J. Antonio Garcia

The energy of a moving quark-antiquark pair in an Script N = 4 SYM plasma

We make use of the AdS/CFT correspondence to determine the energy of an external quark-antiquark pair that moves through strongly-coupled thermal = 4 super-Yang-Mills plasma, both in the rest frame of the plasma and in the rest frame of the pair. It is found that the pair feels no drag force, has an energy that reproduces the expected 1/L (or γ/L) behavior at small quark-antiquark separations, and becomes unbound beyond a certain screening length whose velocity-dependence we determine. We discuss the relation between the high-velocity limit of our results and the lightlike Wilson loop proposed recently as a definition of the jet-quenching parameter.

Equivalence of Faddeev-Jackiw and Dirac approaches for gauge theories

The equivalence between the Dirac method and Faddeev–Jackiw analysis for gauge theories is proven. In particular we trace out, in a stage-by-stage procedure, the standard classification of first and second class constraints of Diracs method in the F–J approach. We also find that the Darboux transformation implied in the F–J reduction process can be viewed as a canonical transformation in Dirac approach. Unlike Diracs method, the F–J analysis is a classical reduction procedure. The quantization can be achieved only in the framework of reduce and then quantize approach with all the known problems that this type of procedure presents. Finally we illustrate the equivalence by means of a particular example.

Holographic lessons for quark dynamics

We give a brief overview of recent results obtained through the gauge/gravity correspondence, concerning the propagation of a heavy quark in strongly-coupled conformal field theories (such as N = 4 super-Yang-Mills), both at zero and finite temperature. In the vacuum, we discuss energy loss, radiation damping, signal propagation and radiation-induced fluctuations. In the presence of a thermal plasma, our emphasis is on early-time energy loss, screening and quark-antiquark evolution after pair creation. Throughout, quark dynamics is seen to be efficiently encapsulated in the usual string worldsheet dynamics.

Rigid and gauge Noether symmetries for constrained systems

We develop the general theory of Noether symmetries for constrained systems, that is, systems that are described by singular Lagrangians. In our derivation, the Dirac bracket structure with respect to the primary constraints appears naturally and plays an important role in the characterization of the conserved quantities associated to these Noether symmetries. The issue of projectability of these symmetries from tangent space to phase space is fully analyzed, and we give a geometrical interpretation of the projectability conditions in terms of a relation between the Noether conserved quantity in tangent space and the presymplectic form defined on it. We also examine the enlarged formalism that results from taking the Lagrange multipliers as new dynamical variables; we find the equation that characterizes the Noether symmetries in this formalism, and we also prove that the standard formulation is a particular case of the enlarged one. The algebra of generators for Noether symmetries is discussed in both the Hamiltonian and Lagrangian formalisms. We find that a frequent source for the appearance of open algebras is the fact that the transformations of momenta in phase space and tangent space only coincide on shell. Our results apply with no distinction to rigid and gauge symmetries; for the latter case we give a general proof of the existence of Noether gauge symmetries for theories with first and second class constraints that do not exhibit tertiary constraints in the stabilization algorithm. Among some examples that illustrate our results, we study the Noether gauge symmetries of the Abelian Chern–Simons theory in 2n+1 dimensions. An interesting feature of this example is that its primary first class constraints can only be identified after the determination of the secondary constraint. The example is worked out retaining all the original set of variables.

BFT embedding of the Green-Schwarz superstring and the pure spinor formalism

We worked out the Batalin-Fradkin-Tyutin (BFT) conversion program of second class constraints to first class constraints in the GS superstring using light cone coordinates. By applying this systematic procedure we were able to obtain a gauge system that is equivalent to the recent model proposed in [1] to relate the GS superstring to the pure spinor formalism.

COUPLINGS BETWEEN GENERALIZED GAUGE FIELDS

We analyze the BRST field-antifield construction for generalized gauge fields consisting of massless mixed representations of the Lorentz Group and we calculate all the strictly gauge invariant interactions between them. All these interactions are higher derivative terms constructed out from the derivatives of the curl of field strength.

A membrane action for WM2 / OM theory

Abstract Through direct examination of the effect of the OM limit on the M2-brane worldvolume action, we derive a membrane action for OM theory, and more generally, for the eleven-dimensional M-theoretic construct known as Galilean or Wrapped M2-brane (WM2) theory, which contains OM theory as a special class of states. In the static gauge, the action in question implies a discrete spectrum for the closed membrane of WM2 theory, which under double dimensional reduction is shown to reproduce the known NCOS/Wound closed string spectrum. We examine as well open membranes ending on each of the three types of M5-branes in WM2 theory (OM theory arising from the ‘longitudinal’ type), and show that the ‘fully transverse’ fivebrane is tensionless. As a prelude to the membrane, we also study the case of the string, where we likewise obtain a reparametrization-invariant action, and make contact with previous work.

No Line on the Horizon: On Uniform Acceleration and Gluonic Fields at Strong Coupling

A bstractWe study a few assorted questions about the behavior of strings on anti-de Sitter spacetime (AdS), or equivalently, ‘flux tubes’ in strongly-coupled conformal field theories (CFTs). For the case where the ‘flux tube’ is sourced by a uniformly accelerated quark (or, more generally, a quark that asymptotes to uniform acceleration in the remote past), we point out that the dual string embedding known heretofore terminates unphysically at the worldsheet horizon, and identify the correct continuation, which is found to encode a gluonic shock wave. For arbitrary quark motion, we show that, contrary to common understanding, the worldsheet horizon does not in general represent a dividing line between the portions of the string respectively dual to the quark and to the gluonic radiation emitted by it.

FADDEEV-JACKIW APPROACH TO GAUGE THEORIES AND INEFFECTIVE CONSTRAINTS

The general conditions for the applicability of the Faddeev–Jackiw approach to gauge theories are studied. When the constraints are effective, a new proof in the Lagrangian framework of the equivalence between this method and the Dirac approach is given. We find, however, that the two methods may give different descriptions for the reduced phase space when ineffective constraints are present. In some cases the Faddeev–Jackiw approach may lose some constraints or some equations of motion. We believe that this inequivalence can be related to the failure of the Dirac conjecture (that says that the Dirac Hamiltonian can be enlarged to an Extended Hamiltonian including all first class constraints, without changes in the dynamics) and we suggest that when the Dirac conjecture fails, the Faddeev–Jackiw approach fails to give the correct dynamics. Finally we present some examples that illustrate this inequivalence.

Weyl invariant p-brane and Dp-brane actions

Abstract Conformal invariant new forms of p -brane and D p -brane actions are proposed. The field content of these actions are: an induced metric, gauge fields, an auxiliary metric and an auxiliary scalar field that implements the Weyl invariance. This scalar field transforms with a conformal weight that depends on the brane dimension. The proposed actions are Weyl invariant in any dimension and the elimination of the auxiliary metric and the scalar field reproduces the Nambu–Goto action for p -branes and the Born–Infeld action for D p -branes. As a consequence of the fact that in the p -brane case, the action is quadratic in ∂ 0 X , we develop a complete construction for the associated canonical formalism, solving the problem in previous formulations of conformal p -brane actions where the Hamiltonian can not be constructed. We obtain the algebra of constraints and identify the generator of the Weyl symmetry. In the construction of the corresponding supersymmetric generalization of this conformal p -brane action we show that the associated κ -symmetry is consistent with the conformal invariance. In the D p -brane case, the actions are quadratic in the gauge fields. These actions can be used to construct new conformal couplings in any dimension p to the auxiliary scalar field now promoted as a dynamical variable.