From bubbles to foam: dilute to dense evolution of hadronic wave function at high energy

We derive the evolution of a hadronic light cone wave function with energy at weak coupling. Our derivation is valid both in the high and the low partonic density limit, and thus encompasses both the JIMWLK and the KLWMIJ evolution. The hadronic wave function is shown to evolve by the action of the Bogoliubov-type operator, which diagonalizes on the soft gluon sector the light-cone hamiltonian in the presence of an arbitrary valence charge density. We find explicitly the action of this operator on the soft as well as the valence degrees of freedom of the theory.Comment: 30 page

Type II pp-wave Matrix Models from Point-like Gravitons

The BMN Matrix model can be regarded as a theory of coincident M-theory gravitons, which expand by Myers dielectric effect into the 2-sphere and 5-sphere giant graviton vacua of the theory. In this note we show that, in the same fashion, Matrix String theory in Type IIA pp-wave backgrounds arises from the action for coincident Type IIA gravitons. In Type IIB, we show that the action for coincident gravitons in the maximally supersymmetric pp-wave background gives rise to a Matrix model which supports fuzzy 3-sphere giant graviton vacua with the right behavior in the classical limit. We discuss the relation between our Matrix model and the Tiny Graviton Matrix theory of hep-th/0406214.Comment: 18 page

Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution

We reinterpret the JIMWLK/KLWMIJ evolution equation as the QCD Reggeon field theory (RFT). The basic "quantum Reggeon field" in this theory is the unitary matrix $R$ which represents the single gluon scattering matrix. We discuss the peculiarities of the Hilbert space on which the RFT Hamiltonian acts. We develop a perturbative expansion in the RFT framework, and find several eigenstates of the zeroth order Hamiltonian. The zeroth order of this perturbation preserves the number of $s$ - channel gluons. The eigenstates have a natural interpretation in terms of the $t$ - channel exchanges. Studying the single $s$ - channel gluon sector we find the eigenstates which include the reggeized gluon and five other colored Reggeons. In the two ($s$ - channel) gluon sector we study only singlet color exchanges. We find five charge conjugation even states. The bound state of two reggeized gluons is the standard BFKL Pomeron. The intercepts of the other Pomerons in the large $N$ limit are $1+\omega_P=1+2\omega$ where $1+\omega$ is the intercept of the BFKL Pomeron, but their coupling in perturbation theory is suppressed by at least $1/N^2$ relative to the double BFKL Pomeron exchange. For the $[27,27]$ Pomeron we find $\omega_{[27,27]}=2\omega+O(1/N)>2\omega$. We also find three charge conjugation odd exchanges, one of which is the unit intercept Bartels-Lipatov-Vacca Odderon, while another one has an interecept greater than unity. We explain in what sense our calculation goes beyond the standard BFKL/BKP calculation. We make additional comments and discuss open questions in our approach.Comment: 58 pages, 4 figures, Extended version. To appear in JHE

On the worldsheet theories of strings dual to free large N gauge theories

We analyze in detail some properties of the worldsheet of the closed string theories suggested by Gopakumar to be dual to free large N SU(N) gauge theories (with adjoint matter fields). We use Gopakumar's prescription to translate the computation of space-time correlation functions to worldsheet correlation functions for several classes of Feynman diagrams, by explicit computations of Strebel differentials. We compute the worldsheet operator product expansion in several cases and find that it is consistent with general worldsheet conformal field theory expectations. A peculiar property of the construction is that in several cases the resulting worldsheet correlation functions are non-vanishing only on a sub-space of the moduli space (say, for specific relations between vertex positions). Another strange property we find is that for a conformally invariant space-time theory, the mapping to the worldsheet does not preserve the special conformal symmetries, so that the full conformal group is not realized as a global symmetry on the worldsheet (even though it is, by construction, a symmetry of all integrated correlation functions).Comment: 60 pages, 17 figures, latex. v2: Added references and a minor correctio

Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions

We consider type II superstrings on AdS backgrounds with Ramond-Ramond flux in various dimensions. We realize the backgrounds as supercosets and analyze explicitly two classes of models: non-critical superstrings on AdS_{2d} and critical superstrings on AdS_p\times S^p\times CY. We work both in the Green--Schwarz and in the pure spinor formalisms. We construct a one-parameter family of flat currents (a Lax connection) leading to an infinite number of conserved non-local charges, which imply the classical integrability of both sigma-models. In the pure spinor formulation, we use the BRST symmetry to prove the quantum integrability of the sigma-model. We discuss how classical \kappa-symmetry implies one-loop conformal invariance. We consider the addition of space-filling D-branes to the pure spinor formalism.Comment: LaTeX2e, 56 pages, 1 figure, JHEP style; v2: references added, typos fixed in some equations; v3: typos fixed to match the published versio

BPS Operators in N=4 SYM: Calogero Models and 2D Fermions

A connection between the gauge fixed dynamics of protected operators in superconformal Yang-Mills theory in four dimensions and Calogero systems is established. This connection generalizes the free Fermion description of the chiral primary operators of the gauge theory formed out of a single complex scalar to more general operators. In particular, a detailed analysis of protected operators charged under an su(1|1)contained in psu(2,2|4) is carried out and a class of operators is identified, whose dynamics is described by the rational super-Calogero model. These results are generalized to arbitrary BPS operators charged under an su(2|3) of the superconformal algebra. Analysis of the non-local symmetries of the super-Calogero model is also carried out, and it is shown that symmetry for a large class of protected operators is a contraction of the corresponding Yangian algebra to a loop algebra.Comment: 29 pages, 3 figure

Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality

We propose gauge theory operators built using a complex Matrix scalar which are dual to brane-anti-brane systems in $AdS_5 \times S^5$, in the zero coupling limit of the dual Yang-Mills. The branes involved are half-BPS giant gravitons. The proposed operators dual to giant-anti-giant configurations satisfy the appropriate orthogonality properties. Projection operators in Brauer algebras are used to construct the relevant multi-trace Matrix operators. These are related to the ``coupled representations'' which appear in 2D Yang-Mills theory. We discuss the implications of these results for the quantum mechanics of a complex matrix model, the counting of non-supersymmetric operators and the physics of brane-anti-brane systems. The stringy exclusion principle known from the properties of half-BPS giant gravitons, has a new incarnation in this context. It involves a qualitative change in the map between brane-anti-brane states to gauge theory operators. In the case of a pair of sphere giant and anti-giant this change occurs when the sum of the magnitudes of their angular momenta reaches $N$.Comment: 52 pages, 10 figure

QCD Reggeon Field Theory for every day: Pomeron loops included

We derive the evolution equation for hadronic scattering amplitude at high energy. Our derivation includes the nonlinear effects of finite partonic density in the hadronic wave function as well as the effect of multiple scatterings for scattering on dense hadronic target. It thus includes Pomeron loops. It is based on the evolution of the hadronic wave function derived in \cite{foam}. The kernel of the evolution equation defines the second quantized Hamiltonian of the QCD Reggeon Field Theory, $H_{RFT}$ beyond the limits considered so far. The two previously known limits of the evolution: dilute target (JIMWLK limit) and dilute projectile (KLWMIJ limit) are recovered directly from our final result. The Hamiltonian $H_{RFT}$ is applicable for the evolution of scattering amplitude for arbitrarily dense hadronic projectiles/targets - from "dipole-dipole" to "nucleus-nucleus" scattering processes.Comment: 35 pages, 5 figure

Noncritical M-Theory in 2+1 Dimensions as a Nonrelativistic Fermi Liquid

We claim that the dynamics of noncritical string theories in two dimensions is related to an underlying noncritical version of M-theory, which we define in terms of a double-scaled nonrelativistic Fermi liquid in 2+1 dimensions. After reproducing Type 0A and 0B string theories as solutions, we study the natural M-theory vacuum. The vacuum energy of this solution can be evaluated exactly, its form suggesting a duality to the Debye model of phonons in a melting solid, and a possible topological nature of the theory. The physical spacetime is emergent in this theory, only for states that admit a hydrodynamic description. Among the solutions of the hydrodynamic equations of motion for the Fermi surface, we find families describing the decay of one two-dimensional string theory into another via an intermediate M-theory phase.Comment: 47 pages, 1 figure; v2: typos corrected, references adde