Noncritical String Field Theory for 2d Quantum Gravity Coupled to (p, q)-Conformal Fields

Abstract

We propose a non-critical string field theory for 2d quantum gravity coupled to (p,q) conformal fields. The Hamiltonian is described by the generators of the W p algebra, and the Schwinger-Dyson equation is equivalent to a vacuum condition imposed on the generators of W p algebra.

The two-point function of c = −2 matter coupled to 2D quantum gravity

“…Secondly, additional assumptions about the field content go into the formal derivation of (1.2) and in particular, the identification of the proper time T of the string field Hamiltonian as the geodesic distance becomes questionable. We shall return to this point later, see also reference [9]. In this paper we determine the two-point function in the case where c = −2 matter is coupled to quantum gravity.…”

CDT and the Big Bang

“…The normal ordering :(·): refers to the α n operators (α n to the left of α m for n > m. This ordering is opposite to the one conventionally used. See [3] for the motivation for such a choice). We then define the "absolute vacuum" |0 by the following condition:…”

“…String field theory is notoriously complicated, but so-called non-critical string field theory [1,2,3] is a lot simpler. An even simpler version is the so-called CDT string field theory [4].…”

Loop equations for loops with Ising spins either all up or all down inc=12noncritical string theory

“…Let the geodesic distance between this point and the two boundaries be D 1 and D 2 (D 1 + D 2 = D). After the two loops meet at a point, they 7 Similar Hamiltonian is constructed by a different method in [24]. Main difference between our Hamiltonian and theirs is that their Hamiltonian does not contain terms corresponding to the singular terms of one-and two-loop amplitudes.…”