We explain how the string spectrum in flat space and pp-waves arises from the large-N limit, at fixed g2YM, of U(N) = 4 super Yang Mills. We reproduce the spectrum by summing a subset of the planar Feynman diagrams. We give a heuristic argument for why we can neglect other diagrams. We also discuss some other aspects of pp-waves and we present a matrix model associated to the DLCQ description of the maximally supersymmetric eleven dimensional pp-waves.

https://iopscience.iop.org/article/10.1088/1126-6708/2002/04/013/pdf

Strings in flat space and pp waves from Script N = 4 Super Yang Mills

We explain how the string spectrum in flat space and pp‐waves arises from the large N limit, at fixed gYM2, of U(N) N = 4 super Yang Mills. We reproduce the spectrum by summing a subset of the planar Feynman diagrams. We give a heuristic argument for why we can neglect other diagrams.

Strings in flat space and pp waves from N = 4 Super Yang Mills

We explain how the string spectrum in flat space and pp-waves arises from the large $N$ limit, at fixed $g^2_{YM}$, of U(N) ${\cal N} =4$ super Yang Mills. We reproduce the spectrum by summing a subset of the planar Feynman diagrams. We give a heuristic argument for why we can neglect other diagrams. We also discuss some other aspects of pp-waves and we present a matrix model associated to the DLCQ description of the maximally supersymmetric eleven dimensional pp-waves.

Strings in flat space and pp waves from ${\cal N}=4$ Super Yang Mills

We describe how to compute planar gluon scattering amplitudes at strong coupling in = 4 super Yang Mills by using the gauge/string duality. The computation boils down to finding a certain classical string configuration whose boundary conditions are determined by the gluon momenta. The results are infrared divergent. We introduce the gravity version of dimensional regularization to define finite quantities. The leading and subleading IR divergencies are characterized by two functions of the coupling that we compute at strong coupling. We compute also the full finite form for the four point amplitude and we find agreement with a recent ansatz by Bern, Dixon and Smirnov.

Gluon scattering amplitudes at strong coupling

We consider all 1/2 BPS excitations of AdS × S configurations in both type-IIB string theory and M-theory. In the dual field theories these excitations are described by free fermions. Configurations which are dual to arbitrary droplets of free fermions in phase space correspond to smooth geometries with no horizons. In fact, the ten dimensional geometry contains a special two dimensional plane which can be identified with the phase space of the free fermion system. The topology of the resulting geometries depends only on the topology of the collection of droplets on this plane. These solutions also give a very explicit realization of the geometric transitions between branes and fluxes. We also describe all 1/2 BPS excitations of plane wave geometries. The problem of finding the explicit geometries is reduced to solving a Laplace (or Toda) equation with simple boundary conditions. We present a large class of explicit solutions. In addition, we are led to a rather general class of AdS5 compactifications of M-theory preserving = 2 superconformal symmetry. We also find smooth geometries that correspond to various vacua of the maximally supersymmetric mass-deformed M2 brane theory. Finally, we present a smooth 1/2 BPS solution of seven dimensional gauged supergravity corresponding to a condensate of one of the charged scalars.

https://iopscience.iop.org/article/10.1088/1126-6708/2004/10/025/pdf

Bubbling AdS space and 1/2 BPS geometries

We consider high-energy fixed-angle scattering of glueballs in confining gauge theories that have supergravity duals. Although the effective description is in terms of the scattering of strings, we find that the amplitudes are hard (power law). This is a consequence of the warped geometry of the dual theory, which has the effect that in an inertial frame the string process is never in the soft regime. At small angle we find hard and Regge behaviors in different kinematic regions.

Hard scattering and gauge/string duality.

Giant gravitons in AdS5 ? S5, and its orbifolds, have a dual field theory representation as states created by chiral primary operators. We argue that these operators are not single-trace operators in the conformal field theory, but rather are determinants and subdeterminants of scalar fields; the stringy exclusion principle applies to these operators. Evidence for this identification comes from three sources: (a) topological considerations in orbifolds, (b) computation of protected correlators using free field theory and (c) a Matrix model argument. The last argument applies to AdS7 ? S4 and the dual (2,0) theory, where we use algebraic aspects of the fuzzy 4-sphere to compute the expectation value of a giant graviton operator along the Coulomb branch of the theory.

https://iopscience.iop.org/article/10.1088/1126-6708/2002/04/034/pdf

Giant gravitons in conformal field theory

http://cds.cern.ch/record/531762/files/0112233.pdf

Implications of gauge unification for time variation of the fine structure constant

We explore the effects of a strongly-coupled, approximately scale-invariant sector on the renormalization of soft supersymmetry breaking terms A useful formalism for deriving exact results for renormalization of soft supersymmetry breaking terms is given in an appendix, and used to generalize previously known results to include the effects of nontrilinear superpotential terms We show that a class of theories which explain the flavor hierarchy without flavor symmetries can also solve the supersymmetric flavor problem by producing nearly degenerate masses for the first two generations of scalar superpartners within each charge sector Effects from trilinear scalar terms are also suppressed, although their initial values must be relatively small Our mechanism results in testable predictions for the superpartner spectrum

Exact Results for Supersymmetric Renormalization and the Supersymmetric Flavor Problem

Giant gravitons in AdS_5 x S^5, and its orbifolds, have a dual field theory representation as states created by chiral primary operators. We argue that these operators are not single-trace operators in the conformal field theory, but rather are determinants and subdeterminants of scalar fields; the stringy exclusion principle applies to these operators. Evidence for this identification comes from three sources: (a) topological considerations in orbifolds, (b) computation of protected correlators using free field theory and (c) a Matrix model argument. The last argument applies to AdS_7 x S^4 and the dual (2,0) theory, where we use algebraic aspects of the fuzzy 4-sphere to compute the expectation value of a giant graviton operator along the Coulomb branch of the theory.

Matthew J. Strassler

Papers

Hard scattering and gauge/string duality.

Giant gravitons in conformal field theory

Implications of gauge unification for time variation of the fine structure constant

Exact Results for Supersymmetric Renormalization and the Supersymmetric Flavor Problem

Giant Gravitons in Conformal Field Theory