Light-cone Green-Schwarz Formalism Research Articles

DDF construction and D-brane boundary states in pure spinor formalism

Open string boundary conditions for non-BPS D-branes in type II string theories discussed in hep-th/0505157 give rise to two sectors with integer (R sector) and half-integer (NS sector) modes for the combined fermionic matter and bosonic ghost variables in pure spinor formalism. Exploiting the manifest supersymmetry of the formalism we explicitly construct the DDF (Del Giudice, Di Vecchia, Fubini) states in both the sectors which are in one-to-one correspondence with the states in light-cone Green-Schwarz formalism. We also give a proof of validity of this construction. A similar construction in the closed string sector enables us to define a physical Hilbert space in pure spinor formalism which is used to project the covariant boundary states of both the BPS and non-BPS instantonic D-branes. These projected boundary states take exactly the same form as those found in light-cone Green-Schwarz formalism and are suitable for computing the cylinder diagram with manifest open-closed duality.

On D-brane boundary state analysis in pure spinor formalism

We explore a particular approach to study D-brane boundary states in Berkovits' pure spinor formalism of superstring theories. In this approach one constructs the boundary states in the relevant conformal field theory by relaxing the pure spinor constraints. This enables us to write down the open string boundary conditions for non-BPS D-branes in type II string theories, generalizing our previous work in light-cone Green-Schwarz formalism. As a first step to explore how to apply these boundary states for physical computations we prescribe rules for computing disk one point functions for the supergravity modes. We also comment on the force computation between two D-branes and point out that it is hard to make the world-sheet open-closed duality manifest in this computation.

Non-BPS D-branes in light-cone Green-Schwarz formalism

Non-BPS D-branes are difficult to describe covariantly in a manifestly supersymmetric formalism. For definiteness we concentrate on type IIB string theory in flat background in light-cone Green-Schwarz formalism. We study both the boundary state and the boundary conformal field theory descriptions of these D-branes with manifest SO(8) covariance and go through various consistency checks. We analyze Sen's original construction of non-BPS D-branes given in terms of an orbifold boundary conformal field theory. We also directly study the relevant world-sheet theory by deriving the open string boundary condition from the covariant boundary state. Both these methods give the same open string spectrum which is consistent with the boundary state, as required by the world-sheet duality. The boundary condition found in the second method is given in terms of bi-local fields that are quadratic in Green-Schwarz fermions. We design a special ``doubling trick'' suitable to handle such boundary conditions and prescribe rules for computing all possible correlation functions without boundary insertions. This prescription has been tested by computing disk one-point functions of several classes of closed string states and comparing the results with the boundary state computation.

Unstable non-BPS D-branes of type-II string theories in light-cone Green–Schwarz formalism

The problem of describing the boundary states of unstable non-BPS D-branes of type-II string theories in light-cone Green–Schwarz (GS) formalism is addressed. Regarding the type II theories in light-cone gauge as different realizations of the SO ̂ (8) k=1 Kac–Moody algebra, the non-BPS D-brane boundary states of these theories are given in terms of the relevant Ishibashi states constructed in this current algebra. Using the expressions for the current modes in terms of the GS variables it is straightforward to reexpress the boundary states in the GS formalism. The problem that remains is the lack of manifest SO (8) covariance in these expressions. We also derive the various known expressions for the BPS and non-BPS D-brane boundary states by starting with the current algebra Ishibashi states.

Finiteness and unitarity of Lorentz-covariant Green-Schwarz superstring amplitudes

In two recent papers, a new method was developed for calculating ten-dimensional superstring amplitudes with an arbitrary number of loops and external massless bosons or fermions, and for expressing the amplitudes in manifestly Lorentz-invariant form. In this paper, all amplitudes with external massless bosons are proven to be finite by explicitly checking for divergences when the Riemann surface degenerates. These amplitudes are then proven to be unitary by choosing light-cone moduli for the surface and comparing with the light-cone Green-Schwarz formalism.

On the theory of vibration-rotation interaction: Nanny Fröman and Per Olof Fröman, Institute of Theoretical Physics, University of Uppsala, Uppsala, Sweden

In two recent papers, a new method was developed for calculating ten-dimensional superstring amplitudes with an arbitrary number of loops and external massless bosons or fermions, and for expressing the amplitudes in manifestly Lorentz-invariant form. In this paper, all amplitudes with external massless bosons are proven to be finite by explicitly checking for divergences when the Riemann surface degenerates. These amplitudes are then proven to be unitary by choosing light-cone moduli for the surface and comparing with the light-cone Green-Schwarz formalism.