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 $s \in [0,1]$, such that for each $s$, 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 $s$-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 $H(s), 0\leq s\leq 1$.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.

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 $(l,b)=({309^\circ}^{+23^\circ}_{-3^\circ}, {18^\circ}^{+11^\circ}_{-10^\circ})$ (\omm=0.19) while the hemisphere of minimum acceleration is in the opposite direction $(l,b)=({129^\circ}^{+23^\circ}_{-3^\circ},{-18^\circ}^{+10^\circ}_{-11^\circ})$ (\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 $30$ 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 $1$. 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