Physical States, Factorization and Nonlinear Structures in Two Dimensional Quantum Gravity

Abstract

The nonlinear structures in 2D quantum gravity coupled to the $(q+1,q)$ minimal model are studied in the Liouville theory to clarify the factorization and the physical states. It is confirmed that the dressed primary states outside the minimal table are identified with the gravitational descendants. Using the discrete states of ghost number zero and one we construct the currents and investigate the Ward identities which are identified with the W and the Virasoro constraints. As nontrivial examples we derive the $L_0$, $L_1$ and $W_{-1}^{(3)}$ equations exactly. $L_n$ and $W_n^{(k)}$ equations are also discussed. We then explicitly show the decoupling of the edge states $O_j(j=0\mathrm{mod}q)$. We consider the interaction theory perturbed by the cosmological constant $O_1$ and the screening charge $S^{+}=O_{2q+1}$. The formalism can be easily generalized to potential models other than the screening charge.

18 pages, LaTex, YITP/U-93-28

References in corpus (7)

• Interaction of Discrete States in Two-Dimensional String Theory
• BRST Analysis of Physical States for 2D (Super) Gravity Coupled to (Super) Conformal Matter
• Ward Identities in Two-Dimensional String Theory
• Brst Cohomology and Physical States in 2D Supergravity Coupled to $\hat{c}\le 1$ Matter
• Quantum Theory of Dilaton Gravity in 1+1 Dimensions
• Quantum Gravity and Black Hole Dynamics in 1+1 Dimensions
• Ward Identities of Liouville Gravity coupled to Minimal Conformal Matter

Cited by in corpus (3)

• On the equivalence of fermionic string to bosonic string in two dimensions
• Ward Identities of W_{\infty} Symmetry and Higher Genus Amplitudes in 2D String Theory
• Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules