79 research outputs found
The conformal current algebra on supergroups with applications to the spectrum and integrability
We compute the algebra of left and right currents for a principal chiral
model with arbitrary Wess-Zumino term on supergroups with zero Killing form. We
define primary fields for the current algebra that match the affine primaries
at the Wess-Zumino-Witten points. The Maurer-Cartan equation together with
current conservation tightly constrain the current-current and current-primary
operator product expansions. The Hilbert space of the theory is generated by
acting with the currents on primary fields. We compute the conformal dimensions
of a subset of these states in the large radius limit. The current algebra is
shown to be consistent with the quantum integrability of these models to
several orders in perturbation theory.Comment: 45 pages. Minor correction
Random volumes from matrices
We propose a class of models which generate three-dimensional random volumes,
where each configuration consists of triangles glued together along multiple
hinges. The models have matrices as the dynamical variables and are
characterized by semisimple associative algebras A. Although most of the
diagrams represent configurations which are not manifolds, we show that the set
of possible diagrams can be drastically reduced such that only (and all of the)
three-dimensional manifolds with tetrahedral decompositions appear, by
introducing a color structure and taking an appropriate large N limit. We
examine the analytic properties when A is a matrix ring or a group ring, and
show that the models with matrix ring have a novel strong-weak duality which
interchanges the roles of triangles and hinges. We also give a brief comment on
the relationship of our models with the colored tensor models.Comment: 33 pages, 31 figures. Typos correcte
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
Boundary operators in minimal Liouville gravity and matrix models
We interpret the matrix boundaries of the one matrix model (1MM) recently
constructed by two of the authors as an outcome of a relation among FZZT
branes. In the double scaling limit, the 1MM is described by the (2,2p+1)
minimal Liouville gravity. These matrix operators are shown to create a
boundary with matter boundary conditions given by the Cardy states. We also
demonstrate a recursion relation among the matrix disc correlator with two
different boundaries. This construction is then extended to the two matrix
model and the disc correlator with two boundaries is compared with the
Liouville boundary two point functions. In addition, the realization within the
matrix model of several symmetries among FZZT branes is discussed.Comment: 26 page
The Impact of Non-Equipartition on Cosmological Parameter Estimation from Sunyaev-Zel'dovich Surveys
The collisionless accretion shock at the outer boundary of a galaxy cluster
should primarily heat the ions instead of electrons since they carry most of
the kinetic energy of the infalling gas. Near the accretion shock, the density
of the intracluster medium is very low and the Coulomb collisional timescale is
longer than the accretion timescale. Electrons and ions may not achieve
equipartition in these regions. Numerical simulations have shown that the
Sunyaev-Zel'dovich observables (e.g., the integrated Comptonization parameter
Y) for relaxed clusters can be biased by a few percent. The Y-mass relation can
be biased if non-equipartition effects are not properly taken into account.
Using a set of hydrodynamical simulations, we have calculated three potential
systematic biases in the Y-mass relations introduced by non-equipartition
effects during the cross-calibration or self-calibration when using the galaxy
cluster abundance technique to constraint cosmological parameters. We then use
a semi-analytic technique to estimate the non-equipartition effects on the
distribution functions of Y (Y functions) determined from the extended
Press-Schechter theory. Depending on the calibration method, we find that
non-equipartition effects can induce systematic biases on the Y functions, and
the values of the cosmological parameters Omega_8, sigma_8, and the dark energy
equation of state parameter w can be biased by a few percent. In particular,
non-equipartition effects can introduce an apparent evolution in w of a few
percent in all of the systematic cases we considered. Techniques are suggested
to take into account the non-equipartition effect empirically when using the
cluster abundance technique to study precision cosmology. We conclude that
systematic uncertainties in the Y-mass relation of even a few percent can
introduce a comparable level of biases in cosmological parameter measurements.Comment: 10 pages, 3 figures, accepted for publication in the Astrophysical
Journal, abstract abridged slightly. Typos corrected in version
Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
We investigate the asymptotic symmetry algebra of (2+1)-dimensional higher
spin, anti-de Sitter gravity. We use the formulation of the theory as a
Chern-Simons gauge theory based on the higher spin algebra hs(1,1). Expanding
the gauge connection around asymptotically anti-de Sitter spacetime, we specify
consistent boundary conditions on the higher spin gauge fields. We then study
residual gauge transformation, the corresponding surface terms and their
Poisson bracket algebra. We find that the asymptotic symmetry algebra is a
nonlinearly deformed W(infinity) algebra with classical central charges. We
discuss implications of our results to quantum gravity and to various
situations in string theory.Comment: 25 pages, no figure; v2. minor corrections, references added, v3.
JHEP published versio
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