1,016 research outputs found
Non-perturbative effects in the BMN limit of N=4 supersymmetric Yang-Mills
One-instanton contributions to the correlation functions of two
gauge-invariant single-trace operators in N=4 SU(N) Yang-Mills theory are
studied in semi-classical approximation in the BMN limit. The most
straightforward examples involve operators with four bosonic impurities. The
explicit form for the correlation functions, which determine the anomalous
dimensions, follows after integration over the large number of bosonic and
fermionic moduli. Our results demonstrate that the instanton contributions
scale appropriately in the BMN limit. We find impressive agreement with the
D-instanton contributions to mass matrix elements of the dual plane-wave IIB
superstring theory, obtained in a previous paper. Not only does the dependence
on the scaled coupling constants match, but the dependence on the mode numbers
of the states is also in striking agreement.Comment: 52 pages, no figures, latex; V2: minor change
Calculating the Prepotential by Localization on the Moduli Space of Instantons
We describe a new technique for calculating instanton effects in
supersymmetric gauge theories applicable on the Higgs or Coulomb branches. In
these situations the instantons are constrained and a potential is generated on
the instanton moduli space. Due to existence of a nilpotent fermionic symmetry
the resulting integral over the instanton moduli space localizes on the
critical points of the potential. Using this technology we calculate the one-
and two-instanton contributions to the prepotential of SU(N) gauge theory with
N=2 supersymmetry and show how the localization approach yields the prediction
extracted from the Seiberg-Witten curve. The technique appears to extend to
arbitrary instanton number in a tractable way.Comment: 24 pages, JHEP.cls, more references and extra discussion on N_F=2N
cas
Instanton counting, Macdonald function and the moduli space of D-branes
We argue the connection of Nekrasov's partition function in the \Omega
background and the moduli space of D-branes, suggested by the idea of geometric
engineering and Gopakumar-Vafa invariants. In the instanton expansion of N=2
SU(2) Yang-Mills theory the Nakrasov's partition function with equivariant
parameters \epsilon_1, \epsilon_2 of toric action on C^2 factorizes correctly
as the character of SU(2)_L \times SU(2)_R spin representation. We show that up
to two instantons the spin contents are consistent with the Lefschetz action on
the moduli space of D2-branes on (local) F_0. We also present an attempt at
constructing a refined topological vertex in terms of the Macdonald function.
The refined topological vertex with two parameters of T^2 action allows us to
obtain the generating functions of equivariant \chi_y and elliptic genera of
the Hilbert scheme of n points on C^2 by the method of topological vertex.Comment: 33 pages, 2 figures, (v2) minor changes, references added, (v3)
Comments and more references adde
Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
Gapped ground states of quantum spin systems have been referred to in the
physics literature as being `in the same phase' if there exists a family of
Hamiltonians H(s), with finite range interactions depending continuously on , such that for each , H(s) has a non-vanishing gap above its
ground state and with the two initial states being the ground states of H(0)
and H(1), respectively. In this work, we give precise conditions under which
any two gapped ground states of a given quantum spin system that 'belong to the
same phase' are automorphically equivalent and show that this equivalence can
be implemented as a flow generated by an -dependent interaction which decays
faster than any power law (in fact, almost exponentially). The flow is
constructed using Hastings' 'quasi-adiabatic evolution' technique, of which we
give a proof extended to infinite-dimensional Hilbert spaces. In addition, we
derive a general result about the locality properties of the effect of
perturbations of the dynamics for quantum systems with a quasi-local structure
and prove that the flow, which we call the {\em spectral flow}, connecting the
gapped ground states in the same phase, satisfies a Lieb-Robinson bound. As a
result, we obtain that, in the thermodynamic limit, the spectral flow converges
to a co-cycle of automorphisms of the algebra of quasi-local observables of the
infinite spin system. This proves that the ground state phase structure is
preserved along the curve of models .Comment: Updated acknowledgments and new email address of S
The Uncertainty in Newton's Constant and Precision Predictions of the Primordial Helium Abundance
The current uncertainty in Newton's constant, G_N, is of the order of 0.15%.
For values of the baryon to photon ratio consistent with both cosmic microwave
background observations and the primordial deuterium abundance, this
uncertainty in G_N corresponds to an uncertainty in the primordial 4He mass
fraction, Y_P, of +-1.3 x 10^{-4}. This uncertainty in Y_P is comparable to the
effect from the current uncertainty in the neutron lifetime, which is often
treated as the dominant uncertainty in calculations of Y_P. Recent measurements
of G_N seem to be converging within a smaller range; a reduction in the
estimated error on G_N by a factor of 10 would essentially eliminate it as a
source of uncertainty in the calculation of the primordial 4He abundance.Comment: 3 pages, no figures, fixed typos, to appear in Phys. Rev.
A new bio-geomorphic model approach accounting for subgrid-scale heterogeneity of biogenic structures
Propagators in Noncommutative Instantons
We explicitly construct Green functions for a field in an arbitrary
representation of gauge group propagating in noncommutative instanton
backgrounds based on the ADHM construction. The propagators for spinor and
vector fields can be constructed in terms of those for the scalar field in
noncommutative instanton background. We show that the propagators in the
adjoint representation are deformed by noncommutativity while those in the
fundamental representation have exactly the same form as the commutative case.Comment: 28 pages, Latex, v2: A few typos correcte
Zero Modes and the Atiyah-Singer Index in Noncommutative Instantons
We study the bosonic and fermionic zero modes in noncommutative instanton
backgrounds based on the ADHM construction. In k instanton background in U(N)
gauge theory, we show how to explicitly construct 4Nk (2Nk) bosonic (fermionic)
zero modes in the adjoint representation and 2k (k) bosonic (fermionic) zero
modes in the fundamental representation from the ADHM construction. The number
of fermionic zero modes is also shown to be exactly equal to the Atiyah-Singer
index of the Dirac operator in the noncommutative instanton background. We
point out that (super)conformal zero modes in non-BPS instantons are affected
by the noncommutativity. The role of Lorentz symmetry breaking by the
noncommutativity is also briefly discussed to figure out the structure of U(1)
instantons.Comment: v3: 24 pages, Latex, corrected typos, references added, to appear in
Phys. Rev.
Searching for a Cosmological Preferred Axis: Union2 Data Analysis and Comparison with Other Probes
We review, compare and extend recent studies searching for evidence for a
preferred cosmological axis. We start from the Union2 SnIa dataset and use the
hemisphere comparison method to search for a preferred axis in the data. We
find that the hemisphere of maximum accelerating expansion rate is in the
direction (\omm=0.19) while the hemisphere of
minimum acceleration is in the opposite direction
(\omm=0.30). The level of anisotropy is described by the normalized
difference of the best fit values of \omm between the two hemispheres in the
context of \lcdm fits. We find a maximum anisotropy level in the Union2 data of
\frac{\Delta \ommax}{\bomm}=0.43\pm 0.06. Such a level does not necessarily
correspond to statistically significant anisotropy because it is reproduced by
about of simulated isotropic data mimicking the best fit Union2 dataset.
However, when combined with the axes directions of other cosmological
observations (bulk velocity flow axis, three axes of CMB low multipole moments
and quasar optical polarization alignment axis), the statistical evidence for a
cosmological anisotropy increases dramatically. We estimate the probability
that the above independent six axes directions would be so close in the sky to
be less than . Thus either the relative coincidence of these six axes is a
very large statistical fluctuation or there is an underlying physical or
systematic reason that leads to their correlation.Comment: 10 pages, 7 figures. Accepted in JCAP (to appear). Extended analysis
with redshift tomography of SnIa, included errorbars and increased number of
axes. The Mathematica 7 files with the data used for the production of the
figures along with a Powerpoint file with additional figures may be
downloaded from http://leandros.physics.uoi.gr/anisotrop
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