TY - JOUR
T1 - Galilean contractions of W-algebras
AU - Rasmussen, Jørgen
AU - Raymond, Christopher
N1 - Publisher Copyright:
© 2017 The Author(s)
PY - 2017/9
Y1 - 2017/9
N2 - Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as W-algebras. Known examples include contractions of pairs of the Virasoro algebra, its N=1 superconformal extension, or the W3 algebra. Here, we introduce a contraction prescription of the corresponding operator-product algebras, or equivalently, a prescription for contracting tensor products of vertex algebras. With this, we work out the Galilean conformal algebras arising from contractions of N=2 and N=4 superconformal algebras as well as of the W-algebras W(2,4), W(2,6), W4, and W5. The latter results provide evidence for the existence of a whole new class of W-algebras which we call Galilean W-algebras. We also apply the contraction prescription to affine Lie algebras and find that the ensuing Galilean affine algebras admit a Sugawara construction. The corresponding central charge is level-independent and given by twice the dimension of the underlying finite-dimensional Lie algebra. Finally, applications of our results to the characterisation of structure constants in W-algebras are proposed.
AB - Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as W-algebras. Known examples include contractions of pairs of the Virasoro algebra, its N=1 superconformal extension, or the W3 algebra. Here, we introduce a contraction prescription of the corresponding operator-product algebras, or equivalently, a prescription for contracting tensor products of vertex algebras. With this, we work out the Galilean conformal algebras arising from contractions of N=2 and N=4 superconformal algebras as well as of the W-algebras W(2,4), W(2,6), W4, and W5. The latter results provide evidence for the existence of a whole new class of W-algebras which we call Galilean W-algebras. We also apply the contraction prescription to affine Lie algebras and find that the ensuing Galilean affine algebras admit a Sugawara construction. The corresponding central charge is level-independent and given by twice the dimension of the underlying finite-dimensional Lie algebra. Finally, applications of our results to the characterisation of structure constants in W-algebras are proposed.
UR - http://www.scopus.com/inward/record.url?scp=85026508833&partnerID=8YFLogxK
U2 - 10.1016/j.nuclphysb.2017.07.006
DO - 10.1016/j.nuclphysb.2017.07.006
M3 - Article
SN - 0550-3213
VL - 922
SP - 435
EP - 479
JO - Nuclear Physics B
JF - Nuclear Physics B
ER -