Dimensional Mutation and Spacelike Singularities

Abstract

I argue that string theory compactified on a Riemann surface crosses over at small volume to a higher dimensional background of supercritical string theory. Several concrete measures of the count of degrees of freedom of the theory yield the consistent result that at finite volume, the effective dimensionality is increased by an amount of order $2h/V$ for a surface of genus $h$ and volume $V$ in string units. This arises in part from an exponentially growing density of states of winding modes supported by the fundamental group, and passes an interesting test of modular invariance. Further evidence for a plethora of examples with the spacelike singularity replaced by a higher dimensional phase arises from the fact that the sigma model on a Riemann surface can be naturally completed by many gauged linear sigma models, whose RG flows approximate time evolution in the full string backgrounds arising from this in the limit of large dimensionality. In recent examples of spacelike singularity resolution by tachyon condensation, the singularity is ultimately replaced by a phase with all modes becoming heavy and decoupling. In the present case, the opposite behavior ensues: more light degrees of freedom arise in the small radius regime. I comment on the emerging zoology of cosmological singularities that results.

15 pages, harvmac big. v2: 18 pages, harvmac big; added computation of density of states and modular invariance check, enhanced discussion of multiplicity of solutions all sharing the feature of increased density of states, added references

References in corpus (11)

• A Matrix Big Bang
• The Annular Report on Non-Critical String Theory
• de Sitter Space in Non-Critical String Theory
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• A New Handle on de Sitter Compactifications
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Cited by in corpus (31)

• String Cosmology: A Review
• Simple de Sitter Solutions
• Quantum Quench across a Holographic Critical Point
• The Inside Story: Quasilocal Tachyons and Black Holes
• Effective Dynamics of the Matrix Big Bang
• Cosmologies with Null Singularities and their Gauge Theory Duals
• Holographic Quantum Quench
• Inflection Point Inflation and Time Dependent Potentials in String Theory
• Matrix Membrane Big Bangs and D-brane Production
• Supercritical stability, transitions and (pseudo)tachyons
• A Short Review of Time Dependent Solutions and Space-like Singularities in String Theory
• New Dimensions for Wound Strings: The Modular Transformation of Geometry to Topology
• Pre-Inflationary Spacetime in String Cosmology
• New solutions with accelerated expansion in string theory
• D-instantons and Closed String Tachyons in Misner Space
• Les Houches lectures on inflationary observables and string theory
• Matrix Model in a Class of Time Dependent Supersymmetric Backgrounds
• Thermal AdS(3), BTZ and competing winding modes condensation
• String spectra near some null cosmological singularities
• Dimensional Duality
• Closed string tachyons, flips and conifolds
• Singularities and Closed String Tachyons
• Expanding F-Theory
• Bubbles Unbound: Bubbles of Nothing Without Kaluza-Klein
• Dynamical Cobordisms in General Relativity and String Theory
• Supercriticality of a Class of Critical String Cosmological Solutions
• The Geometry of The Entropic Principle and the Shape of the Universe
• Compactified Strings as Quantum Statistical Partition Function on the Jacobian Torus
• De Sitter Quantum Mechanics and Inflationary Matrix Cosmology of Self-tuned Universe
• A correspondence between strings in the Hagedorn phase and asymptotically de Sitter space
• Exact null tachyons from RG flows