Dual polyhedron

Combinatorics

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Geometry

Duality (order theory)

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Mathematical physics

Conformal map

Journal of High Energy Physics

A bstract The $$ T\overline{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> deformation of a conformal field theory has a dual description as a cutoff AdS 3 spacetime, at least at the level of pure 3d gravity. We generalize this deformation in such a way that it builds up a patch of bulk dS 3 spacetime instead. At each step along the trajectory in the space of 2 d theories, the theory is deformed by a specific combination of $$ T\overline{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> and the two-dimensional cosmological constant. This provides a concrete holographic dual for the warped throat on the gravity side of the dS/dS duality, at leading order in large central charge. We also analyze a sequence of excitations of this throat on both sides of the duality, as well as the entanglement entropy. Our results point toward a mechanism for obtaining de Sitter solutions starting from seed conformal field theories with AdS duals.

dS/dS and $$ T\overline{T} $$