Quantum evolution across singularities

Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular time-dependent backgounds and free quantum fields on the two-dimensional compactified Milne universe. Due to the presence of the singularities in the time dependence, the conventional quantum-mechanical evolution is not well-defined for such systems. We propose a natural way, mathematically analogous to renormalization in conventional quantum field theory, to construct unitary quantum evolution across the singularity. We carry out this procedure explicitly for free fields on the compactified Milne universe and compare our results with the matching conditions considered in earlier work (which were based on the covering Minkowski space).Comment: revised with an emphasis on local counterterm subtraction rather than analyticity; version to be submitted for publicatio

Light-like Big Bang singularities in string and matrix theories

Important open questions in cosmology require a better understanding of the Big Bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be particularly tractable. We give a status report on the current understanding of such light-like Big Bang models, presenting both solved and open problems.Comment: 20 pages, invited review for Class. Quant. Grav; v3: section 2.3 shortened, discussion on DLCQ added in section 3.1, published versio

Orbifold boundary states from Cardy's condition

Boundary states for D-branes at orbifold fixed points are constructed in close analogy with Cardy's derivation of consistent boundary states in RCFT. Comments are made on the interpretation of the various coefficients in the explicit expressions, and the relation between fractional branes and wrapped branes is investigated for $\mathbb{C}^2/\Gamma$ orbifolds. The boundary states are generalised to theories with discrete torsion and a new check is performed on the relation between discrete torsion phases and projective representations.Comment: LaTeX2e, 50 pages, 5 figures. V3: final version to appear on JHEP (part of a section moved to an appendix, titles of some references added, one sentence in the introduction expanded

Behavior of tachyon in string cosmology based on gauged WZW model

We investigate a string theoretic cosmological model in the context of the gauged Wess-Zumino-Witten model. Our model is based on a product of non-compact coset space and a spectator flat space; $[SL(2,R)/U(1)]_k \times {\bf R}^2$. We extend the formerly studied semiclassical consideration with infinite Kac-Moody level $k$ to a finite one. In this case, the tachyon field appears in the effective action, and we solve the Einstein equation to determine the behavior of tachyon as a function of time. We find that tachyon field dominates over dilaton field in early times. In particular, we consider the energy conditions of the matter fields consisting of the dilaton and the tachyon which affect the initial singularity. We find that not only the strong energy but also the null energy condition is violated.Comment: 10 figure

p-branes on the waves

We present a large family of simple, explicit ten-dimensional supergravity solutions describing extended extremal supersymmetric Ramond-Ramond p-branes embedded into time-dependent dilaton-gravity plane waves of an arbitrary (isotropic) profile, with the brane world-volume aligned parallel to the propagation direction of the wave. Generalizations to the non-extremal case are not analyzed explicitly, but can be pursued as indicated.Comment: 11 pages; v.2 minor notation changes, minor typos corrected (published version

Quantum evolution across singularities: the case of geometrical resolutions

We continue the study of time-dependent Hamiltonians with an isolated singularity in their time dependence, describing propagation on singular space-times. In previous work, two of us have proposed a "minimal subtraction" prescription for the simplest class of such systems, involving Hamiltonians with only one singular term. On the other hand, Hamiltonians corresponding to geometrical resolutions of space-time tend to involve multiple operator structures (multiple types of dependence on the canonical variables) in an essential way. We consider some of the general properties of such (near-)singular Hamiltonian systems, and further specialize to the case of a free scalar field on a two-parameter generalization of the null-brane space-time. We find that the singular limit of free scalar field evolution exists for a discrete subset of the possible values of the two parameters. The coordinates we introduce reveal a peculiar reflection property of scalar field propagation on the generalized (as well as the original) null-brane. We further present a simple family of pp-wave geometries whose singular limit is a light-like hyperplane (discontinuously) reflecting the positions of particles as they pass through it.Comment: 25 pages, 1 figur

D-Brane Potentials from Multi-Trace Deformations in AdS/CFT

It is known that certain AdS boundary conditions allow smooth initial data to evolve into a big crunch. To study this type of cosmological singularity, one can use the dual quantum field theory, where the non-standard boundary conditions are reflected by the presence of a multi-trace potential unbounded below. For specific AdS_4 and AdS_5 models, we provide a D-brane (or M-brane) interpretation of the unbounded potential. Using probe brane computations, we show that the AdS boundary conditions of interest cause spherical branes to be pushed to the boundary of AdS in finite time, and that the corresponding potential agrees with the multi-trace deformation of the dual field theory. Systems with expanding spherical D3-branes are related to big crunch supergravity solutions by a phenomenon similar to geometric transition.Comment: 26 pages, 3 figures, v4: a few typos fixed

Holography and Cosmological Singularities

Certain null singularities in ten dimensional supergravity have natural holographic duals in terms of Matrix Theory and generalizations of the AdS/CFT correspondence. In many situations the holographic duals appear to be well defined in regions where the supergravity develops singularities. We describe some recent progress in this area.Comment: Anomaly equation corrected. References adde

One-Loop Effect of Null-Like Cosmology's Holographic Dual Super-Yang-Mills

We calculate the 1-loop effect in super-Yang-Mills which preserves 1/4-supersymmetries and is holographically dual to the null-like cosmology with a big-bang singularity. Though the bosonic and fermionic spectra do not agree precisely, we do obtain vanishing 1-loop vacuum energy for generic warped plane-wave type backgrounds with a big-bang singularity. Moreover, we find that the cosmological "constant" contributed either by bosons or fermions is time-dependent. The issues about the particle production of some background and about the UV structure are also commented. We argue that the effective higher derivative interactions are suppressed as long as the Fourier transform of the time-dependent coupling is UV-finite. Our result holds for scalar configurations that are BPS but with arbitrary time-dependence. This suggests the existence of non-renormalization theorem for such a new class of time-dependent theories. Altogether, it implies that such a super-Yang-Mills is scale-invariant, and that its dual bulk quantum gravity might behave regularly near the big bang.Comment: 20 pages, v2 add comments and references, v3 clarify BPS condition & add new discussion on particle production and UV structure, v4&v5 minor changes, final to JHE