5,802 research outputs found
Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
In the case of SU(2), associated by the AGT relation to the 2d Liouville
theory, the Seiberg-Witten prepotential is constructed from the Bohr-Sommerfeld
periods of 1d sine-Gordon model. If the same construction is literally applied
to monodromies of exact wave functions, the prepotential turns into the
one-parametric Nekrasov prepotential F(a,\epsilon_1) with the other epsilon
parameter vanishing, \epsilon_2=0, and \epsilon_1 playing the role of the
Planck constant in the sine-Gordon Shroedinger equation, \hbar=\epsilon_1. This
seems to be in accordance with the recent claim in arXiv:0908.4052 and poses a
problem of describing the full Nekrasov function as a seemingly straightforward
double-parametric quantization of sine-Gordon model. This also provides a new
link between the Liouville and sine-Gordon theories.Comment: 10 page
Is Strong Gravitational Radiation predicted by TeV-Gravity?
In TeV-gravity models the gravitational coupling to particles with energies
E\sim m_{Pl} \sim 10 TeV is not suppressed by powers of ultra-small ratio
E/M_{Pl} with M_{Pl} \sim 10^{19} GeV. Therefore one could imagine strong
synchrotron radiation of gravitons by the accelerating particles to become the
most pronounced manifestation of TeV-gravity at LHC. However, this turns out to
be not true: considerable damping continues to exist, only the place of
E/M_{Pl} it taken by a power of a ratio \theta\omega/E, where the typical
frequency \omega of emitted radiation, while increased by a number of
\gamma-factors, can not reach E/\vartheta unless particles are accelerated by
nearly critical fields. Moreover, for currently available magnetic fields B
\sim 10 Tesla, multi-dimensionality does not enhance gravitational radiation at
all even if TeV-gravity is correct.Comment: 7 pages, LaTe
Stabilization of dipole solitons in nonlocal nonlinear media
We address the stabilization of dipole solitons in nonlocal nonlinear
materials by two different approaches. First, we study the properties of such
solitons in thermal nonlinear media, where the refractive index landscapes
induced by laser beams strongly depend on the boundary conditions and on the
sample geometry. We show how the sample geometry impacts the stability of
higher-order solitons in thermal nonlinear media and reveal that dipole
solitons can be made dynami-cally stable in rectangular geometries in contrast
to their counterparts in thermal samples with square cross-section. Second, we
discuss the impact of the saturation of the nonlocal nonlinear response on the
properties of multipole solitons. We find that the saturable response also
stabi-lizes dipole solitons even in symmetric geometries, provided that the
input power exceeds a criti-cal value.Comment: 29 pages, 8 figures, to appear in Phys. Rev.
Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
The AGT relation identifies the Nekrasov functions for various N=2 SUSY gauge
theories with the 2d conformal blocks, which possess explicit Dotsenko-Fateev
matrix model (beta-ensemble) representations the latter being polylinear
combinations of Selberg integrals. The "pure gauge" limit of these matrix
models is, however, a non-trivial multiscaling large-N limit, which requires a
separate investigation. We show that in this pure gauge limit the Selberg
integrals turn into averages in a Brezin-Gross-Witten (BGW) model. Thus, the
Nekrasov function for pure SU(2) theory acquires a form very much reminiscent
of the AMM decomposition formula for some model X into a pair of the BGW
models. At the same time, X, which still has to be found, is the pure gauge
limit of the elliptic Selberg integral. Presumably, it is again a BGW model,
only in the Dijkgraaf-Vafa double cut phase.Comment: 21 page
Genus-one correction to asymptotically free Seiberg-Witten prepotential from Dijkgraaf-Vafa matrix model
We find perfect agreements on the genus-one correction to the prepotential of
SU(2) Seiberg-Witten theory with N_f=2, 3 between field theoretical and
Dijkgraaf-Vafa-Penner type matrix model results.Comment: 12 pages; v2: minor revision; v3: more structured, submitted versio
Generalized matrix models and AGT correspondence at all genera
We study generalized matrix models corresponding to n-point Virasoro
conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT
correspondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge
theories with generalized quiver diagrams. We obtain the generalized matrix
models from the perturbative evaluation of the Liouville correlation functions
and verify the consistency of the description with respect to degenerations of
the Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2
gauge theory as the spectral curve of the generalized matrix model, thus
providing a check of AGT correspondence at all genera.Comment: 19 pages; v2: version to appear in JHE
Hitchin Equation, Singularity, and N=2 Superconformal Field Theories
We argue that Hitchin's equation determines not only the low energy effective
theory but also describes the UV theory of four dimensional N=2 superconformal
field theories when we compactify six dimensional theory on a
punctured Riemann surface. We study the singular solution to Hitchin's equation
and the Higgs field of solutions has a simple pole at the punctures; We show
that the massless theory is associated with Higgs field whose residual is a
nilpotent element; We identify the flavor symmetry associated with the puncture
by studying the singularity of closure of the moduli space of solutions with
the appropriate boundary conditions. For the mass-deformed theory the residual
of the Higgs field is a semi-simple element, we identify the semi-simple
element by arguing that the moduli space of solutions of mass-deformed theory
must be a deformation of the closure of the moduli space of the massless
theory. We also study the Seiberg-Witten curve by identifying it as the
spectral curve of the Hitchin's system. The results are all in agreement with
Gaiotto's results derived from studying the Seiberg-Witten curve of four
dimensional quiver gauge theory.Comment: 42 pages, 20 figures, Hitchin's equation for N=2 theory is derived by
comparing different order of compactification of six dimensional theory on
T^2\times \Sigma. More discussion about flavor symmetries. Typos are
correcte
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