Abstract
Abstract By using the matrix model representation, we show that correlation numbers of boundary-changing operators (BCOs) in $(2,2p+1)$ minimal Liouville gravity satisfy some identities, which we call the null identities. These identities enable us to express the correlation numbers of BCOs in terms of those of boundary-preserving operators. We also discuss a physical implication of the null identities as the manifestation of the boundary interaction.
Highlights
The 2-dimensional gravity coupled with a minimal model of CFT has been studied as a good example of well-defined quantum gravitational theories [1], which allows a non-perturbative discrete formulation given by matrix models [2, 3, 4, 5]
We demonstrate that the correlation numbers of boundary changing operators (BCO) satisfy some nontrivial identities, which we call null identities
We considered correlation numbers of boundary changing and preserving operators in the
Summary
The 2-dimensional gravity coupled with a minimal model of CFT has been studied as a good example of well-defined quantum gravitational theories [1], which allows a non-perturbative discrete formulation given by matrix models [2, 3, 4, 5]. Where fm′ 1 and fm′ 2 are new polynomials of M with degree m1 and m2, respectively This shows that the sources of BCOs, which were originally encoded in the coefficients of gm1m2(M ), are redundant and can be absorbed into the redefinitions of the sources of the boundary preserving operators in fm and fm. In terms of the original parametrization, this implies that there exist differentials ∇n (n = 1, 2, · · · , min(m1, m2)) such that they are given by linear combinations of the derivatives of the sources and satisfy ∇n(Fm1m2) = 0 This is the simplest example of what we call the null identities. We present the case with three boundary parameters in some detail
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