q-deformation of corner vertex operator algebras by Miura transformation

Abstract

Abstract Recently, Gaiotto and Rapcak proposed a generalization of W N algebra by considering the symmetry at the corner of the brane intersection (corner vertex operator algebra). The algebra, denoted as Y L,M,N , is characterized by three non-negative integers L, M, N. It has a manifest triality automorphism which interchanges L, M, N, and can be obtained as a reduction of W 1+∞ algebra with a “pit” in the plane partition representation. Later, Prochazka and Rapcak proposed a representation of Y L,M,N in terms of L + M + N free bosons by a generalization of Miura transformation, where they use the fractional power differential operators. In this paper, we derive a q-deformation of the Miura transformation. It gives a free field representation for q-deformed Y L,M,N , which is obtained as a reduction of the quantum toroidal algebra. We find that the q-deformed version has a “simpler” structure than the original one because of the Miki duality in the quantum toroidal algebra. For instance, one can find a direct correspondence between the operators obtained by the Miura transformation and those of the quantum toroidal algebra. Furthermore, we can show that the both algebras share the same screening operators.

Keywords

• Conformal and W Symmetry
• Conformal Field Theory
• Higher Spin Symmetry
• Quantum Groups