On localized tachyon condensation in C2/Zn and C3

Abstract

We study some aspects of localized tachyon condensation on non-supersymmetric orbifolds of the form C 2 /Z n and C 3 /Z n . We discuss the gauged linear sigma models for these orbifolds. We show how several features of the decay of orbifolds of C 3 can be realised in terms of orbifolds of C

On tachyons, gauged linear sigma models, and flip transitions

“…Then thinking of an unstable C 3 /Z N orbifold as the UV fixed point with several unstable directions (see figure 7), we know from [10] that the f inal endpoints of tachyon condensation do not include terminal singularities and are always supersymmetric spaces (generally smooth spaces such as supersymmetric Calabi-Yau manifolds, with supersymmetric singularities also permitted) for type-II string theories. These final endpoints can be thought of as the culmination of condensation of all tachyons, chiral and nonchiral, 20 and are the absolute minima of the tachyon potential. Thus the depth of the tachyon potential for a given orbifold is basically the height of the orbifold "hill" maximum above the absolute minima, i.e., the (smooth) moduli space.…”

“…Thus the depth of the tachyon potential for a given orbifold is basically the height of the orbifold "hill" maximum above the absolute minima, i.e., the (smooth) moduli space. 20 As seen in [10] (in the type-II example discussed there), condensation of purely chiral tachyons will in general result in geometric terminal singularities which will then continue to decay via the nonchiral tachyonic blowup modes to finally result in supersymmetric spaces. Tachyons In an off-shell formulation of string theory, one expects that the tachyon potential 21 for a given orbifold C 3 /Z N (1, p, q) is a function V (T ) describing the dynamics of all the tachyon fields T i in the system, with parameters N, p, q.…”

“…However unlike C/Z N , where the most relevant tachyon decay channel leads to flat space, C 2 /Z N and C 3 /Z N orbifolds typically do not decay to supersymmetric spaces via the most relevant tachyon: the endpoints themselves are typically unstable to tachyon condensation via subsequent tachyons. Expressions involving condensation of a single tachyon appear in [23,25,20]. Using these, one can thus attempt an iterative guess for the depth V (T ) by summing over all tachyons (mass M 2 , R-charge R) present in the orbifold,…”

“…Explicit GLSM descriptions (and mirror descriptions) of tachyons in nonsupersymmetric orbifolds have appeared in, e.g., [8]- [20].…”

Phases of unstable conifolds

“…This kind of behaviour also arises in the context of singular spaces in 3 complex dimensions where much more complicated and interesting phenomena happen. Two types of 3-dimensional nonsupersymmetric unstable singularities, particularly rich both in physical content and mathematical structure, are conifolds [4] and orbifolds [5,6] (see also [7]), thought of as local singularities in some compact space, the full spacetime then being of the form R 3,1 × M. The conifold-like singularities [4] (reviewed in Sec. 2) are toric (as are orbifolds), labelled by a charge matrix Q = ( n 1 n 2 −n 3 −n 4 ) ,…”