Instantons, finite N=2 Sp(N) theories and the AdS/CFT correspondence

We examine ADHM multi-instantons in the conformal N=2 supersymmetric Sp(N) gauge theory with one anti-symmetric tensor and four fundamental hypermultiplets. We argue that the ADHM construction and measure can also be deduced from purely field theoretic considerations and also from the dynamics of D-instantons in the presence of D3-branes, D7-branes and an orientifold O7-plane. The measure then admits a large-N saddle-point approximation where the D3-branes disappear but the background is changed to AdS_5 x S^5/Z_2, as expected on the basis of the AdS/CFT correspondence. The large-N measure displays the fractionation of D-instantons at the singularity S^3 in S^5/Z_2 and is described for instanton number k by a certain O(k) matrix model.Comment: 16 pages, jhep.cl

Semi-classical decay of monopoles in N=2 gauge theory

It is shown how monopoles and dyons decay on curves of marginal stability in the moduli space of vacua at weak coupling in pure N=2 gauge theory with arbitrary gauge group. The analysis involves a semi-classical treatment of the monopole and rests on the fact that the monopole moduli space spaces for a magnetic charge vector equal to a non-simple root enlarge discontinuously at the curves of marginal stability. This enlargement of the moduli space describes the freedom for the monopole to be separated into stable constituent monopoles. Such decays do not occur in the associated theory with N=4 supersymmetry because in this case there exist bound-states at threshold.Comment: 17 pages, plain tex with macro included. Minor changes, more references include

Strong Coupling N=2 Gauge Theory with Arbitrary Gauge Group

A complete definition of the cycles, on the auxiliary Riemann surface defined by Martinec and Warner for describing pure N=2 gauge theories with arbitrary group, is provided. The strong coupling monodromies around the vanishing cycles are shown to arise from a set of dyons which becomes massless at the singularities. It is shown how the correct weak coupling monodromies are reproduced and how the dyons have charges which are consistent with the spectrum that can be calculated at weak coupling using conventional semi-classical methods. In particular, the magnetic charges are co-root vectors as required by the Dirac-Schwinger-Zwanziger quantization condition.Comment: 18 Pages, Latex (amstex package), 4 figures included with eps

Vacua of N=1 Supersymmetric QCD from Spin Chains and Matrix Models

We consider the vacuum structure of the finite N=2 theory with N_f=2N fundamental hypermultiplets broken to N=1 by a superpotential for the adjoint chiral multiplet. We do this in two ways: firstly, by compactification to three dimensions, in which case the effective superpotential is the Hamiltonian of an integrable spin chain. In the second approach, we consider the Dijkgraaf-Vafa holomorphic matrix model. We prove that the two approaches agree as long as the couplings of the two theories are related in a particular way involving an infinite series of instanton terms. The case of gauge group SU(2) with N_f=4 is considered in greater detail.Comment: 28 pages, 2 figure

Tau-Functions and Generalized Integrable Hierarchies

The tau-function formalism for a class of generalized ``zero-curvature'' integrable hierarchies of partial differential equations, is constructed. The class includes the Drinfel'd-Sokolov hierarchies. A direct relation between the variables of the zero-curvature formalism and the tau-functions is established. The formalism also clarifies the connection between the zero-curvature hierarchies and the Hirota-type hierarchies of Kac and Wakimoto.Comment: 23 page

A Comment on the chi_y Genus and Supersymmetric Quantum Mechanics

In this note we show that a simple modification of supersymmetric quantum mechanics involving a mass term for half the fermions naturally leads to a derivation of the integral formula for the chi_y genus, a quantity that interpolates between the Euler characteristic and arithmetic genus. We note that this modification naturally arises in the moduli space dynamics of monopoles or instantons in theories with 16 supercharges partially broken to 8 supercharges by mass terms.Comment: 6 pages, JHEP, References adde

The Effect of Gravitational Tidal Forces on Vacuum Polarization: How to Undress a Photon

The effect of gravitational tidal forces on photon propagation in curved spacetime is investigated. It is found that the imaginary part of the local refractive index Im n(u;w) may be negative as well as positive, corresponding to a local amplification as well as attenuation of the amplitude of the renormalized photon field. This is interpreted in terms of the effect of tidal forces on the virtual e^+e^- cloud surrounding the bare photon field---a positive/negative Im n(u;w) corresponds to an increased dressing/undressing of the bare photon. Below threshold decays of the photon to e^+e^- pairs can occur. Photon undressing in the vicinity of a black hole singularity is described as an example. These results are shown to be consistent with unitarity and the optical theorem in curved spacetime, which is derived here both in a local form and integrated over the photon trajectory.Comment: 13 pages, 1 figure, minor correction

The Unbearable Beingness of Light, Dressing and Undressing Photons in Black Hole Spacetimes

Gravitational tidal forces acting on the virtual e+ e- cloud surrounding a photon endow spacetime with a non-trivial refractive index. This has remarkable properties unique to gravitational theories including superluminal low-frequency propagation, in apparent violation of causality, and amplification of the renormalized photon field, in apparent violation of unitarity. Using the geometry of null congruences and the Penrose limit, we illustrate these phenomena and their resolution by tracing the history of a photon as it falls into the near-singularity region of a black hole.Comment: 8 pages, Essay awarded third prize in the Gravity Research Foundation essay competition 201

Causality and Micro-Causality in Curved Spacetime

We consider how causality and micro-causality are realised in QED in curved spacetime. The photon propagator is found to exhibit novel non-analytic behaviour due to vacuum polarization, which invalidates the Kramers-Kronig dispersion relation and calls into question the validity of micro-causality in curved spacetime. This non-analyticity is ultimately related to the generic focusing nature of congruences of geodesics in curved spacetime, as implied by the null energy condition, and the existence of conjugate points. These results arise from a calculation of the complete non-perturbative frequency dependence of the vacuum polarization tensor in QED, using novel world-line path integral methods together with the Penrose plane-wave limit of spacetime in the neighbourhood of a null geodesic. The refractive index of curved spacetime is shown to exhibit superluminal phase velocities, dispersion, absorption (due to \gamma \to e^+e^-) and bi-refringence, but we demonstrate that the wavefront velocity (the high-frequency limit of the phase velocity) is indeed c, thereby guaranteeing that causality itself is respected.Comment: 16 pages, 11 figures, JHEP3, microcausality now shown to be respected even when the Kramers-Kronig relation is violate

`Superluminal' Photon Propagation in QED in Curved Spacetime is Dispersive and Causal

It is now well-known that vacuum polarisation in QED can lead to superluminal low-frequency phase velocities for photons propagating in curved spacetimes. In a series of papers, we have shown that this quantum phenomenon is dispersive and have calculated the full frequency dependence of the refractive index, explaining in detail how causality is preserved and various familiar results from quantum field theory such as the Kramers-Kronig dispersion relation and the optical theorem are realised in curved spacetime. These results have been criticised in a recent paper by Akhoury and Dolgov arXiv:1003.6110 [hep-th], who assert that photon propagation is neither dispersive nor necessarily causal. In this note, we point out a series of errors in their work which have led to this false conclusion.Comment: 11 page