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Register a new userA Duality in Two-Dimensional Gravity
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We demonstrate an equivalence between two integrable flows defined in a polynomial ring quotiented by an ideal generated by a polynomial. This duality of integrable systems allows us to systematically exploit the Korteweg-de Vries hierarchy and its tau-function to propose amplitudes for non-compact topological gravity on Riemann surfaces of arbitrary genus. We thus quantise topological gravity coupled to non-compact topological matter and demonstrate that this phase of topological gravity at N=2 matter central charge larger than three is equivalent to the phase with matter of central charge smaller than three.
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We propose a new type of gauge in two-dimensional quantum gravity. We investigate pure gravity in this gauge, and find that the system reduces to quantum mechanics of loop length $l$. Furthermore, we rederive the $c!=!0$ string field theory which was discovered recently. In particular, the pregeometric form of the Hamiltonian is naturally reproduced.
We show that string theory on a compact negatively curved manifold, preserving a U(1)^{b_1} winding symmetry, grows at least b_1 new effective dimensions as the space shrinks. The winding currents yield a D-dual description of a Riemann surface of genus h in terms of its 2h dimensional Jacobian torus, perturbed by a closed string tachyon arising as a potential energy term in the worldsheet sigma model. D-branes on such negatively curved manifolds also reveal this structure, with a classical moduli space consisting of a b_1-torus. In particular, we present an AdS/CFT system which offers a non-perturbative formulation of such supercritical backgrounds. Finally, we discuss generalizations of this new string duality.
In this work, kinks with non-canonical kinetic energy terms are studied in a type of two-dimensional dilaton gravity model. The linear stability issue is generally discussed for arbitrary static solutions with the aid of supersymmetric quantum mechanics theory, and the stability criteria are obtained. As an explicit example, a model with cuscuton term is studied. After rewriting the equations of motion into simpler first-order formalism and choosing a polynomial superpotential, an exact self-gravitating kink solution is obtained. The impacts of the cuscuton term are discussed.
We consider correlation functions of operators and the operator product expansion in two-dimensional quantum gravity. First we introduce correlation functions with geodesic distances between operators kept fixed. Next by making two of the operators closer, we examine if there exists an analog of the operator product expansion in ordinary field theories. Our results suggest that the operator product expansion holds in quantum gravity as well, though special care should be taken regarding the physical meaning of fixing geodesic distances on a fluctuating geometry.
The BFSS matrix model provides an example of gauge-theory / gravity duality where the gauge theory is a model of ordinary quantum mechanics with no spatial subsystems. If there exists a general connection between areas and entropies in this model similar to the Ryu-Takayanagi formula, the entropies must be more general than the usual subsystem entanglement entropies. In this note, we first investigate the extremal surfaces in the geometries dual to the BFSS model at zero and finite temperature. We describe a method to associate regulated areas to these surfaces and calculate the areas explicitly for a family of surfaces preserving $SO(8)$ symmetry, both at zero and finite temperature. We then discuss possible entropic quantities in the matrix model that could be dual to these regulated areas.
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