Noncommutative Sp(2,R) Gauge Theories - A Field Theory Approach to Two-Time Physics

Phase-space and its relativistic extension is a natural space for realizing Sp(2,R) symmetry through canonical transformations. On a Dx2 dimensional covariant phase-space, we formulate noncommutative field theories, where Sp(2,R) plays a role as either a global or a gauge symmetry group. In both cases these field theories have potential applications, including certain aspects of string theories, M-theory, as well as quantum field theories. If interpreted as living in lower dimensions, these theories realize Poincare' symmetry linearly in a way consistent with causality and unitarity. In case Sp(2,R) is a gauge symmetry, we show that the spacetime signature is determined dynamically as (D-2,2). The resulting noncommutative Sp(2,R) gauge theory is proposed as a field theoretical formulation of two-time physics: classical field dynamics contains all known results of `two-time physics', including the reduction of physical spacetime from D to (D-2) dimensions, with the associated `holography' and `duality' properties. In particular, we show that the solution space of classical noncommutative field equations put all massless scalar, gauge, gravitational, and higher-spin fields in (D-2) dimensions on equal-footing, reminiscent of string excitations at zero and infinite tension limits.Comment: 32 pages, LaTe

Hamiltonian Noether theorem for gauge systems and two time physics

The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al. model and, with special emphasis, to two time physics.Comment: 20 pages, Latex, references added, the "massless" sense of (87) is clarifie

Exact Results in ABJM Theory from Topological Strings

Recently, Kapustin, Willett and Yaakov have found, by using localization techniques, that vacuum expectation values of Wilson loops in ABJM theory can be calculated with a matrix model. We show that this matrix model is closely related to Chern-Simons theory on a lens space with a gauge supergroup. This theory has a topological string large N dual, and this makes possible to solve the matrix model exactly in the large N expansion. In particular, we find the exact expression for the vacuum expectation value of a 1/6 BPS Wilson loop in the ABJM theory, as a function of the 't Hooft parameters, and in the planar limit. This expression gives an exact interpolating function between the weak and the strong coupling regimes. The behavior at strong coupling is in precise agreement with the prediction of the AdS string dual. We also give explicit results for the 1/2 BPS Wilson loop recently constructed by Drukker and TrancanelliComment: 18 pages, two figures, small misprints corrected and references added, final version to appear in JHE

Chiral effective potential in N=1/2{\cal N}={1/2} non-commutative Wess-Zumino model

We study a structure of holomorphic quantum contributions to the effective action for ${\cal N}={1/2}$ noncommutative Wess-Zumino model. Using the symbol operator techniques we present the one-loop chiral effective potential in a form of integral over proper time of the appropriate heat kernel. We prove that this kernel can be exactly found. As a result we obtain the exact integral representation of the one-loop effective potential. Also we study the expansion of the effective potential in a series in powers of the chiral superfield $\Phi$ and derivative $D^2{\Phi}$ and construct a procedure for systematic calculation of the coefficients in the series. We show that all terms in the series without derivatives can be summed up in an explicit form.Comment: LaTeX, JHEP style, 32 pages, typos corrected, references adde

USp(2k) Matrix Model: Nonperturbative Approach to Orientifolds

We discuss theoretical implications of the large k USp(2k) matrix model in zero dimension. The model appears as the matrix model of type IIB superstrings on a large $T^{6}/Z^{2}$ orientifold via the matrix twist operation. In the small volume limit, the model behaves four dimensional and its T dual is six-dimensional worldvolume theory of type I superstrings in ten spacetime dimensions. Several theoretical considerations including the analysis on planar diagrams, the commutativity of the projectors with supersymmetries and the cancellation of gauge anomalies are given, providing us with the rationales for the choice of the Lie algebra and the field content. A few classical solutions are constructed which correspond to Dirichlet p-branes and some fluctuations are evaluated. The particular scaling limit with matrix T duality transformation is discussed which derives the F theory compactification on an elliptic fibered K3.Comment: LaTeX, 29 pages, 3 figures. PostScript problems are fixe

Tachyon Dynamics in Open String Theory

In this review we describe our current understanding of the properties of open string tachyons on an unstable D-brane or brane-antibrane system in string theory. The various string theoretic methods used for this study include techniques of two dimensional conformal field theory, open string field theory, boundary string field theory, non-commutative solitons etc. We also describe various attempts to understand these results using field theoretic methods. These field theory models include toy models like singular potential models and p-adic string theory, as well as more realistic version of the tachyon effective action based on Dirac-Born-Infeld type action. Finally we study closed string background produced by the `decaying' unstable D-branes, both in the critical string theory and in the two dimensional string theory, and describe the open string completeness conjecture that emerges out of this study. According to this conjecture the quantum dynamics of an unstable D-brane system is described by an internally consistent quantum open string field theory without any need to couple the system to closed strings. Each such system can be regarded as a part of the `hologram' describing the full string theory.Comment: LaTex file, 169 pages, based on lectures at various schools; v2: references adde

Wilson loops in strongly coupled noncommutative gauge theories

We discuss Wilson loop averages in 4-dimensional non-commutative superYang-Mills theory using the dual supergravity description. We postulate that the Wilson loops are located at the mimimum length scale $R$ in the fifth radial coordinate. We find that they exhibit a crossover from Coulomb type of behaviour for large loops, for which non-commutativity is unimportant, to area law for small loops, for which non-commutativity effects are large. The string tension, which can be read off from the area law, is controlled by the non-commutativity scale. The crossover itself, however, appears to involve loops of size of order $R$ which is much larger than the non-commutativity scale. The existence of the area law in non-commutative super Yang-Mills theory which persists up to a large crossover length scale provides further evidence for connection to an underlying string theory.Comment: 18 pages, Revised version to appear in Phys. Rev.

Super-W(infinity) Asymptotic Symmetry of Higher-Spin AdS(3) Supergravity

We consider (2+1)-dimensional (N, M)-extended higher-spin anti-de Sitter supergravity and study its asymptotic symmetries. The theory is described by the Chern-Simons action based on a real, infinite-dimensional higher-spin superalgebra. We specify consistent boundary conditions on the higher-spin super-gauge connection corresponding to asymptotically anti-de Sitter spacetimes. We then determine the residual gauge transformations that preserve these asymptotic conditions and compute their Poisson bracket algebra. We find that the asymptotic symmetry is enhanced from the higher-spin superalgebra to some (N,M)-extended super-W(infinity) nonlinear superalgebra. The latter has the same classical central charge as pure Einstein gravity. Special attention is paid to the (1,1)-case. Truncation to the bosonic sector yields the previously found W(infinity) algebra, while truncation to the underlying finite-dimensional superalgebra reproduces the N-extended superconformal algebra (in its nonlinear version for N>2). We discuss string theory realization of these higher-spin anti-de Sitter supergravity theories as well as relations to previous treatments of super-W(infinity) in the literature.Comment: References added. (N>2)-Extended supersymmetric models argued to be rigid with respect to lambda-deformation. Comments on G(3)-case adde

Collective Dipole Model of AdS/CFT and Higher Spin Gravity

We formulate a first quantized construction of the AdS_{d+1}/CFT_d correspondence using the bi-local representation of the free d-dimensional large N vector model. The earlier reconstruction of AdS_4 higher-spin gravity provides a scheme where the AdS spacetime (and higher-spin fields) are given by the composite bi-local fields. The underlying first quantized, world-sheet picture is extracted in the present work and generalized to any dimension. A higher-spin AdS particle model is shown to emerge from the collective bi-particle system of Minkowski particles through a canonical transformation. As such this construction provides a simple explicit mechanism of the AdS/CFT correspondence.Comment: 16 pages, no figures; v2: references added; v3: minor change