691 research outputs found
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
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
Alloys in catalysis: phase separation and surface segregation phenomena in response to the reactive environment
Alloys play a crucial role in several heterogeneous catalytic processes, and their applications are expected to rise rapidly. This is essentially related to the vast number of configurations and type of surface sites that multi-component materials can afford. It is well established that the chemical composition at the surface of an alloy usually differs from that in the bulk. This phenomenon, referred to as surface segregation, is largely controlled by the surface free energy. However, surface energy alone cannot safely predict the active surface state of a solid catalyst, since the contribution of other parameters such as size and support effects, as well as influence of the adsorbates, play a major role. This can lead to numerous surface configurations as for example over the length of a catalytic reactor, as the chemical potential of the gas phase changes continuously over the catalyst bed and hence different reactions may prevail at different catalyst bed segments. Thanks to the rapid improvement of the analytical surface science characterization techniques and theoretical methodologies, the potential effects induced by alloyed catalysts are better understood. For catalysis, the relevance of measurements performed on well-defined surfaces under idealized ultrahigh vacuum conditions has been questioned and studies in environments that closely resemble conditions of working alloy catalysts are needed. In this review we focus on experimental and theoretical studies related to in situ (operando) observations of surface segregation and phase separation phenomena taking place on the outermost surface layers of alloy catalysts. The combination of first principles theoretical treatment and in situ observation opens up new perspectives of designing alloy catalysts with tailored properties
Analytic Continuation of Liouville Theory
Correlation functions in Liouville theory are meromorphic functions of the
Liouville momenta, as is shown explicitly by the DOZZ formula for the
three-point function on the sphere. In a certain physical region, where a real
classical solution exists, the semiclassical limit of the DOZZ formula is known
to agree with what one would expect from the action of the classical solution.
In this paper, we ask what happens outside of this physical region. Perhaps
surprisingly we find that, while in some range of the Liouville momenta the
semiclassical limit is associated to complex saddle points, in general
Liouville's equations do not have enough complex-valued solutions to account
for the semiclassical behavior. For a full picture, we either must include
"solutions" of Liouville's equations in which the Liouville field is
multivalued (as well as being complex-valued), or else we can reformulate
Liouville theory as a Chern-Simons theory in three dimensions, in which the
requisite solutions exist in a more conventional sense. We also study the case
of "timelike" Liouville theory, where we show that a proposal of Al. B.
Zamolodchikov for the exact three-point function on the sphere can be computed
by the original Liouville path integral evaluated on a new integration cycle.Comment: 86 pages plus appendices, 9 figures, minor typos fixed, references
added, more discussion of the literature adde
Loop and surface operators in N=2 gauge theory and Liouville modular geometry
Recently, a duality between Liouville theory and four dimensional N=2 gauge
theory has been uncovered by some of the authors. We consider the role of
extended objects in gauge theory, surface operators and line operators, under
this correspondence. We map such objects to specific operators in Liouville
theory. We employ this connection to compute the expectation value of general
supersymmetric 't Hooft-Wilson line operators in a variety of N=2 gauge
theories.Comment: 60 pages, 11 figures; v3: further minor corrections, published
versio
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
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
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
AGT on the S-duality Wall
Three-dimensional gauge theory T[G] arises on a domain wall between
four-dimensional N=4 SYM theories with the gauge groups G and its S-dual G^L.
We argue that the N=2^* mass deformation of the bulk theory induces a
mass-deformation of the theory T[G] on the wall. The partition functions of the
theory T[SU(2)] and its mass-deformation on the three-sphere are shown to
coincide with the transformation coefficient of Liouville one-point conformal
block on torus under the S-duality.Comment: 14 pages, 3 figures. v2: Revised the analysis in sections 3.3 and 4.
Notes and references added. Version to appear in JHE
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
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