1,470 research outputs found
Frobenius manifolds, Integrable Hierarchies and Minimal Liouville Gravity
We use the connection between the Frobrenius manifold and the Douglas string
equation to further investigate Minimal Liouville gravity. We search a solution
of the Douglas string equation and simultaneously a proper transformation from
the KdV to the Liouville frame which ensure the fulfilment of the conformal and
fusion selection rules. We find that the desired solution of the string
equation has explicit and simple form in the flat coordinates on the Frobenious
manifold in the general case of (p,q) Minimal Liouville gravity.Comment: 17 pages; v2: typos removed, some comments added, minor correction
Torus Amplitudes in Minimal Liouville Gravity and Matrix Models
We evaluate one-point correlation numbers on the torus in the Liouville
theory coupled to the conformal matter M(2,2p+1). We find agreement with the
recent results obtained in the matrix model approach.Comment: 10 page
Geodesic description of Heavy-Light Virasoro blocks
We continue to investigate the dual description of the Virasoro conformal
blocks arising in the framework of the classical limit of the AdS/CFT
correspondence. To give such an interpretation in previous studies, certain
restrictions were necessary. Our goal here is to consider more general
situation available through the worldline approximation to the dual AdS
gravity. Namely, we are interested in computing the spherical conformal blocks
without the previously imposed restrictions on the conformal dimensions of the
internal channels. The duality is realised as an equality of the so-called
heavy-light limit of the n-point conformal block and the action of n-2
particles propagating in some AdS-like background with either a conical
singularity or a BTZ black hole. We describe a procedure that allows relaxing
the constraint on the intermediate channels. To obtain an explicit expression
for the conformal block on the CFT side, we use a recently proposed recursion
procedure and find full agreement between the results of the boundary and bulk
computations.Comment: 13 pages, v3: refs added, typos remove
Conformal blocks of W_N Minimal Models and AGT correspondence
We study the AGT correspondence between four-dimensional supersymmetric gauge
field theory and two-dimensional conformal field theories in the context of W_N
minimal models. The origin of the AGT correspondence is in a special integrable
structure which appears in the properly extended conformal theory. One of the
basic manifestations of this integrability is the special orthogonal basis
which arises in the extended theory. We propose modification of the AGT
representation for the W_N conformal blocks in the minimal models. The
necessary modification is related to the reduction of the orthogonal basis.
This leads to the explicit combinatorial representation for the conformal
blocks of minimal models and employs the sum over N-tupels of Young diagrams
with additional restrictions.Comment: 16 pages; v2: typos removed, more comments, references added; v3:
minor corrections, references added, JHEP versio
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