1,405 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
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
Four-point function in Super Liouville Gravity
We consider the 2D super Liouville gravity coupled to the minimal
superconformal theory. We analyze the physical states in the theory and give
the general form of the n-point correlation numbers on the sphere in terms of
integrals over the moduli space. The three-point correlation numbers are
presented explicitly. For the four-point correlators, we show that the integral
over the moduli space reduces to the boundary terms if one of the fields is
degenerate. It turns out that special logarithmic fields are relevant for
evaluating these boundary terms. We discuss the construction of these fields
and study their operator product expansions. This analysis allows evaluating
the four-point correlation numbers. The derivation is analogous to the one in
the bosonic case and is based on the recently derived higher equations of
motion of the super Liouville field theory.Comment: 25 pages, references adde
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
Holographic duals of large-c torus conformal blocks
We study CFT2 conformal blocks on a torus and their holographic realization.
The classical conformal blocks arising in the regime where conformal dimensions
grow linearly with the large central charge are shown to be holographically
dual to the geodesic networks stretched in the thermal AdS bulk space. We
discuss the n-point conformal blocks and their duals, the 2-point case is
elaborated in full detail. We develop various techniques to calculate both
quantum and classical conformal block functions. In particular, we show that
exponentiated global torus blocks reproduce classical torus blocks in the
specific perturbative regimes of the conformal parameter space.Comment: 37 pages, v2: more comments, Appendix E --> Section 7.1, refs added,
journal versio
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