Dynamic linear response of the SK spin glass coupled microscopically to a bath

The dynamic linear response theory of a general Ising model weakly coupled to a heat bath is derived employing the quantum statistical theory of Mori, treating the Hamiltonian of the spin bath coupling as a perturbation, and applying the Markovian approximation. Both the dynamic susceptibility and the relaxation function are expressed in terms of the static susceptibility and the static internal field distribution function. For the special case of the SK spin glass this internal field distribution can be related to the solutions of the TAP equations in the entire temperature region. Application of this new relation and the use of numerical solutions of the modified TAP equations leads for finite but large systems to explicit results for the distribution function and for dynamic linear response functions. A detailed discussion is presented which includes finite size effects. Due to the derived temperature dependence of the Onsager-Casimir coefficients a frequency-dependent shift of the cusp temperature of the real part of the dynamic susceptibility is found.Comment: 15 pages, 4 figures, submitted to J.Phys.A: Math. Ge

Modified TAP equations for the SK spin glass

The stability of the TAP mean field equations is reanalyzed with the conclusion that the exclusive reason for the breakdown at the spin glass instability is an inconsistency for the value of the local susceptibility. A new alternative approach leads to modified equations which are in complete agreement with the original ones above the instability. Essentially altered results below the instability are presented and the consequences for the dynamical mean field equations are discussed.Comment: 7 pages, 2 figures, final revised version to appear in Europhys. Let

Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO

We demonstrate that a recently proposed classical double copy procedure to construct the effective action of two massive particles in dilaton-gravity from the analogous problem of two color charged particles in Yang-Mills gauge theory fails at next-to-next-to-leading orders in the post-Minkowskian (3PM) or post-Newtonian (2PN) expansions

Spin dependent D-brane interactions and scattering amplitudes in matrix theory

Spin interactions beteween two moving Dp-branes are analyzed using the Green-Schwarz formalism of boundary states. This approach turns out to be extremely efficient to compute all the spin effects related by supersymmetry to the leading v^4/r^7-p term. All these terms are shown to be scale invariant, supporting a matrix model description of supergravity interactions. By employing the LSZ reduction formula for matrix theory and the mentioned supersymmetric effective potential for D0-branes, we compute the t-pole of graviton-graviton and three form-three form scattering in matrix theory. The results are found to be in complete agreement with tree level supergravity in the corresponding kinematical regime and provide, moreover, an explicit map between these degrees of freedom in both theories.Comment: 8 pages, no figures, talk presented at the conference "Quantum aspects of gauge theories, supergravity and unification", Corfu, Greece, to appear in the proceeding

The chiral supereigenvalue model

A supereigenvalue model with purely positive bosonic eigenvalues is presented and solved by considering its superloop equations. This model represents the supersymmetric generalization of the complex one-matrix model, in analogy to the relation between the supereigenvalue and the Hermitian one-matrix model. Closed expressions for all planar multi-superloop correlation functions are found. Moreover an iterative scheme allows the calculation of higher genus contributions to the free energy and the correlators. Explicit results for genus one are given

On the Integrability of large N Plane-Wave Matrix Theory

We show the three-loop integrability of large N plane-wave matrix theory in a subsector of states comprised of two complex light scalar fields. This is done by diagonalizing the theory's Hamiltonian in perturbation theory and taking the large N limit. At one-loop level the result is known to be equal to the Heisenberg spin-1/2 chain, which is a well-known integrable system. Here, integrability implies the existence of hidden conserved charges and results in a degeneracy of parity pairs in the spectrum. In order to confirm integrability at higher loops, we show that this degeneracy is not lifted and that (corrected) conserved charges exist. Plane-wave matrix theory is intricately connected to N=4 Super Yang-Mills, as it arises as a consistent reduction of the gauge theory on a three-sphere. We find that after appropriately renormalizing the mass parameter of the plane-wave matrix theory the effective Hamiltonian is identical to the dilatation operator of N=4 Super Yang-Mills theory in the considered subsector. Our results therefore represent a strong support for the conjectured three-loop integrability of planar N=4 SYM and are in disagreement with a recent dual string theory finding. Finally, we study the stability of the large N integrability against nonsupersymmetric deformations of the model

The Matrix Theory S-Matrix

The technology required for eikonal scattering amplitude calculations in Matrix theory is developed. Using the entire supersymmetric completion of the v^4/r^7 Matrix theory potential we compute the graviton-graviton scattering amplitude and find agreement with eleven dimensional supergravity at tree level.Comment: 10 pages, RevTeX, no figure

Planar plane-wave matrix theory at the four loop order

We study SU(N) plane-wave matrix theory up to fourth perturbative order in its large N planar limit. The effective Hamiltonian in the closed su(2) subsector of the model is explicitly computed through a specially tailored computer program to perform large scale distributed symbolic algebra and generation of planar graphs. The number of graphs here was in the deep billions. The outcome of our computation establishes the four-loop integrability of the planar plane-wave matrix model. To elucidate the integrable structure we apply the recent technology of the perturbative asymptotic Bethe Ansatz to our model. The resulting S-matrix turns out to be structurally similar but nevertheless distinct to the so far considered long-range spin-chain S-matrices of Inozemtsev, Beisert-Dippel-Staudacher and Arutyunov-Frolov-Staudacher in the AdS/CFT context. In particular our result displays a breakdown of BMN scaling at the four-loop order. That is, while there exists an appropriate identification of the matrix theory mass parameter with the coupling constant of the N=4 superconformal Yang-Mills theory which yields an eigth order lattice derivative for well seperated impurities (naively implying BMN scaling) the detailed impurity contact interactions ruin this scaling property at the four-loop order. Moreover we study the issue of ``wrapping'' interactions, which show up for the first time at this loop-order through a Konishi descendant length four operator