Branes at C**4 / Lambda singularity from toric geometry

Mar, 1999
25 pages
Published in:
  • JHEP 04 (1999) 012
e-Print:
Report number:
  • SNUTP-99-011

Citations per year

199920032007201120155102
Abstract:
We study toric singularities of the form of \C^4/\Ga for finite abelian groups \Ga \subset SU(4). In particular, we consider the simplest case \Ga=\Z_2 \times \Z_2 \times \Z_2 and find explicitly charge matrices for partial resolutions of this orbifold by extending the method by Morrison and Plesser. We obtain three kinds of algebraic equations, z1z2z3z4=z52,z1z2z3=z42z5z_1 z_2 z_3 z_4=z_5^2, z_1 z_2 z_3=z_4^2 z_5 and z1z2z5=z3z4z_1 z_2 z_5 = z_3 z_4 where ziz_i's parametrize \C^5. When we put NN D1 branes at this singularity, it is known that the field theory on the worldvolume of NN D1 branes is T-dual to 2×2×22 \times 2 \times 2 brane cub model. We analyze geometric interpretation for field theory parameters and moduli space.
  • membrane model
  • geometry: torus
  • singularity
  • orbifold
  • moduli space
  • symmetry: Z(2)**3