108 research outputs found
Boundary operators in minimal Liouville gravity and matrix models
We interpret the matrix boundaries of the one matrix model (1MM) recently
constructed by two of the authors as an outcome of a relation among FZZT
branes. In the double scaling limit, the 1MM is described by the (2,2p+1)
minimal Liouville gravity. These matrix operators are shown to create a
boundary with matter boundary conditions given by the Cardy states. We also
demonstrate a recursion relation among the matrix disc correlator with two
different boundaries. This construction is then extended to the two matrix
model and the disc correlator with two boundaries is compared with the
Liouville boundary two point functions. In addition, the realization within the
matrix model of several symmetries among FZZT branes is discussed.Comment: 26 page
FZZT Brane Relations in the Presence of Boundary Magnetic Fields
We show how a boundary state different from the (1,1) Cardy state may be
realised in the (m,m+1) minimal string by the introduction of an auxiliary
matrix into the standard two hermitian matrix model. This boundary is a natural
generalisation of the free spin boundary state in the Ising model. The
resolvent for the auxiliary matrix is computed using an extension of the
saddle-point method of Zinn-Justin to the case of non-identical potentials. The
structure of the saddle-point equations result in a Seiberg-Shih like relation
between the boundary states which is valid away from the continuum limit, in
addition to an expression for the spectral curve of the free spin boundary
state. We then show how the technique may be used to analyse boundary states
corresponding to a boundary magnetic field, thereby allowing us to generalise
the work of Carroll et al. on the boundary renormalisation flow of the Ising
model, to any (m,m+1) model.Comment: 23 pages, 5 figures (3 new). Two new sections added giving examples
of the construction. Explanations clarified. Minor changes to the conclusion
but main results unchanged. Matches published versio
Beyond LLM in M-theory
The Lin, Lunin, Maldacena (LLM) ansatz in D = 11 supports two independent
Killing directions when a general Killing spinor ansatz is considered. Here we
show that these directions always commute, identify when the Killing spinors
are charged, and show that both their inner product and resulting geometry are
governed by two fundamental constants. In particular, setting one constant to
zero leads to AdS7 x S4, setting the other to zero gives AdS4 x S7, while flat
spacetime is recovered when both these constants are zero. Furthermore, when
the constants are equal, the spacetime is either LLM, or it corresponds to the
Kowalski-Glikman solution where the constants are simply the mass parameter.Comment: 1+30 pages, footnote adde
- …