Classical Open String Research Articles

String field theory solution for any open string background. Part II

Generalizing previous work, we give a new analytic solution in Witten’s open bosonic string field theory which can describe any open string background. The central idea is to use Riemann surface degenerations as a mechanism for taming OPE singularities. This requires leaving the familiar subalgebra of wedge states with insertions, but the payoff is that the solution makes no assumptions about the reference and target D-brane systems, and is therefore truly general. For example, unlike in previous work, the solution can describe time dependent backgrounds and multiple copies of the reference D-brane within the universal sector. The construction also resolves some subtle issues resulting from associativity anomalies, giving a more complete understanding of the relation between the degrees of freedom of different D-brane systems, and a nonperturbative proof of background independence in classical open bosonic string field theory.

Yukawa couplings and masses of non-chiral states for the Standard Model on D6-branes on $ {T^{{6}}}/\mathbb{Z}_{{6}}^{\prime } $

The perturbative leading order open string three-point couplings for the Standard Model with hidden USp(6) on fractional D6-branes on T6/Z6' from arXiv:0806.3039 [hep-th], arXiv:0910.0843 [hep-th] are computed. Physical Yukawa couplings consisting of holomorphic Wilsonian superpotential terms times a non-holomorphic prefactor involving the corresponding classical open string Kaehler metrics are given, and mass terms for all non-chiral matter states are derived. The lepton Yukawa interactions are at leading order flavour diagonal, while the quark sector displays a more intricate pattern of mixings. While N=2 supersymmetric sectors acquire masses via only two D6-brane displacements - which also provide the hierarchies between up- and down-type Yukawas within one quark or lepton generation -, the remaining vector-like states receive masses via perturbative three-point couplings to some Standard Model singlet fields with vevs along flat directions. Couplings to the hidden sector and messengers for supersymmetry breaking are briefly discussed.

Thermodynamic Bethe ansatz equations for minimal surfaces in AdS 3

We study classical open string solutions with a null polygonal boundary in AdS 3 in relation to gluon scattering amplitudes in \( \mathcal{N} = 4 \) super Yang-Mills at strong coupling. We derive in full detail the set of integral equations governing the decagonal and the dodecagonal solutions and identify them with the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models. By evaluating the free energy in the conformal limit we compute the central charges, from which we observe general correspondence between the polygonal solutions in AdS n and generalized parafermions.

A note on string solutions inAdS3

We systematically search for classical open string solutions in AdS3 within the general class expressed by elliptic functions (i.e., the genus-one finite-gap solutions). By explicitly solving the reality and Virasoro conditions, we give a classification of the allowed solutions. When the elliptic modulus degenerates, we find a class of solutions with six null boundaries, among which two pairs are collinear. By adding the S1 sector, we also find four-cusp solutions with null boundaries expressed by the elliptic functions.

Dirac Formulation of Free Open String

Dirac formulation of open relativistic strings as systems with constraints is made explicitly. Classical theory is given in the standard light-cone and covariant center-of-mass gauges. It is mentioned that the well-known result D = 26 is affected by using the standard quantization of the mutually independent nonphysical boson creation and annihilation operators. It is shown that in the Dirac formulation these operators are not independent in both the gauges. Concepts of Physics, Vol. IV, No. 4 (2007) DOI: 10.2478/v10005-007-0023-x 487 We give some new conditions on these operators and show that the theory is consistent with Poincare algebra in any dimension D. 488 Concepts of Physics, Vol. IV, No. 4 (2007) Dirac Formulation of Free Open String 1 Hamilton description of classical open string We will study the Nambu–Goto [1] free open string in dimension D. We assume the sign convention gμν = diag(−1, 1, . . . , 1), where μ, ν = 0, 1, . . . , D − 1. The string is described by the functions X(τ, σ), where τ ∈ R and σ ∈ 〈0, π〉. The classical string is described by Lagrangian L(X) = −ω ∫ π 0 Ldσ, where ω > 0 is a constant and the Lagrangian density L(τ, σ) is L = √( ẊX ′ )2 − (Ẋ)2(X ′)2 . A dot means partial derivation with respect to τ , a dash with respect to σ, and XY = gμνXY ν = XμY ν . The boundary conditions are X ′ μ(τ, 0) = X ′ μ(τ, π) = 0. In the Hamiltonian formulation we define momenta Pμ(τ, σ) = δL δẊμ(σ) = ω Ẋμ(X ′X ′)−X ′ μ(ẊX ′) √( ẊX ′ )2 − (Ẋ)2(X ′)2 . (1) From (1) we obtain the relations Φ1 = 1 2 ( P 2 + ω ( X ′ )2) = 0 , Φ2 = PX ′ = 0 (2) called constraints. For the Poisson brackets of two functionals F (X,P ) and G(X,P ) we have { F,G } = ∫ π 0 ( δF δXμ(σ) δG δPμ(σ) − δF δPμ(σ) δG δXμ(σ) ) dσ . (3) In particular, the relation { X(σ), P ν(σ′) } = gδ(σ − σ′) is valid. The Hamiltonian of the system with constraints (2) is

NONCOMMUTATIVE HOMOTOPY ALGEBRAS ASSOCIATED WITH OPEN STRINGS

We discuss general properties of A∞-algebras and their applications to the theory of open strings. The properties of cyclicity for A∞-algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for A∞-algebras and cyclic A∞-algebras and discuss various consequences of it. In particular, it is applied to classical open string field theories and it is shown that all classical open string field theories on a fixed conformal background are cyclic A∞-isomorphic to each other. The same results hold for classical closed string field theories, whose algebraic structure is governed by cyclic L∞-algebras.

Open Spinning Strings

We find classical open string solutions in the $AdS_5\times S^5/\Zop_2$ orientifold with angular momenta along the five-sphere. The energy of these solutions has an expansion in integral powers of $\lambda$ with sigma-model corrections suppressed by inverse powers of $J$ - the total angular momentum. This gives a prediction for the exact anomalous dimensions of operators in the large $N$ limit of an ${\cal N}=2$ $Sp(N)$ Super-Yang-Mills theory with matter. We also find a simple map between open and closed string solutions. This gives a prediction for an all-loop planar relationship between the anomalous dimensions of single-trace and two-quark operators in the dual gauge theory.

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.

Open string fluctuations in AdS space with and without torsion

The equations of motion and boundary conditions for the fluctuations around a classical open string, in a curved space-time with torsion, are considered in compact and world-sheet covariant form. The rigidly rotating open strings in Anti de Sitter space with and without torsion are investigated in detail. By carefully analyzing the tangential fluctuations at the boundary, we show explicitly that the physical fluctuations (which at the boundary are combinations of normal and tangential fluctuations) are finite, even though the world-sheet is singular there. The divergent 2-curvature thus seems less dangerous than expected, in these cases. The general formalism can be straightforwardly used also to study the (bosonic part of the) fluctuations around the closed strings, recently considered in connection with the AdS/CFT duality, on AdS_5 \times S^5 and AdS_3 \times S^3 \times T^4.

Homotopy algebra morphism and geometry of classical string field theories

We discuss general properties of classical string field theories with symmetric vertices in the context of deformation theory. For a given conformal background, there are many string field theories corresponding to different decomposition of moduli space of Riemann surfaces. It is shown that any classical open string field theories on a fixed conformal background are A ∞-quasi-isomorphic to each other. This indicates that they have isomorphic moduli space of classical solutions. The minimal model theorem in A ∞-algebras plays a key role in these results. Its natural and geometric realization on formal supermanifolds is also given. The same results hold for classical closed string field theories, whose algebraic structures are governed by L ∞-algebras.

D-branes in an AdS3 background

We study the possible D-brane configurations in an AdS_3 x S^3 x T^4 background with a NS-NS B field. We use its WZW model description and the boundary state formalism, and we analyze the bosonic and the N=1 supersymmetric cases separately. We also discuss the corresponding classical open string sigma model. We determine the spacetime supersymmetry preserved by the supersymmetric D-brane configurations.

Oriented Open-Closed String Theory Revisited

String theory on D-brane backgrounds is open-closed string theory. Given the relevance of this fact, we give details and elaborate upon our earlier construction of oriented open-closed string field theory. In order to incorporate explicitly closed strings, the classical sector of this theory is open strings with a homotopy associativeA∞algebraic structure. We build a suitable Batalin–Vilkovisky algebra on moduli spaces of bordered Riemann surfaces, the construction of which involves a few subtleties arising from the open string punctures and cyclicity conditions. All vertices coupling open and closed strings through disks are described explicitly. Subalgebras of the algebra of surfaces with boundaries are used to discuss symmetries of classical open string theory induced by the closed string sector, and to write classical open string field theory on general closed string backgrounds. We give a preliminary analysis of the ghost-dilaton theorem.

Classical open string models in four-dimensional Minkowski spacetime.

Classical bosonic open string models in four-dimensinal Minkowski spacetime are discussed. Special attention is paid to the choice of edge conditions, which can follow consistently from the action principle. We consider Lagrangians that can depend on second order derivatives of world sheet coordinates. A revised interpretation of the variational problem for such string theories is given. We derive a general form of a boundary term that can be added to the open string action to control edge conditions and modify conservation laws. An extended boundary problem for minimal surface is examined. Following the treatment of this model in the geometric approach, we obtain that classical open string states correspond to solutions of a complex Liouville equation. In contrast with the Nambu-Goto case, the Liouville potential is finite and constant at world sheet boundaries. The phase part of the potential defines topological sectors of solutions.

Quantum open string theory with manifest closed string factorization

We present a quantum theory of covariant open and closed strings that satisfies manifestly the full BV master equation. The classical action includes interacting open strings and free closed strings. All open-closed string self-interactions appear at the quantum level. The string diagrams, arising from a new minimal area problem, make all amplitudes manifestly factorizable in every open and closed string channel. As by-products we obtain a global closed string symmetry of classical open string theory, and a gauge invariant action for open strings propagating in closed string backgrounds.

String lengths in covariant string field theory and [formula omitted

The recent work of the authors deriving a field theory with Parisi-Sourlas symmetries from the point particle is extended to the bosonic string. Upon proper gauge fixing of the classical open string the resulting BRST field theory is OSp(26, 2 2 )-invariant and contains the coordinates for the proper time and the string length, as well as the additional compensating ghost coordinates. The corresponding free gauge theory is also presented and shown to yield the BRST theory upon gauge fixing. The interacting gauge-invariant and BRST theories are also given.