218 research outputs found
Two AdS2 branes in the Euclidean AdS3
We compute the density of open strings stretching between AdS2 branes in the
Euclidean AdS3. This is done by solving the factorization constraint of a
degenerate boundary field, and the result is checked by a Cardy-type
computation. We mention applications to branes in the Minkowskian AdS3 and its
cigar coset.Comment: 5 pages, some arguments clarified, version published in JHE
Boundary three-point function on AdS2 D-branes
Using the H3+-Liouville relation, I explicitly compute the boundary
three-point function on AdS2 D-branes in H3+, and check that it exhibits the
expected symmetry properties and has the correct geometrical limit. I then find
a simple relation between this boundary three-point function and certain fusing
matrix elements, which suggests a formal correspondence between the AdS2
D-branes and discrete representations of the symmetry group. Concluding
speculations deal with the fuzzy geometry of AdS2 D-branes, strings in the
Minkowskian AdS3, and the hypothetical existence of new D-branes in H3+.Comment: 27 pages, v2: significant clarifications added in sections 4.3 and
A family of solvable non-rational conformal field theories
We find non-rational conformal field theories in two dimensions, which are
solvable due to their correlators being related to correlators of Liouville
theory. Their symmetry algebra consists of the dimension-two stress-energy
tensor, and two dimension-one fields. The theories come in a family with two
parameters: the central charge c and a complex number m. The special case m=0
corresponds to Liouville theory (plus two free bosons), and m=1 corresponds to
the H3+ model. In the case m=2 we show that the correlators obey third-order
differential equations, which are associated to a subsingular vector of the
symmetry algebra.Comment: 14 pages, v2: role of subsingular vectors clarifie
Minisuperspace limit of the AdS3 WZNW model
We derive the three-point function of the AdS3 WZNW model in the
minisuperspace limit by Wick rotation from the H3+ model. The result is
expressed in terms of Clebsch-Gordan coefficients of the Lie algebra sl(2,R).
We also introduce a covariant basis of functions on AdS3, which can be
interpreted as bulk-boundary propagators.Comment: 19 pages, v2: added section 2.4 about the completeness of bases of
function
Some comments on Anti-de Sitter D-branes
We present some preliminary investigations about the AdS2*S2 D3-branes in
AdS3*S3. We analyse the quadratic fluctuations of Dirac-Born-Infeld action
around a given semi-classical D-brane configuration and compare them with
results obtained by using conformal field theory techniques. We finally study
classical motions of open strings attached to those D-branes and analyse the
role of the spectral flow in this context.Comment: 12 pages, no figure
On AGT description of N=2 SCFT with N_f=4
We consider Alday-Gaiotto-Tachikawa (AGT) realization of the Nekrasov
partition function of N=2 SCFT. We focus our attention on the SU(2) theory with
N_f=4 flavor symmetry, whose partition function, according to AGT, is given by
the Liouville four-point function on the sphere. The gauge theory with N_f=4 is
known to exhibit SO(8) symmetry. We explain how the Weyl symmetry
transformations of SO(8) flavor symmetry are realized in the Liouville theory
picture. This is associated to functional properties of the Liouville
four-point function that are a priori unexpected. In turn, this can be thought
of as a non-trivial consistency check of AGT conjecture. We also make some
comments on elementary surface operators and WZW theory.Comment: 18 pages. v2, a misinterpretation in the gauge theory side has been
corrected; title and introduction were changed accordingl
Winding Strings in AdS_3
Correlation functions of one unit spectral flowed states in string theory on
AdS_3 are considered. We present the modified Knizhnik-Zamolodchikov and null
vector equations to be satisfied by amplitudes containing states in winding
sector one and study their solution corresponding to the four point function
including one w=1 field. We compute the three point function involving two one
unit spectral flowed operators and find expressions for amplitudes of three w=1
states satisfying certain particular relations among the spins of the fields.
Several consistency checks are performed.Comment: 35 pages. v2. Important additions: one more author, complete results
for the 3-point function with two w=1 states and new section with computation
of 4-point function with one w=1 state. Acknowledgments and references
modifie
Continuously Crossing u=z in the H3+ Boundary CFT
For AdS boundary conditions, we give a solution of the H3+ two point function
involving degenerate field with SL(2)-label b^{-2}/2, which is defined on the
full (u,z) unit square. It consists of two patches, one for z<u and one for
u<z. Along the u=z "singularity", the solutions from both patches are shown to
have finite limits and are merged continuously as suggested by the work of
Hosomichi and Ribault. From this two point function, we can derive
b^{-2}/2-shift equations for AdS_2 D-branes. We show that discrete as well as
continuous AdS_2 branes are consistent with our novel shift equations without
any new restrictions.Comment: version to appear in JHEP - 12 pages now; sign error with impact on
some parts of the interpretation fixed; material added to become more
self-contained; role of bulk-boundary OPE in section 4 more carefully
discussed; 3 references adde
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