1. [1]
    E. Witten, Two-dimensional models with (0, 2) supersymmetry: perturbative aspects, Adv. Theor. Math. Phys. 11 (2007) [hep-th/0504078] [INSPIRE].
  2. [2]
    N.A. Nekrasov, Lectures on curved beta-gamma systems, pure spinors and anomalies, hep-th/0511008 [INSPIRE].
  3. [3]
    F. Malikov, V. Schechtman and A. Vaintrob, Chiral de Rham complex, Commun. Math. Phys. 204 (1999) 439 [math.AG/9803041] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  4. [4]
    F. Malikov and V. Schechtman, Chiral de Rham complex. II, in Differential topology, infinite-dimensional Lie algebras, and applications, Amer. Math. Soc. Transl. Ser. 2 194 (1999) 149 [math.AG/9901065].
  5. [5]
    A. Kapustin, Chiral de Rham complex and the half-twisted σ-model, hep-th/0504074 [INSPIRE].
  6. [6]
    N. Berkovits, Pure spinor formalism as an N = 2 topological string, JHEP 10 (2005) 089 [hep-th/0509120] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    M.-C. Tan, Two-dimensional twisted σ-models and the theory of chiral differential operators, Adv. Theor. Math. Phys. 10 (2006) 759 [hep-th/0604179] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    M.-C. Tan, The half-twisted orbifold σ-model and the chiral de Rham complex, Adv. Theor. Math. Phys. 12 (2008) 547 [hep-th/0607199] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    P. Grassi and G. Policastro, Curved beta-gamma systems and quantum Koszul resolution, hep-th/0602153 [INSPIRE].
  10. [10]
    P.A. Grassi, G. Policastro and E. Scheidegger, Partition functions, localization and the chiral de Rham complex, hep-th/0702044 [INSPIRE].
  11. [11]
    Y. Aisaka and E.A. Arroyo, Hilbert space of curved beta gamma systems on quadric cones, JHEP 08 (2008) 052 [arXiv:0806.0586] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    E. Frenkel and A. Losev, Mirror symmetry in two steps: A-I-B, Commun. Math. Phys. 269 (2006) 39 [hep-th/0505131] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    N. Berkovits, Super Poincaré covariant quantization of the superstring, JHEP 04 (2000) 018 [hep-th/0001035] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    P. Grassi and J. Morales Morera, Partition functions of pure spinors, Nucl. Phys. B 751 (2006) 53 [hep-th/0510215] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    E. Aldo Arroyo, Pure spinor partition function using Padé approximants, JHEP 07 (2008) 081 [arXiv:0806.0643] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    Y. Aisaka, E.A. Arroyo, N. Berkovits and N. Nekrasov, Pure spinor partition function and the massive superstring spectrum, JHEP 08 (2008) 050 [arXiv:0806.0584] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    N. Berkovits and N. Nekrasov, The character of pure spinors, Lett. Math. Phys. 74 (2005) 75 [hep-th/0503075] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  18. [18]
    R.P. Stanley, Invariants of finite groups and their applications to combinatorics, Bull. Amer. Math. Soc. 1 (1979) 475.MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    L. Smith, Polynomial invariants of finite groups a survey of recent developments, Bull. Amer. Math. Soc. 34 (1997) 211.MathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    B. Feng, A. Hanany and Y.-H. He, Counting gauge invariants: the Plethystic program, JHEP 03 (2007) 090 [hep-th/0701063] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    V.G. Kac and P. Cheung, Quantum calculus, Springer, Germany (2002).CrossRefMATHGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.School of Basic Sciences, Indian Institute of Technology BhubaneswarBhubaneswarIndia
  2. 2.Department of Theoretical PhysicsIndian Association for the Cultivation of ScienceCalcuttaIndia

Personalised recommendations