Abstract
Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.
Highlights
Where the spacetime is allowed to change topology, has been recently solved to all orders in perturbation theory in the topological expansion [14]
We explore the physics of the deformations in the semi-classical gravity approximation, the leading behavior of the matrix model, and the full non-perturbative definition, contrasting the three approaches and identifying several phenomena
In ref. [25] an alternative matrix model definition of JT gravity was provided which is free from such instabilities and reproduces the perturbative physics of ref
Summary
The issue is solved by picking the (unique) solution to the implicit equation (1.6) that yields a single valued function u0(x) in the region x < 0 This modifies the leading spectral density from (1.5) to:. The issue originates in a multi-valued solution u0(x) to the leading genus string equation (1.9), but in this case in the region x < 0 (see figure 9). This makes the issue substantially different and results in a breakdown of the perturbative expansion of the matrix model. Several appendices contain details and results used in the main text
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