Counting Parameter Research Articles

Fermion BMN operators, the dilatation operator of = 4 SYM, and pp-wave string interactions

The goal of this paper is to study the BMN correspondence in the fermionic sector. On the field theory side, we compute matrix elements of the dilatation operator in N=4 Super Yang-Mills for BMN operators containing two fermion impurities. Our calculations are performed up to and including O(lambda') in the 't Hooft coupling and O(g_2) in the Yang-Mills genus counting parameter. On the string theory side, we compute the corresponding matrix elements of the interacting string Hamiltonian in string field theory, using the three-string interaction vertex constructed by Spradlin and Volovich (and subsequently elaborated by Pankiewicz and Stefanski). In string theory we use the natural string basis, and in field theory the basis which is isomorphic to it. We find that the matrix elements computed in field theory and the corresponding string amplitudes derived from the three-string vertex are, in all cases, in perfect agreement.

Lectures on the plane‐wave string/gauge theory duality

AbstractThese lectures give an introduction to the novel duality relating type IIB string theory in a maximally supersymmetric plane‐wave background to 𝒩 = 4, d = 4, U(N) super Yang‐Mills theory in a particular large N and large R‐charge limit due to Berenstein, Maldacena and Nastase. In the first part of these lectures the duality is derived from the AdS/CFT correspondence by taking a Penrose limit of the AdS5 × S5 geometry and studying the corresponding double‐scaling limit on the gauge theory side. The resulting free plane‐wave superstring is then quantized in light‐cone gauge. On the gauge theory side of the correspondence the composite super Yang‐Mills operators dual to string excitations are identified, and it is shown how the string spectrum can be mapped to the planar scaling dimensions of these operators. In the second part of these lectures we study the correspondence at the interacting respectively non‐planar level. On the gauge theory side it is demonstrated that the large N large R‐charge limit in question preserves contributions from Feynman graphs of all genera through the emergence of a new genus counting parameter – in agreement with the string genus expansion for non‐zero gs. Effective quantum mechanical tools to compute higher genus contributions to the scaling dimensions of composite operators are developed and explicitly applied in a genus one computation. We then turn to the interacting string theory side and give an elementary introduction into light‐cone superstring field theory in a plane‐wave background and point out how the genus one prediction from gauge theory can be reproduced. Finally, we summarize the present status of the plane‐wave string/gauge theory duality.

ChandraObservations of “The Antennae” Galaxies (NGC 4038/4039). IV. The X‐Ray Source Luminosity Function and the Nature of Ultraluminous X‐Ray Sources

We derive the X-ray luminosity function (XLF) of the X-ray source population detected in the Chandra observation of NGC4038/39 (the Antennae). We explicitly include photon counting and spectral parameter uncertainties in our calculations. The cumulative XLF is well represented by a flat power law ($\alpha=-0.47$), similar to those describing the XLFs of other star-forming systems (e.g. M82, the disk of M81), but different from those of early type galaxies. This result associates the X-ray source population in the Antennae with young High Mass X-ray Binaries. In comparison with less actively star-forming galaxies, the XLF of the Antennae has a highly significant excess of sources with luminosities above 10^{39} erg\s (Ultra Luminous Sources; ULXs). We discuss the nature of these sources, based on the XLF and on their general spectral properties, as well as their optical counterparts discussed in Paper III. We conclude that the majority of the ULXs cannot be intermediate mass black-holes (M > 10-1000 \msun) binaries, unless they are linked to the remnants of massive Population III stars (the Madau & Rees model). Instead, their spatial and multiwavelength properties can be well explained by beamed emission as a consequence of supercritical accretion. Binaries with a neutron star or moderate mass black-hole (up to 20\msun), and B2 to A type star companions would be consistent with our data. In the beaming scenario, the XLF should exibit caracteristic breaks that will be visible in future deeper observations of the Antennae.

PP-wave string interactions from perturbative Yang-Mills theory

Recently, Berenstein et al. have proposed a duality between a sector of N=4 super-Yang-Mills theory with large R-charge J, and string theory in a pp-wave background. In the limit considered, the effective 't Hooft coupling has been argued to be lambda'=g_{YM}^2 N/J^2=1/(mu p^+ alpha')^2. We study Yang-Mills theory at small lambda' (large mu) with a view to reproducing string interactions. We demonstrate that the effective genus counting parameter of the Yang-Mills theory is g_2^2=J^4/N^2=(4 pi g_s)^2 (mu p^+ alpha')^4, the effective two-dimensional Newton constant for strings propagating on the pp-wave background. We identify g_2 sqrt{lambda'} as the effective coupling between a wide class of excited string states on the pp-wave background. We compute the anomalous dimensions of BMN operators at first order in g_2^2 and lambda' and interpret our result as the genus one mass renormalization of the corresponding string state. We postulate a relation between the three-string vertex function and the gauge theory three-point function and compare our proposal to string field theory. We utilize this proposal, together with quantum mechanical perturbation theory, to recompute the genus one energy shift of string states, and find precise agreement with our earlier computation.

Excited heavy baryons and their symmetries III: Phenomenology

Phenomenological applications of an effective theory of low-lying excited states of charm and bottom isoscalar baryons are discussed at leading and next-to-leading order in the combined heavy-quark and large- N c expansion. The combined expansion is formulated in terms of the counting parameter λ∼1/ m Q ,1/ N c ; the combined expansion is in powers of λ 1/2. We work up to next-to-leading order. We obtain model-independent predictions for the excitation energies, the semileptonic form factors and electromagnetic decay rates. At leading order in the combined expansion these observables are given in terms of one phenomenological constant which can be determined from the excitation energy of the first excited state of Λ c baryon. At next-to-leading order an additional phenomenological constant is required. The spin-averaged mass of the doublet of the first orbitally excited state of Λ b is predicted to be approximately 5920 MeV. It is shown that in the combined limit at leading and next-to-leading order there is only one independent form factor describing Λ b→Λ cℓ ν ̄ ; similarly, Λ b→Λ c ∗ℓ ν ̄ and Λ b→Λ c1ℓ ν ̄ decays are described by a single independent form factor. These form factors are calculated at leading and next-to-leading order in the combined expansion. The value of the Λ b→Λ cℓ ν ̄ form factor at zero recoil is predicted to be 0.998 at leading order which is very close to HQET value of unity. The electromagnetic decay rates of the first excited states of Λ c and Λ b are determined at leading and next-to-leading order. The ratio of radiative decay rates Γ(Λ c ∗→Λ cγ)/Γ(Λ b1→Λ bγ) is predicted to be approximately 0.2, greatly different from the heavy-quark effective theory value of unity.

Fermions and nonperturbative supersymmetry breaking in the one-dimensional superstring

The one-dimensional superstring of Marinari and Parisi is analyzed taking into account the fermionic sector. The original matrix model is reduced to a manifestly supersymmetric quantum mechanics of eigenvalues with an effective superpotential. Unlike the bosonic sector, the fermionic sector has long-range interactions between the eigenvalues. It is shown that in the double-scaling limit the dynamics of the top eigenvalue can be described in terms of scaled supercharges. The one-eigenvalue instanton and the corresponding fermionic zero mode responsible for supersymmetry breaking are identified. The supersymmetry breaking parameter is calculated and is shown to be nonzero. The nonperturbative breaking of supersymmetry in this string model goes as exp(- C/ ϰ), where ϰ 2 is the loop counting parameter. This is much stronger than the exp(− C/ ϰ 2) nonperturbative effects characteristic of low-energy field theory. Possible implications of this result for critical string theory are discussed.