67 research outputs found
Liouville field theory with heavy charges. II. The conformal boundary case
We develop a general technique for computing functional integrals with fixed
area and boundary length constraints. The correct quantum dimensions for the
vertex functions are recovered by properly regularizing the Green function.
Explicit computation is given for the one point function providing the first
one loop check of the bootstrap formula.Comment: LaTeX 26 page
Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks
We construct, generalizing appropriately the method applied by J. Teschner in
the case of the Virasoro conformal blocks, the braiding and fusion matrices of
the Neveu-Schwarz super-conformal blocks. Their properties allow for an
explicit verification of the bootstrap equation in the NS sector of the N=1
supersymmetric Liouville field theory.Comment: 41 pages, 3 eps figure
Liouville Correlation Functions from Four-dimensional Gauge Theories
We conjecture an expression for the Liouville theory conformal blocks and
correlation functions on a Riemann surface of genus g and n punctures as the
Nekrasov partition function of a certain class of N=2 SCFTs recently defined by
one of the authors. We conduct extensive tests of the conjecture at genus 0,1.Comment: 32 pages, 8 figures; v2: minor corrections, published versio
D-branes and Closed String Field Theory
We construct BRST invariant solitonic states in the OSp invariant string
field theory for closed bosonic strings. Our construction is a generalization
of the one given in the noncritical case. These states are made by using the
boundary states for D-branes, and can be regarded as states in which D-branes
or ghost D-branes are excited. We calculate the vacuum amplitude in the
presence of solitons perturbatively and show that the cylinder amplitude for
the D-brane is reproduced. The results imply that these are states with even
number of D-branes or ghost D-branes.Comment: 36 pages, 3 figures, LaTeX; typos correcte
H(3)+ correlators from Liouville theory
We prove that arbitrary correlation functions of the H(3)+ model on a sphere
have a simple expression in terms of Liouville theory correlation functions.
This is based on the correspondence between the KZ and BPZ equations, and on
relations between the structure constants of Liouville theory and the H(3)+
model. In the critical level limit, these results imply a direct link between
eigenvectors of the Gaudin Hamiltonians and the problem of uniformization of
Riemann surfaces. We also present an expression for correlation functions of
the SL(2)/U(1) coset model in terms of correlation functions in Liouville
theory.Comment: 24 pages, v3: minor changes, references adde
ZZ brane amplitudes from matrix models
We study instanton contribution to the partition function of the one matrix
model in the k-th multicritical region, which corresponds to the (2,2k-1)
minimal model coupled to Liouville theory. The instantons in the one matrix
model are given by local extrema of the effective potential for a matrix
eigenvalue and identified with the ZZ branes in Liouville theory. We show that
the 2-instanton contribution in the partition function is universal as well as
the 1-instanton contribution and that the connected part of the 2-instanton
contribution reproduces the annulus amplitudes between the ZZ branes in
Liouville theory. Our result serves as another nontrivial check on the
correspondence between the instantons in the one matrix model and the ZZ branes
in Liouville theory, and also suggests that the expansion of the partition
function in terms of the instanton numbers are universal and gives
systematically ZZ brane amplitudes in Liouville theory.Comment: 29 pages, 4 figures; v2:how to scale x is generalized;
v3:introduction and the last section are revised, typos correcte
D-branes in Unoriented Non-critical Strings and Duality in SO(N) and Sp(N) Gauge Theories
We exhibit exact conformal field theory descriptions of SO(N) and Sp(N) pairs
of Seiberg-dual gauge theories within string theory. The N=1 gauge theories
with flavour are realized as low energy limits of the worldvolume theories on
D-branes in unoriented non-critical superstring backgrounds. These unoriented
backgrounds are obtained by constructing exact crosscap states in the
SL(2,R)/U(1) coset conformal field theory using the modular bootstrap method.
Seiberg duality is understood by studying the behaviour of the boundary and
crosscap states under monodromy in the closed string parameter space.Comment: 23 pages, 2 figure
Liouville Perturbation Theory
A comparison is made between proposals for the exact three point function in
Liouville quantum field theory and the nonperturbative weak coupling expansion
developed long ago by Braaten, Curtright, Ghandour, and Thorn. Exact agreement
to the order calculated (i.e. up to and including corrections of order
O(g^{10})) is found.Comment: 6 pages, LaTe
Liouville Field Theory on an Unoriented Surface
Liouville field theory on an unoriented surface is investigated, in
particular, the one point function on a RP^2 is calculated. The constraint of
the one point function is obtained by using the crossing symmetry of the two
point function. There are many solutions of the constraint and we can choose
one of them by considering the modular bootstrap.Comment: 13 pages, no figures, LaTeX, minor changes, equations in section 4
are correcte
The quantum dilogarithm and representations quantum cluster varieties
We construct, using the quantum dilogarithm, a series of *-representations of
quantized cluster varieties. This includes a construction of infinite
dimensional unitary projective representations of their discrete symmetry
groups - the cluster modular groups. The examples of the latter include the
classical mapping class groups of punctured surfaces.
One of applications is quantization of higher Teichmuller spaces.
The constructed unitary representations can be viewed as analogs of the Weil
representation. In both cases representations are given by integral operators.
Their kernels in our case are the quantum dilogarithms.
We introduce the symplectic/quantum double of cluster varieties and related
them to the representations.Comment: Dedicated to David Kazhdan for his 60th birthday. The final version.
To appear in Inventiones Math. The last Section of the previous versions was
removed, and will become a separate pape
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