Ghost systems: A vertex algebra point of view

Nuclear Physics B

Volumn 518, Issue 3, 1998, Pages 669-688

  Eholzer, W ^a   Feher L ^b   Honecker, A ^c  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF SZEGED   (Hungary)

^c SISSA   (Italy)

Author keywords

Conformal field theory; Invariant subalgebras; Twisted representations; W algebras

Indexed keywords

EID: 0032507539     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(98)00061-3     Document Type: Article

References (47)

1. [1] D. Friedan, E. Martinec and S. Shenker, Conformal invariance, supersymmetry and string theory, Nucl. Phys. B 271 (1986) 93.
2. [2] S. Guruswamy and A.W.W. Ludwig, Relating c < 0 and c > 0 conformal field theories, preprint hep-th/9612172, IC/96/273.
3. [3] L.S. Georgiev and I.T. Todorov, Characters and partition function for the Wen-Wu CFT model of the Haldane-Rezayi quantum Hall state, preprint hep-th/9611084, INRNE-TH-96/13.
4. [4] V. Gurarie, M. Flohr and C. Nayak, The Haldane-Rezayi quantum Hall state and conformal field theory, Nucl. Phys. B 498 (1997) 513, cond-mat/9701212.
5. [5] G. Moore and N. Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. B 360 (1991) 362.
6. [6] H. Saleur, Polymers and percolation in two dimensions and twisted N = 2 supersymmetry, Nucl. Phys. B 382 (1992) 486.
7. [7] D. Bernard, (Perturbed) conformal field theory applied to 2D disordered systems: An introduction, in Low-Dimensional Applications of Quantum Field Theory, eds. L. Baulieu, V. Kazakov, M. Picco, P. Windley (Plenum Press, New York, 1997) p. 19, hep-th/9509137.
8. [8] Z. Maassarani and D. Serban, Non-unitary conformal field theory and logarithmic operators for disordered systems, Nucl. Phys. B 489 (1997) 603, hep-th/9605062.
9. [9] P. di Francesco, P. Mathieu and D. Sénéchal, Conformal Field Theory, Graduate Texts in Contemporary Physics (Springer, New York, 1997).
10. [10] J. de Boer and L. Fehér, Wakimoto realizations of current algebras: An explicit construction, Commun. Math. Phys. 189 (1997) 759, hep-th/9611083.
11. [11] J. Rasmussen, Free field realizations of affine current superalgebras, screening currents and primary fields, Nucl. Phys. B 510 (1998) 688, hep-th/9706091.
12. [12] H.G. Kausch, Curiosities at c = -2, preprint hep-th/9510149, DAMTP 95-52.
13. [13] P. Ginsparg, Curiosities at c = 1, Nucl. Phys. B 295 (1988) 153.
14. [14] E.B. Kiritsis, Proof of the completeness of the classification of rational conformal theories with c = 1, Phys. Lett. B 217 (1989) 427.
15. [15] R.E. Borcherds, Vertex algebras, Kac-Moody algebras, and the monster, Proc. Natl. Acad. Sci. USA 83 (1986) 3068.
16. 1+∞, Transform. Groups 1 (1996) 41, hep-th/9512150.
17. [17] R. Blumenhagen, W. Eholzer, A. Honecker, K. Hornfeck and R. Hübel, Coset realization of unifying W algebras, Int. J. Mod. Phys. A 10 (1995) 2367, hep-th/9406203.
18. [18] L. Fehér, L. O'Raifeartaigh, P. Ruelle, I. Tsutsui and A. Wipf, On Hamiltonian reductions of the Wess-Zumino-Novikov-Witten theories, Phys. Rep. 222 (1992) 1.
19. [19] E. Frenkel, V. Kac and M. Wakimoto, Characters and fusion rules for W algebras via quantized Drinfeld-Sokolov reduction, Commun. Math. Phys. 147 (1992) 295.
20. [20] J. de Boer and T. Tjin, The relation between quantum W algebras and Lie algebras, Commun. Math. Phys. 160 (1994) 317, hep-th/9302006.
21. [21] A.N. Schellekens, Meromorphic c = 24 conformal field theories, Commun. Math. Phys. 153 (1993) 159, hep-th/9205072.
22. 1+∞ symmetry, Phys. Rev. Lett. 72 (1994) 1902, hep-th/9310181.
23. [23] M. Flohr and R. Varnhagen, Infinite symmetry in the fractional quantum Hall effect, J. Phys. A: Math. Gen. 27 (1994) 3999, hep-th/9309083.
24. [24] V. Kac and A. Radul, Quasifinite highest weight modules over the Lie algebra of differential operators on the circle, Commun. Math. Phys. 157 (1993) 429, hep-th/9308153.
25. N) with central charge N, Commun. Math. Phys. 170 (1995) 337, hep-th/9405121.
26. 1+∞ algebra, Commun. Math. Phys. 172 (1995) 377, hep-th/9405093.
27. 1+∞, Commun. Math. Phys. 190 (1997), hep-th/9612078.
28. [28] V. Kac, Vertex Algebras for Beginners, University Lecture Series, Vol. 10 (American Mathematical Society, Providence, R.I., 1997).
29. [29] V.G. Kac and A.K. Raina, Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras, Advanced Series in Mathematical Physics, Vol. 2 (World Scientific, Singapore, 1987).
30. [30] A. Schwimmer and N. Seiberg, Comments on the N = 2, 3, 4 superconformal algebras in two dimensions, Phys. Lett. B 184 (1987) 191.
31. [31] B. Feigin and E. Frenkel, Bosonic ghost system and the Virasoro algebra, Phys. Lett. B 246 (1990) 71.
32. [32] A. Honecker, Automorphisms of W-algebras and extended rational conformal field theories, Nucl. Phys. B 400 (1993) 574, hep-th/9211130.
33. [33] H. Weyl, The Classical Groups, Their Invariants and Representations (Princeton University Press, Princeton, 1946).
34. [34] J. de Boer, L. Fehér and A. Honecker, A class of W-algebras with infinitely generated classical limit, Nucl. Phys. B 420 (1994) 409, hep-th/9312049.
35. [35] P. Ginsparg, Applied conformal field theory, in Fields, Strings and Critical Phenomena, ed. E. Brézin, J. Zinn-Justin, Proceedings of the Les Houches Summer School 1988 (North-Holland, Amsterdam, 1990) p. 1.
36. [36] A.B. Zamolodchikov, Infinite additional symmetries in two-dimensional conformal quantum field theory, Theor. Math. Phys. 65 (1986) 1205.
37. [37] P. Bouwknegt, A. Ceresole, P. van Nieuwenhuizen and J. McCarthy, Extended Sugawara construction for the superalgebra SU(M + 1|N + 1). II. The third-order Casimir algebra, Phys. Rev. D 40 (1989) 415.
38. [38] H.G. Kausch, Extended conformal algebras generated by a multiplet of primary fields, Phys. Lett. B 259 (1991) 448.
39. [39] W. Eholzer, A. Honecker and R. Hübel, How complete is the classification of W-symmetries?, Phys. Lett. B 308 (1993) 42, hep-th/9302124.
40. [40] R. Blumenhagen, W. Eholzer, A. Honecker, K. Hornfeck and R. Hübel, Unifying W-algebras, Phys. Lett. B 332 (1994) 51, hep-th/9404113.
41. 3 algebra, and Friedan-Martinec-Shenker bosonization, preprint q-alg/9708008.
42. [42] K. Hornfeck, W-Algebras with set of primary fields of dimensions (3,4,5) and (3,4,5,6), Nucl. Phys. B 407 (1993) 237, hep-th/9212104.
43. [43] H.G. Kausch, G.M.T. Watts, A study of W-algebras using Jacobi identities, Nucl. Phys. B 354 (1991) 740.
44. [44] V. Gurarie, Logarithmic operators in conformal field theory, Nucl. Phys. B 410 (1993) 535, hep-th/9303160.
45. [45] M.A.I. Flohr, On fusion rules in logarithmic conformal field theories, Int. J. Mod. Phys. A 12 (1997) 1943, hep-th/9605151.
46. [46] M.R. Gaberdiel and H.G. Kausch, A rational logarithmic conformal field theory, Phys. Lett. B 386 (1996) 131, hep-th/9606050.
47. [47] P. Goddard, Meromorphic conformal field theory, in Infinite dimensional Lie algebras and groups, Proc. CIRM-Luminy Conference 1988, ed. V.G. Kac (World Scientific, Singapore, 1989) p. 556.