Time Dependent Orbifold Research Articles

Dirac quantization of membrane winding uniformly in time dependent orbifold

We present quantum theory of a membrane propagating in the vicinity of a time dependent orbifold singularity. The dynamics of a membrane, with the parameters space topology of a torus, winding uniformly around compact dimension of the embedding spacetime is mathematically equivalent to the dynamics of a closed string in a flat FRW spacetime. The construction of the physical Hilbert space of a membrane makes use of the kernel space of self-adjoint constraint operators. It is a subspace of the representation space of the constraints algebra. There exist non-trivial quantum states of a membrane evolving across the singularity.

Propagation of extended objects across singularity of time dependent orbifold

In this paper we argue that the compactified Milne space is a promising model of the cosmological singularity. It is shown that extended objects like strings propagate in a well-defined manner across the singularity of the embedding space. Then a proposal for quantization of extended objects in the case of a membrane is given.

Propagation of extended objects across singularity of time dependent orbifold

AbstractIn this paper we argue that the compactified Milne space is a promising model of the cosmological singularity. It is shown that extended objects like strings propagate in a well‐defined manner across the singularity of the embedding space. Then a proposal for quantization of extended objects in the case of a membrane is given.

Excited states of a string in a time-dependent orbifold

We present analytical results on the propagation of a classical string in nonzero modes through the singularity of the compactified Milne space. We restrict our analysis to a string winding around the compact dimension of spacetime. The compact dimension undergoes contraction to a point followed by re-expansion. We demonstrate that the classical dynamics of the string in excited states is non-singular in the entire spacetime.

Propagation of a string across the cosmological singularity

Our results concern the transition of a quantum string through the singularity of the compactified Milne (CM) space. We restrict our analysis to the string winding around the compact dimension (CD) of spacetime. The CD undergoes contraction to a point followed by re-expansion. We demonstrate that both the classical and quantum dynamics of the considered string are well defined. Most of the presently available calculations strongly suggest that the singularity of a time-dependent orbifold is useless as a model of the cosmological singularity. We believe that our results bring, to some extent, this claim into question.

On smooth time-dependent orbifolds and null singularities

We study string theory on a non-singular time-dependent orbifold of flat space, known as the `null-brane'. The orbifold group, which involves only space-like identifications, is obtained by a combined action of a null Lorentz transformation and a constant shift in an extra direction. In the limit where the shift goes to zero, the geometry of this orbifold reproduces an orbifold with a light-like singularity, which was recently studied by Liu, Moore and Seiberg (hep-th/0204168). We find that the backreaction on the geometry due to a test particle can be made arbitrarily small, and that there are scattering processes which can be studied in the approximation of a constant background. We quantize strings on this orbifold and calculate the torus partition function. We construct a basis of states on the smooth orbifold whose tree level string interactions are nonsingular. We discuss the existence of physical modes in the singular orbifold which resolve the singularity. We also describe another way of making the singular orbifold smooth which involves a sandwich pp-wave.

Strings in Time-Dependent Orbifolds

We continue and extend our earlier investigation ``Strings in a Time-Dependent Orbifold'' (hep-th/0204168). We formulate conditions for an orbifold to be amenable to perturbative string analysis and classify the low dimensional orbifolds satisfying these conditions. We analyze the tree and torus amplitudes of some of these orbifolds. The tree amplitudes exhibit a new kind of infrared divergences which are a result of some ultraviolet effects. These UV enhanced IR divergences can be interpreted as due to back reaction of the geometry. We argue that for this reason the three dimensional parabolic orbifold is not amenable to perturbation theory. Similarly, the smooth four dimensional null-brane tensored with sufficiently few noncompact dimensions also appears problematic. However, when the number of noncompact dimensions is sufficiently large perturbation theory in these time dependent backgrounds seems consistent.

Strings in a Time-Dependent Orbifold

We consider string theory in a time dependent orbifold with a null singularity. The singularity separates a contracting universe from an expanding universe, thus constituting a big crunch followed by a big bang. We quantize the theory both in light-cone gauge and covariantly. We also compute some tree and one loop amplitudes which exhibit interesting behavior near the singularity. Our results are compatible with the possibility that strings can pass through the singularity from the contracting to the expanding universe, but they also indicate the need for further study of certain divergent scattering amplitudes.