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We develop a new background independent Moyal star formalism in bosonic open string field theory. The new star product is formulated in a half-phase-space, and because phase space is independent of any background fields, the interactions are background independent. In this basis there is a large amount of symmetry, including a supersymmetry OSp(d|2) that acts on matter and ghost degrees of freedom, and simplifies computations. The BRST operator that defines the quadratic kinetic term of string field theory may be regarded as the solution of the equation of motion A*A=0 of a purely cubic background independent string field theory. We find an infinite number of non-perturbative solutions to this equation, and are able to associate them to the BRST operator of conformal field theories on the worldsheet. Thus, the background emerges from a spontaneous-type breaking of a purely cubic highly symmetric theory. The form of the BRST field breaks the symmetry in a tractable way such that the symmetry continues to be useful in practical perturbative computations as an expansion around some background. The new Moyal basis is called the $sigma $-basis, where $sigma$ is the worldsheet parameter of an open string. A vital part of the new star product is a natural and crucially needed mid-point regulator in this continuous basis, so that all computations are finite. The regulator is removed after renormalization and then the theory is finite only in the critical dimension. Boundary conditions for D-branes at the endpoints of the string are naturally introduced and made part of the theory as simple rules in algebraic computations. A byproduct of our approach is an astonishing suggestion of the formalism: the roots of ordinary quantum mechanics may originate in the rules of non-commutative interactions in string theory.
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We construct rolling tachyon solutions of open and boundary string field theory (OSFT and BSFT, respectively), in the bosonic and supersymmetric (susy) case. The wildly oscillating solution of susy OSFT is recovered, together with a family of time-dependent BSFT solutions for the bosonic and susy string. These are parametrized by an arbitrary constant r involved in solving the Green equation of the target fields. When r=0 we recover previous results in BSFT, whereas for r attaining the value predicted by OSFT it is shown that the bosonic OSFT solution is the derivative of the boundary one; in the supersymmetric case the relation between the two solutions is more complicated. This technical correspondence sheds some light on the nature of wild oscillations, which appear in both theories whenever r>0.
Nonassociative structures have appeared in the study of D-branes in curved backgrounds. In recent work, string theory backgrounds involving three-form fluxes, where such structures show up, have been studied in more detail. We point out that under certain assumptions these nonassociative structures coincide with nonassociative Malcev algebras which had appeared in the quantum mechanics of systems with non-vanishing three-cocycles, such as a point particle moving in the field of a magnetic charge. We generalize the corresponding Malcev algebras to include electric as well as magnetic charges. These structures find their classical counterpart in the theory of Poisson-Malcev algebras and their generalizations. We also study their connection to Stueckelbergs generalized Poisson brackets that do not obey the Jacobi identity and point out that nonassociative string theory with a fundamental length corresponds to a realization of his goal to find a non-linear extension of quantum mechanics with a fundamental length. Similar nonassociative structures are also known to appear in the cubic formulation of closed string field theory in terms of open string fields, leading us to conjecture a natural string-field theoretic generalization of the AdS/CFT-like (holographic) duality.
We continue our study of effective field theory via homotopy transfer of $L_infty$-algebras, and apply it to tree-level non-Wilsonian effective actions of the kind discussed by Sen in which the modes integrated out are comparable in mass to the modes that are kept. We focus on the construction of effective actions for string states at fixed levels and in particular on the construction of weakly constrained double field theory. With these examples in mind, we discuss closed string theory on toroidal backgrounds and resolve some subtle issues involving vertex operators, including the proper form of cocycle factors and of the reflector state. This resolves outstanding issues concerning the construction of covariant closed string field theory on toroidal backgrounds. The weakly constrained double field theory is formally obtained from closed string field theory on a toroidal background by integrating out all but the doubly massless states and homotopy transfer then gives a prescription for determining the theorys vertices and symmetries. We also discuss consistent truncation in the context of homotopy transfer.
In this paper we derive the tree-level S-matrix of the effective theory of Goldstone bosons known as the non-linear sigma model (NLSM) from string theory. This novel connection relies on a recent realization of tree-level open-superstring S-matrix predictions as a double copy of super-Yang-Mills theory with Z-theory --- the collection of putative scalar effective field theories encoding all the alpha-dependence of the open superstring. Here we identify the color-ordered amplitudes of the NLSM as the low-energy limit of abelian Z-theory. This realization also provides natural higher-derivative corrections to the NLSM amplitudes arising from higher powers of alpha in the abelian Z-theory amplitudes, and through double copy also to Born-Infeld and Volkov-Akulov theories. The Kleiss-Kuijf and Bern-Carrasco-Johansson relations obeyed by Z-theory amplitudes thereby apply to all alpha-corrections of the NLSM. As such we naturally obtain a cubic-graph parameterization for the abelian Z-theory predictions whose kinematic numerators obey the duality between color and kinematics to all orders in alpha.
The expectation values of energy density and pressure of a quantum field inside a wedge-shaped region appear to violate the expected relationship between torque and total energy as a function of angle. In particular, this is true of the well-known Deutsch--Candelas stress tensor for the electromagnetic field, whose definition requires no regularization except possibly at the vertex. Unlike a similar anomaly in the pressure exerted by a reflecting boundary against a perpendicular wall, this problem cannot be dismissed as an artifact of an ad hoc regularization.
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