We propose a precise duality between pure de Sitter quantum gravity in 2+1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> dimensions and a double-scaled matrix integral. This duality unfolds in two distinct aspects. First, by carefully quantizing the gravitational phase space, we arrive at a novel proposal for the quantum state of the universe at future infinity. We compute cosmological correlato…

We propose a duality between the complex Liouville string and a two-matrix integral. The complex Liouville string is defined by coupling two Liouville theories with complex central charges c = 13 ± i \lambda <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>=</mml:mo> <mml:mn>13</mml:mn> <mml:mo>±</mml:mo> <mml:mi>i</mml:mi> <mml:mi>λ</mml:mi> </mml:mrow> </mml:math> on the worldsheet. The matrix integral is characterized by its spectral curve which al…

We introduce the complex Liouville string, a solvable string theory defined by coupling two Liouville theories with complex conjugate central charges <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>c</a:mi><a:mo>∈</a:mo><a:mn>13</a:mn><a:mo>+</a:mo><a:mi>i</a:mi><a:mi mathvariant="double-struck">R</a:mi></a:mrow></a:math> on the world sheet. We compute its amplitudes from first principles and establish a duality with a double-scaled two-matrix integral. We also analyze general w…

We introduce a new two-dimensional string theory defined by coupling two copies of Liouville CFT with complex central charge c=13± i \lambda <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>=</mml:mo> <mml:mn>13</mml:mn> <mml:mo>±</mml:mo> <mml:mi>i</mml:mi> <mml:mi>λ</mml:mi> </mml:mrow> </mml:math> on the worldsheet. This string theory defines a novel, consistent and controllable model of two-dimensional quantum gravity. We use the exact solution of…

We propose a precise duality between pure de Sitter quantum gravity in 2+1 dimensions and a double-scaled matrix integral. This duality unfolds in two distinct aspects. First, by carefully quantizing the gravitational phase space, we arrive at a novel proposal for the quantum state of the universe at future infinity. We compute cosmological correlators of massive particles in the universe specified by this wavefunction. Integrating these correlators over the metric at future infinity yields gauge-invariant observa…