The Virasoro minimal string

Abstract

We introduce a critical string theory in two dimensions and demonstrate that this theory, viewed as two-dimensional quantum gravity on the worldsheet, is equivalent to a double-scaled matrix integral. The worldsheet theory consists of Liouville CFT with central charge c≥≥ 25 coupled to timelike Liouville CFT with central charge 26-c. The double-scaled matrix integral has as its leading density of states the universal Cardy density of primaries in a two-dimensional CFT, thus motivating the name Virasoro minimal string. The duality holds for any value of the continuous parameter cc and reduces to the JT gravity/matrix integral duality in the large central charge limit. It thus provides a precise stringy realization of JT gravity. The main observables of the Virasoro minimal string are quantum analogues of the Weil-Petersson volumes, which are computed as absolutely convergent integrals of worldsheet CFT correlators over the moduli space of Riemann surfaces. By exploiting a relation of the Virasoro minimal string to three-dimensional gravity and intersection theory on the moduli space of Riemann surfaces, we are able to give a direct derivation of the duality. We provide many checks, such as explicit numerical - and in special cases, analytic - integration of string diagrams, the identification of the CFT boundary conditions with asymptotic boundaries of the two-dimensional spacetime, and the matching between the leading non-perturbative corrections of the worldsheet theory and the matrix integral. As a byproduct, we discover natural conformal boundary conditions for timelike Liouville CFT.

Engineering perturbative string duals for symmetric product orbifold CFTs

“…(2.21) 6 As we have pointed out in a footnote for eq. (2.13), the number R0 can also come out to be half-integer.…”

“…In this case the best studied examples involve Jackiw-Teitelboom (JT) gravity or deformations thereof on the dual side. In particular, the holographic relation between a new critical string theory, dubbed the Virasoro minimal string, and certain double scaled matrix integrals was recently proven in [6]. This includes the famous duality between JT gravity and matrix integrals of Saad et.…”

“…As was discussed in some detail also in [12], this condition is only satisfied for s even in case the quantity R 0 is integer. 6 The expression we displayed still contains an integration over the insertion points y a of the perturbing operator of the orbifold model. The integrand, on the other hand, does no longer depend on the y a explicitly, but only implicitly through the locations z ν and u a of the branch points on Σ 0 as well as through the functions ãΓ ν , bΓ a and ξ j .…”