Open String Modes Research Articles

Formula omitted]-Trek II: [formula omitted] operations, open Wilson lines and the Seiberg–Witten map

Generalizations of the ∗-product (e.g., n-ary ∗ n operations) appear in various places in the discussion of noncommutative gauge theories. These include the one-loop effective action of noncommutative gauge theories, the couplings between massless closed and open string modes, and the Seiberg–Witten map between the ordinary and noncommutative Yang–Mills fields. We propose that the natural way to understand the ∗ n operations is through the expansion of an open Wilson line. We establish the connection between an open Wilson line and the ∗ n operations and use it to (I) write down a gauge invariant effective action for the one-loop F 4 terms in the noncommutative N=4 SYM theory; (II) find the gauge invariant couplings between the noncommutative SYM modes and the massless closed string modes in flat space; (III) propose a closed form for the Seiberg–Witten map in the U(1) case.

Open string decoupling and tachyon condensation

The amplitudes in perturbative open string theory are examined as functions of the tachyon condensate parameter. The boundary state formalism demonstrates the decoupling of the open string modes at the non-perturbative minima of the tachyon potential via a degeneration of open world-sheets and identifies an independence of the coupling constants $g_s$ and $g_{YM}$ at general values of the tachyon condensate. The closed sector is generated at the quantum level; it is also generated at the classical level through the condensation of the propagating open string modes on the D-brane degrees of freedom.

Temperature of D3-branes off extremality

We discuss non-extremal rotating D3-branes. We solve the wave equation for scalars in the supergravity background of certain distributions of branes and compute the absorption coefficients. The form of these coefficients is similar to the gray-body factors associated with black-hole scattering. They are given in terms of two different temperature parameters, indicating that fields (open string modes) do not remain in thermal equilibrium as we move off extremality. This should shed some light on the origin of the disagreement between the supergravity and conformal field theory results on the free energy of a system of non-coincident D-branes.

OPEN STRINGS AND NONCOMMUTATIVE GEOMETRY OF BRANES ON GROUP MANIFOLDS

In this letter we review some recent work on the noncommutative geometry of branes on group manifolds. In particular, we show how fuzzy spaces arise in this context from an exact worldsheet description and we sketch the construction of a low-energy effective action for massless open string modes. The latter is given by a combination of a Yang–Mills and a Chern–Simons like functional on the fuzzy world-volume. It can be used to study condensation on various brane configurations in curved backgrounds.

1+1 DIMENSIONAL NCOS AND ITS U(N) GAUGE THEORY DUAL

We study some aspects of open string theories on D-branes with critical electric fields. We show that the massless open string modes that move in the direction of the electric field decouple. In the 1+1 dimensional case the dual theory is U(N) SYM with electric flux, and the decoupling of massless open strings is dual to the decoupling of the U(1) degrees of freedom. We also show that, if the direction along the electric field is compact, then there are finite energy winding closed string modes. They are dual to Higgs branch excitations of the SYM theory, and their energetics works accordingly. These properties provide new non-trivial evidence for the duality.

Gauge fields and fermions in tachyon effective field theories

In this paper we incorporate gauge fields into the tachyon field theory models for unstable D-branes in bosonic and in Type II string theories. The chosen couplings yield massless gauge fields and an infinite set of equally spaced massive gauge fields on codimension one branes. A lack of a continuum spectrum is taken as evidence that the stable tachyon vacuum does not support conventional gauge excitations. For the bosonic string model we find two possible solvable couplings, one closely related to Born-Infeld forms and the other allowing a detailed comparison to the open string modes on bosonic D-branes. We also show how to include fermions in the type II model. They localize correctly on stable codimension one branes resulting in bose-fermi degeneracy at the massless level. Finally, we establish the solvability of a large class of models that include kinetic terms with more than two derivatives.

Stable massive states in(1+1)-dimensional noncommutative open string theory

We study the case of open string theory on a D1-brane in a critical electric field. It was argued by Klebanov and Maldacena that the massless open string modes of this theory decouple from the massive modes, corresponding to a decoupling of the U(1) degrees of freedom in the $\mathrm{U}(N)$ gauge theory dual. To provide further support for the decoupling, we present several examples of open string disk amplitudes. Because of the decoupling, many of the massive open string states are stable, indicating the presence of a number of correspondingly stable states in the gauge theory. We provide a lengthy list of these stable states. However, when the theory is compactified in the spatial direction of the electric field, we demonstrate that such sufficiently massive states may decay into wound-closed strings.

LOOP VARIABLES AND GAUGE-INVARIANT INTERACTIONS — I

We describe a method of writing down interacting equations for all the modes of the bosonic open string. It is a generalization of the loop variable approach that was used earlier for the free, and lowest order interacting cases. The generalization involves, as before, the introduction of a parameter to label the different strings involved in an interaction. The interacting string has thus becomes a "band" of finite width. The interaction equations expressed in terms of loop variables, has a simple invariance that is exact even off shell. A consistent definition of space–time fields requires the fields to be functions of all the infinite number of gauge coordinates (in addition to space–time coordinates). The theory is formulated in one higher dimension, where the modes appear massless. The dimensional reduction that is needed to make contact with string theory (which has been discussed earlier for the free case) is not discussed here.

$1+1$ dimensional NCOS and its $U(N)$ gauge theory dual

We study some aspects of open string theories on D-branes with critical electric fields. We show that the massless open string modes that move in the direction of the electric field decouple. In the 1+1 dimensional case the dual theory is U(N) SYM with electric flux, and the decoupling of massless open strings is dual to the decoupling of the U(1) degrees of freedom. We also show that, if the direction along the electric field is compact, then there are finite energy winding closed string modes. They are dual to Higgs branch excitations of the SYM theory, and their energetics works accordingly. These properties provide new non-trivial evidence for the duality.

DIRAC-BORN-INFELD ACTION FROM DIRICHLET σ-MODEL

In a recent paper we discussed, among other things, the effect of duality transformations on the open bosonic string theory. Namely, we conjectured that a macroscopic object, the D-brane, effectively interacts with closed and open string modes in the low energy limit. This conjecture was supported by a string scattering amplitude calculation. In this letter we report on a σ-model calculation in the mixed Dirichlet-Neumann theory. We find an action of the Dirac-Born-Infeld type restricted to (26−k)-dimensions.

Loop variables, the renormalization group and gauge invariant equations of motion in string field theory

We derive, within the framework of the renormalization group, gauge invariant equations of motion for the massive modes of the free open bosonic string. We present explicit results for the massive “spin-2” and “spin-3” fields. An auxiliary field analogous to the bosonized ghost enters the calculation as an extra space-time coordinate and the string modes are, in some sense, massless in D + 1 dimensions. The basic entity is a non-local loop variable and it is necessary to introduce an infinite number of new coordinates analogous to those in the K-P hierarchy, to describe reparametrizations of the boundary of the Riemann surface. The gauge transformations have a particularly simple form.

Magnetic string fields

We construct the string field in Witten's open bosonic string field theory which corresponds to a constant magnetic field. We express the answer both in the standard basis of open string modes, and in more natural basis which requires changes in the zero-zero Neumann coefficients of the three-string vertex. We discuss the feasibility of using string field theory to search for new solutions of the classical string equations.