Closed String States Research Articles

Open-closed string duality at tree level.

We study the decay of unstable D-branes in string theory in the presence of an electric field, and show that the classical open string theory results for various properties of the final state agree with the properties of closed string states into which the system is expected to decay. This suggests a duality between tree level open string theory on unstable D-branes and closed strings at high density.

Shape and holography: studies of dual operators to giant gravitons

In this paper we study the conjectured dual operators to a near maximal giant graviton and their open string fluctuations in the large N limit. Using matrix model estimates we show that the spectrum of states near the D-brane operator is consistent with a Fock space of open plus closed string states. We also give an argument that these operators, in spite of having large R charge of order N, are amenable to being studied with standard perturbative techniques, which organize themselves in a 1/ N expansion. Also the spectrum of operators dual to massless fluctuations on the D-brane is shown to be protected from weak to strong coupling at leading order, so it is possible to read the shape of the dual operator by understanding how the spherical harmonics of the D-brane fluctuations appear.

Closed string amplitudes in open string field theory

We investigate gauge invariant operators corresponding to on-shell closed string states in open string field theory. Using both oscillator representation and conformal mapping techniques, we calculate a two closed string tachyon amplitude that connects two gauge invariant operators by an open string propagator.We find that this amplitude is in a complete agreement with the usual disc amplitude.

Tadpoles and closed string backgrounds in open string field theory

We investigate the quantum structure of Witten's cubic open bosonic string field theory by computing the one-loop contribution to the open string tadpole using both oscillator and conformal field theory methods. We find divergences and a breakdown of BRST invariance in the tadpole diagram arising from tachyonic and massless closed string states, and we discuss ways of treating these problems. For a Dp-brane with sufficiently many transverse dimensions, the tadpole can be rendered finite by analytically continuing the closed string tachyon by hand; this diagram then naturally incorporates the (linearized) shift of the closed string background due to the presence of the brane. We observe that divergences at higher loops will doom any straightforward attempt at analyzing general quantum effects in bosonic open string field theory on a Dp-brane of any dimension, but our analysis does not uncover any potential obstacles to the existence of a sensible quantum open string field theory in the supersymmetric case.

Gauge/gravity correspondence from open/closed string duality

We compute the annulus diagram corresponding to the interaction of a fractional D3 brane with a gauge field on its world-volume and a stack of N fractional D3 branes on the orbifolds C^2 /Z_2 and C^3/Z_2 x Z_2. We show that its logarithmic divergence can be equivalently understood as due either to massless open string states circulating in the loop or to massless closed string states exchanged between two boundary states. This follows from the fact that, under open/closed string duality, massless states in the open and closed string channels are matched into each other without mixing with massive states. This explains why the perturbative properties of many gauge theories living on the worldvolume of less supersymmetric and nonconformal branes have been recently obtained from their corresponding supergravity solution.

Gauge-string correspondence in curved space

We discuss Gubser-Klebanov-Polyakov proposal for the gauge/string theory correspondence for gauge theories in curved space. Specifically, we consider Klebanov-Tseytlin cascading gauge theory compactified on S^3. We explain regime when this gauge theory is a small deformation of the superconformal N=1 gauge theory on the world volume of regular D3-branes at the tip of the conifold. We study closed string states on the leading Regge trajectory in this background, and attempt to identify the dual gauge theory twist two operators.

SolitonicD-branes and brane annihilation

We point out some intriguing analogies between field theoretic solitons (topological defects) and D-branes. Annihilating soliton-antisoliton pairs can produce stable solitons of lower dimensionality. Solitons that localize massless gauge fields in their world volume automatically imply the existence of open flux tubes ending on them and closed flux tubes propagating in the bulk. We discuss some aspects of this localization on explicit examples of unstable wall-anti-wall systems. The annihilation of these walls can be described in terms of tachyon condensation which renders the world-volume gauge field non-dynamical. During this condensation the world volume gauge fields (open string states) are resonantly excited. These can later decay into closed strings, or get squeezed into a network flux tubes similar to a network of cosmic strings formed at a cosmological phase transition. Although, as in the $D$-brane case, perturbatively one can find exact time-dependent solutions, when the energy of the system stays localized in the plane of the original soliton, such solutions are unstable with respect to decay into open and closed string states. Thus, when a pair of such walls annihilates, the energy is carried away (at least) by closed string excitations (``glueballs''), which are the lowest energy excitations about the bulk vacuum. Suggested analogies can be useful for the understanding of the complicated D-brane dynamics and of the production of topological defects and reheating during brane collision in the early universe.

On a modification of the boundary-state formalism in off-shell string theory

We examine the application of boundary states in computing amplitudes in off-shell open string theory. We find a straightforward generalization of a boundary state which produces the correct matrix elements with on-shell closed string states.

Open Wilson Lines as States of Closed String

System of a D-brane in bosonic string theory on a constant $B$ field background is studied in order to obtain further insight into the bulk-boundary duality. Boundary states which describe arbitrary numbers of open-string tachyons and gluons are given. UV behaviors of field theories on the non-commutative world-volume are investigated by using these states. We take zero-slope limits of generating functions of one-loop amplitudes of gluons (and open-string tachyons) in which the region of the small open-string proper time is magnified. Existence of $B$ field allows the limits to be slightly different from the standard field theory limits of closed-string. They enable us to capture world-volume theories at a trans-string scale. In this limit the generating functions are shown to be factorized by two curved open Wilson lines (and their analogues) and become integrals on the space of paths with a Gaussian distribution around straight lines. These indicate a possibility that field theories on the non-commutative world-volume are topological at such a trans-string scale. We also give a proof of the Dhar-Kitazawa conjecture by making an explicit correspondence between the closed-string states and the paths. Momentum eigenstates of closed-string or momentum loops also play an important role in these analyses.

D-branes as Gopakumar-Minwalla-Strominger solitons in vacuum string field theory

In this paper we map the D-brane projector states in the vacuum string field theory to the noncommutative GMS solitons based on the recently proposed map of Witten's star to Moyal's star. We find that the singular geometry conditions of Moore and Taylor are associated with the commutative modes of these projector states in our framework. The properties of the candidate closed string state and the wedge state are also discussed, and the possibility of the non-GMS soliton in VSFT is commented.

Gravitational Radiation of Rolling Tachyon

In this paper we compute the radiation of the massless closed string states due to the non-vanishing coupling to the rolling open string tachyon with co-dimensions larger than 2, and discuss the effect of back reaction to the motion of the rolling tachyon. We find that for small string coupling, the tachyonic matter remains in the late time, but it will completely evaporate away over a short time of few string scales if the string coupling is huge. Comment on the implication of our results to the g-theorem of boundary conformal field theory is given.

Large angular momentum closed strings colliding with D-branes

We investigate colliding processes of closed strings with large angular momenta with D-branes. We give explicit CFT calculations for closed string states with an arbitrary number of bosonic excitations and no or one fermion excitation. The results reproduce the correspondence between closed string states and single trace operators in the boundary gauge theory recently suggested by Berenstein, Maldacena and Nastase.

The singular geometry of the sliver

We consider "sliver" states which act as projection operators in the matter star product of Witten's cubic string field theory. These sliver states, which might be associated with Dirichlet p-branes, are not finite norm states in the matter string Hilbert space. We describe the singularities of these states, and demonstrate that the sliver states are composed of strings having singular geometric features. These singularities take a particularly simple form in the zero slope limit alpha' -> 0, where the star algebra factorizes into a product of the algebra of functions on space-time and the noncommutative star product of fields associated with higher string modes. An analogy to the sliver geometry suggests a natural mechanism for describing closed string states in open string field theory.

Some remarks on D-branes in AdS3

We investigate the relation between the algebraic construction of boundary states in AdS_3 and the target space analysis of D-branes and show the consistency of the two descriptions. We compute, in the semiclassical regime, the overlap of a localized closed string state with boundary states and identify the latter with D-branes wrapping conjugacy classes in AdS_3. The string partition function on the disk is shown to reproduce the spacetime DBI action. Other consistency checks are performed. We also comment on the role of the spectral flow symmetry of the underlying SL(2,R)/U(1) coset model in constructing D-branes that correspond to degenerate representations of SL(2,R).

Effective string tension and renormalizability: string theory in a noncommutative space

We show that the one loop amplitudes of open and closed string theory in a constant background two-form tensor field are characterized by an effective string tension larger than the fundamental string tension, and by the appearance of antisymmetric and symmetric noncommutativity parameters. We derive the form of the phase functions normalizing planar and nonplanar tachyon scattering amplitudes in this background, verifying the decoupling of the closed string sector in the regime of infinite momentum transfer. We show that the functional dependence of the phase functions on the antisymmetric star product of external momenta permits interpretation as a finite wavefunction renormalization of vertex operators in the open string sector. Using world-sheet duality we clarify the regimes of finite and zero momentum transfer between boundaries, demonstrating the existence of poles in the nonplanar amplitude when the momentum transfer equals the mass of an on-shell closed string state. Neither noncommutativity parameter has any impact on the renormalizability of open and closed string theory in the Wilsonian sense. We comment on the relationship to noncommutative scalar field theory and the UV-IR correspondence.

Search for quantum spacetime foam

The possibility that quantum fluctuations in the structure of spacetime at the Planck scale might be subject to experimental probes in discussed. The effects of spacetime foam in an approach inspired by string theory, in which solitonic D-brane excitations are taken into account when considering the ground state, are studied. The properties of this medium are described by analyzing the recoil of a D particle which is induced by the scattering of a closed-string state. This recoil causes an energy-dependent perturbation of the background metric, which in turn induces an energy-dependent refractive index in vacuo, and stochastic fluctuations of the light cone. Distant astrophysical sources such as Gamma-Ray Bursters (GRBs) may be used to test this possibility, and an illustrative analysis of GRBs whose redshifts have been measured is presented. The propagation of massive particles through such a quantum spacetime foam is also discussed.

The geometry of WZW branes

The structures in target space geometry that correspond to conformally invariant boundary conditions in WZW theories are determined both by studying the scattering of closed string states and by investigating the algebra of open string vertex operators. In the limit of large level, we find branes whose world volume is a regular conjugacy class or, in the case of symmetry breaking boundary conditions, a ‘twined’ version thereof. In particular, in this limit one recovers the commutative algebra of functions over the brane world volume, and open strings connecting different branes disappear. At finite level, the branes get smeared out, yet their approximate localization at (twined) conjugacy classes can be detected unambiguously. It is also established that in any rational conformal field theory the structure constants of the algebra of boundary operators coincide with specific entries of fusing matrices.

D-brane recoil and supersymmetry breaking as a relaxation process

We propose a new mechanism for the formation of conical singularities on D-branes by means of recoil resulting from scattering of closed string states propagating in the (large) transverse dimensions. By viewing the (spatial part of the) four-dimensional world as a 3-brane with large transverse dimensions the above mechanism can lead to supersymmetry obstruction at the TeV scale. The vacuum remains supersymmetric while the mass spectrum picks up a supersymmetry obstructing mass splitting. The state with “broken” supersymmetry is not an equilibrium ground state, but is rather an excited state of the D-brane which relaxes to the supersymmetric ground state asymptotically in (cosmic) time.

Klein bottles and simple currents

The standard Klein bottle coefficient in the construction of open descendants is shown to equal the Frobenius-Schur indicator of a conformal field theory. Other consistent Klein bottle projections are shown to correspond to simple currents. These observations enable us to generalize the standard open string construction from C-diagonal parent theories to include non-standard Klein bottles. Using (generalizations of) the Frobenius-Schur indicator we prove positivity and integrality of the resulting open and closed string state multiplicities for standard as well as non-standard Klein bottles.

Fundamental strings as black bodies

We show that the decay spectrum of massive excitations in perturbative string theories is thermal when averaged over the (many) initial degenerate states. We first compute the inclusive photon spectrum for open strings at the tree level showing that a black body spectrum with the Hagedorn temperature emerges in the averaging. A similar calculation for a massive closed string state with winding and Kaluza-Klein charges shows that the emitted graviton spectrum is thermal with a “grey-body” factor, which approaches one near extremality. These results uncover a simple physical meaning of the Hagedorn temperature and provide an explicit microscopic derivation of the black body spectrum from a unitary S matrix.